CleanEnergyWIKI - User contributions [en]

Basic Optics - Outreach Kit

2010-04-14T19:03:44Z

128.95.39.187: /* Quantum Dots Solutions */

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<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
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</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

<br clear='all'>
[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

<br clear='all'>
'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]
<br clear='all'>

=== Color filters ===

<br clear='all'>
[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color.

a. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through. The deluxe filter paddle also has a polarizing filter and a diffraction grating.

b. Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.If an organic solar cell appears red colored what does tell you about its absorption spectrum? The color of reflected light from a material represents the color of light that is not absorbed.

c. Print out the “red reveal” hidden message sheets. Ask students to find a filter that reveals the hidden message. The red filter will mask all the colors that are similar to red in the picture. This makes cyan, blue and purple layer that shows up as black because light from these is blocked by the red filter. Red and yellow on the design show up as white when viewed through the red filter. You can also learn [[how to make a red reveal message]].

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal.pdf</embed_document>
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal2.pdf</embed_document>

*Reseach Connection Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

<br clear='all'>
'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source.

a. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb.

b. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum. Try using other filters to isolated different lines. What rule can you come up with about what color filters do to the full color spectrum of light? ( A color filter blocks all colors except for the color it appears to be. Similarly reflective colors absorb all light except for the color they can be observed to reflect)

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.

*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
<br clear='all'>

=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===
[[Image:Glowpaper.png|thumb|300px|Phosphorescent paper is only excited by certain colors of light.]]

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Quantum Dots Solutions ===
[[Image:Quantumdots.png|thumb|300px|Quantum dot solutions in visible light above, and UV light below.]]
'''Materials can be made that designed that absorb and emit radiation at specific wavelengths.'''
These vials contain extremely small 2-5nm particles of cadmium selenium that have been grown to specific sizes because of their light absorbing qualities. These particles exhibit fluorescence; they absorb light at one color and emit light at a different wavelength. In the visible spectrum they absorb and emit yellow and pale red. They absorb ultraviolet and fluoresce in green, red and orange.

a. Examine the vials in regular light. Predict what color the vials will appear under UV light.

b. Expose the vials to UV light and discuss why this is different.

*Research Connection: It is possible us quantum dots as a light antenna to absorb light and pass energy to another chemical. Some quantum dots for example could be used to trap infrared (IR ) light which would help solar cells work on cloudy days when IR passes through the clouds but visible light is mostly blocked.
<br clear='all'>

=== Electroluminescent Panel ===

Electricity can be used to excite a material and make it emit light. Electroluminescent panels have a transparent conductor layer, a layer of phosphor and a metal back electrode. When the front and back electrode are energized with a high frequency current the phosphor in between is stimulated and emits light.

*Research Connection: Electroluminescent panels are similar to the structure of Organic Light Emitting Diodes (OLEDs). Instead of a layer of phosphor the OLED contains an organic chemical that emits light after being excited with electricity. The organic chemicals can be tuned to get specific colors. OLEDs are now used for flat displays and televisions.

=== Laser pointer ===

<br clear='all'>
'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

<br clear='all'>
[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

<br clear='all'>
'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
<br clear='all'>

Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
<br clear='all'>
*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

<br clear='all'>
[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

<br clear='all'>
[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

== Basic Light Poster ==

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/Basiclight_poster.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Basiclight_poster.pptx Download PowerPoint file]

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7
* [http://www.amazon.com/Green-Laser-Pointer-Astronomy-Military/dp/B0013HR77S/ref=sr_1_3?ie=UTF8&m=A3V6BK4D0HKA8F&s=electronics&qid=1271101852&sr=1-3 HDE green laser $11.05]
* LED Flashlights with color filters

How to make a red reveal message

2010-04-14T16:26:32Z

128.95.39.187:

1) Use Photoshop to create a distracting pattern with red, magenta, yellow on different layers. Patterns can be rows of nonsense letters, textures or repeating patterns. Try to make these coincide with the position of the message lines so that it obscures the message. The crazier the patterns the better.

2) Add the message layer below these in cyan color, this will appear black when viewed through the red filter. Make it 50% transparent so that it is less obvious against the other layers.

3) Use the Multiply Blend on the upper masking layers so that it blends with the cyan beneath and not just cut it off.

[http://depts.washington.edu/cmditr/media/Redrevealmessage.psd Download Photoshop sample file to make your own hidden message]

You could also print out the hiding layers by themselves have have students draw their messages with a cyan magic marker.

How to make a red reveal message

2010-04-14T16:22:11Z

128.95.39.187:

How to make a red reveal message

2010-04-14T16:20:25Z

128.95.39.187: New page: 1) Use Photoshop to create a distracting pattern with red, magenta, yellow on different layers. Patterns can be rows of nonsense letters, textures or repeating patterns. Try to make these ...

1) Use Photoshop to create a distracting pattern with red, magenta, yellow on different layers. Patterns can be rows of nonsense letters, textures or repeating patterns. Try to make these coincide with the position of the message lines so that it obscures the message.

2) Add the message layer below these in cyan color, this will appear black when viewed through the red filter. Make it 50% transparent so that it is less obvious against the other layers.

3) Use the Multiply Blend on the upper masking layers so that it blends with the cyan beneath and not just cut it off. you can also experiment with the opacity of layers.

[http://depts.washington.edu/cmditr/media/Redrevealmessage.psd Download Photoshop sample file to make your own hidden message]

Basic Optics - Outreach Kit

2010-04-14T15:50:44Z

128.95.39.187: /* Color filters */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Photovoltaics- Outreach Kit|Next Topic]]</td>
</tr>
</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

<br clear='all'>
[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

<br clear='all'>
'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]
<br clear='all'>

=== Color filters ===

<br clear='all'>
[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color.

a. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through. The deluxe filter paddle also has a polarizing filter and a diffraction grating.

b. Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.If an organic solar cell appears red colored what does tell you about its absorption spectrum? The color of reflected light from a material represents the color of light that is not absorbed.

c. Print out the “red reveal” hidden message sheets. Ask students to find a filter that reveals the hidden message. The red filter will mask all the colors that are similar to red in the picture. This makes cyan, blue and purple layer that shows up as black because light from these is blocked by the red filter. Red and yellow on the design show up as white when viewed through the red filter. You can also learn [[how to make a red reveal message]].

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal.pdf</embed_document>
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal2.pdf</embed_document>

*Reseach Connection Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

<br clear='all'>
'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source.

a. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb.

b. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum. Try using other filters to isolated different lines. What rule can you come up with about what color filters do to the full color spectrum of light? ( A color filter blocks all colors except for the color it appears to be. Similarly reflective colors absorb all light except for the color they can be observed to reflect)

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.

*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
<br clear='all'>

=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===
[[Image:Glowpaper.png|thumb|300px|Phosphorescent paper is only excited by certain colors of light.]]

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Quantum Dots Solutions ===
[[Image:Quantumdots.png|thumb|300px|Quantum dot solutions in visible light above, and UV light below.]]
'''Materials can be made that designed that absorb and emit radiation at specific wavelengths.'''
These vials contain extremely small 2-5nm particles of cadmium selenium that have been grown to specific sizes because of their light absorbing qualities. These particles exhibit fluorescence; they absorb light at one color and emit light at a different wavelength. In the visible spectrum they absorb and emit yellow and pale red. They absorb ultraviolet and fluoresce in green, red and orange.

a. Examine the vials in regular light. Predict what color the vials will appear under UV light.

b. Expose the vials to UV light and discuss why this is different.

*Research Connection: It is possible us quantum dots as a light antenna to absorb light and pass energy to another chemical. Some quantum dots for example could be used to trap infrared (IR ) light which would help solar cells work on cloudy days when IR passes through the clouds but visible light is mostly blocked.
<br clear='all'>

=== Laser pointer ===

<br clear='all'>
'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

<br clear='all'>
[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

<br clear='all'>
'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
<br clear='all'>

Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
<br clear='all'>
*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

<br clear='all'>
[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

<br clear='all'>
[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

== Basic Light Poster ==

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/Basiclight_poster.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Basiclight_poster.pptx Download PowerPoint file]

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7
* [http://www.amazon.com/Green-Laser-Pointer-Astronomy-Military/dp/B0013HR77S/ref=sr_1_3?ie=UTF8&m=A3V6BK4D0HKA8F&s=electronics&qid=1271101852&sr=1-3 HDE green laser $11.05]
* LED Flashlights with color filters

Basic Optics - Outreach Kit

2010-04-12T19:55:03Z

128.95.39.187: /* Color filters */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Photovoltaics- Outreach Kit|Next Topic]]</td>
</tr>
</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

<br clear='all'>
[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

<br clear='all'>
'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]
<br clear='all'>

=== Color filters ===

<br clear='all'>
[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color.

a. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through. The deluxe filter paddle also has a polarizing filter and a diffraction grating.

b. Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.If an organic solar cell appears red colored what does tell you about its absorption spectrum? The color of reflected light from a material represents the color of light that is not absorbed.

c. Print out the “red reveal” hidden message sheets. Ask students to find a filter that reveals the hidden message. The red filter will mask all the colors that are similar to red in the picture. This makes cyan, blue and purple layer that shows up as black because light from these is blocked by the red filter. Red and yellow on the design show up as white when viewed through the red filter.

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal.pdf</embed_document>
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal2.pdf</embed_document>

*Reseach Connection Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

<br clear='all'>
'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source.

a. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb.

b. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum. Try using other filters to isolated different lines. What rule can you come up with about what color filters do to the full color spectrum of light? ( A color filter blocks all colors except for the color it appears to be. Similarly reflective colors absorb all light except for the color they can be observed to reflect)

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.

*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
<br clear='all'>

=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===
[[Image:Glowpaper.png|thumb|300px|Phosphorescent paper is only excited by certain colors of light.]]

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Quantum Dots Solutions ===
[[Image:Quantumdots.png|thumb|300px|Quantum dot solutions in visible light above, and UV light below.]]
'''Materials can be made that designed that absorb and emit radiation at specific wavelengths.'''
These vials contain extremely small 2-5nm particles of cadmium selenium that have been grown to specific sizes because of their light absorbing qualities. These particles exhibit fluorescence; they absorb light at one color and emit light at a different wavelength. In the visible spectrum they absorb and emit yellow and pale red. They absorb ultraviolet and fluoresce in green, red and orange.

a. Examine the vials in regular light. Predict what color the vials will appear under UV light.

b. Expose the vials to UV light and discuss why this is different.

*Research Connection: It is possible us quantum dots as a light antenna to absorb light and pass energy to another chemical. Some quantum dots for example could be used to trap infrared (IR ) light which would help solar cells work on cloudy days when IR passes through the clouds but visible light is mostly blocked.
<br clear='all'>

=== Laser pointer ===

<br clear='all'>
'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

<br clear='all'>
[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

<br clear='all'>
'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
<br clear='all'>

Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
<br clear='all'>
*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

<br clear='all'>
[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

<br clear='all'>
[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

== Basic Light Poster ==

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/Basiclight_poster.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Basiclight_poster.pptx Download PowerPoint file]

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7
* [http://www.amazon.com/Green-Laser-Pointer-Astronomy-Military/dp/B0013HR77S/ref=sr_1_3?ie=UTF8&m=A3V6BK4D0HKA8F&s=electronics&qid=1271101852&sr=1-3 HDE green laser $11.05]
* LED Flashlights with color filters

Basic Optics - Outreach Kit

2010-04-12T19:51:45Z

128.95.39.187: /* Sources for Building your own kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Photovoltaics- Outreach Kit|Next Topic]]</td>
</tr>
</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

<br clear='all'>
[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

<br clear='all'>
'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]
<br clear='all'>

=== Color filters ===

<br clear='all'>
[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color.

a. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through. The deluxe filter paddle also has a polarizing filter and a diffraction grating.

b. Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.If an organic solar cell appears red colored what does tell you about its absorption spectrum? The color of reflected light from a material represents the color of light that is not absorbed.

c. Print out the “red reveal” hidden message sheets. As student to find a filter that reveals the hidden message. The red filter will mask all the colors that are similar to close to red in the picture. This leaves only the cyan layer that shows up as black.

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal.pdf</embed_document>
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal2.pdf</embed_document>

*Reseach Connection Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

<br clear='all'>
'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source.

a. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb.

b. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum. Try using other filters to isolated different lines. What rule can you come up with about what color filters do to the full color spectrum of light? ( A color filter blocks all colors except for the color it appears to be. Similarly reflective colors absorb all light except for the color they can be observed to reflect)

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.

*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
<br clear='all'>

=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===
[[Image:Glowpaper.png|thumb|300px|Phosphorescent paper is only excited by certain colors of light.]]

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Quantum Dots Solutions ===
[[Image:Quantumdots.png|thumb|300px|Quantum dot solutions in visible light above, and UV light below.]]
'''Materials can be made that designed that absorb and emit radiation at specific wavelengths.'''
These vials contain extremely small 2-5nm particles of cadmium selenium that have been grown to specific sizes because of their light absorbing qualities. These particles exhibit fluorescence; they absorb light at one color and emit light at a different wavelength. In the visible spectrum they absorb and emit yellow and pale red. They absorb ultraviolet and fluoresce in green, red and orange.

a. Examine the vials in regular light. Predict what color the vials will appear under UV light.

b. Expose the vials to UV light and discuss why this is different.

*Research Connection: It is possible us quantum dots as a light antenna to absorb light and pass energy to another chemical. Some quantum dots for example could be used to trap infrared (IR ) light which would help solar cells work on cloudy days when IR passes through the clouds but visible light is mostly blocked.
<br clear='all'>

=== Laser pointer ===

<br clear='all'>
'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

<br clear='all'>
[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

<br clear='all'>
'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
<br clear='all'>

Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
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*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

<br clear='all'>
[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

<br clear='all'>
[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

== Basic Light Poster ==

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/Basiclight_poster.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Basiclight_poster.pptx Download PowerPoint file]

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7
* [http://www.amazon.com/Green-Laser-Pointer-Astronomy-Military/dp/B0013HR77S/ref=sr_1_3?ie=UTF8&m=A3V6BK4D0HKA8F&s=electronics&qid=1271101852&sr=1-3 HDE green laser $11.05]
* LED Flashlights with color filters

Photovoltaics- Outreach Kit

2010-04-12T19:48:38Z

128.95.39.187: /* Sources for Building your own kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Basic Optics - Outreach Kit|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Lasers and Telecommunication- Outreach Kit|Next Topic]]</td>
</tr>
</table>

== Overview ==
Photovoltaics (PV) or solar cells are one of the most promising sources for renewable electrical energy. The first generation cells were made from silicon crystals like those used computer semiconductor chips. These are efficient but very expensive. Silicon PV were first widely used where the cost of wiring to the grid was impractical such as in satellites or to power remote sensors along pipelines or railway tracks. Materials research and improved manufacturing techniques have brought the price down to where they are beginning to become practical for home energy systems. Plastic solar cells that use organic chemicals instead of silicon may be the next breakthrough. These demos show some basic devices and engage students in quantifying their performance and considering how basic science relates to engineering design.

== User Guide ==

=== Solar Car - Solar battery charger ===

'''Solar energy can be converted to electrical energy using a solar cell.''' Demonstrate the solar car, the motor and rotor, and solar battery charger. Place the solar car in the full sun. What happens when the car passes into the shade? Demonstrate that the small silicon cell doesn’t generate enough energy to power the single LED but the larger amorphous silicon panel can power the light, even in indirect sunlight. Compare the solar electricity to power from a battery. See if they know about batteries polarity. Predict what would happen to the motor if you switch the leads to the solar cell. Reverse the polarity and the disc on the motor will rotate in the opposite direction.

*'''Research Connection:''' CMDITR is building a new kind of solar cell that uses an organic chemical to trap light and then transfer electrons to conductive layers.

=== Three types of solar cells. ===

'''There are several kinds of solar cells which differ power, cost, durability, and preferred applications.'''
Demonstrate the various types of solar cells in the kit by connecting them to a motor, voltmeter or LED.
a. Single crystal and Multicrystaline cell. The smaller cells in the kit are rated .45 volts and 400ma. Crystalline silicon solar cells (c-Si) can have efficiencies from 10-12% . They are produced from ingots of solid silicon and are rigid. These are the cells that most often used in space station where power density and durability are most important.

b. Amorphous silicon battery charger. The panel is rated 7.2 volt / 200ma and has diode built into the circuit to prevent battery discharge into the panel when it is dark. Amorphous silicon is made by depositing an extremely thin layer of silicon on a conductive polymer. As a result the panel is flexible. (a-Si) Amorphous silicon has a comparatively low 6% efficiency because the silicon is poorly organized creating barriers to charge movement but it makes up for this with a lower cost and ease of manufacturing.

c. Copper indium selenide (CIS) CIS and Copper indium gallium selenide cells (CIGS) have 14-20% efficiency. These cells must be full encapsulated to prevent release of toxic selenium. These cells have an open circuit voltage of 5 volts and a short circuit current of 95ma. Max power output is 3.9 volts at 64mA.

d. Organic photovoltaics (OPV)- currently maximum is 5-6.5 %. The Konarka Power Plastic is one of the few commercially available OPV panel. The advantage of organic or plastic solar cells is that they have the potential of extremely low material and manufacturing cost and they are flexible. A disadvantage is that organic materials have a limited lifetime especially in full sun and exposed to water and oxygen.

e. Dye Sensitized Solar Cell (DSS)Demonstrate the dye sensitize solar cell. Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Lightly coat the other slide with the carbon soot from a candle slide. Pinch the slides together with the binder clips so that the slides are offset exposing the conductive ITO layer. Apply iodide solution as an electrolyte and then.

f. Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.
Research Connection: CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.

*'''Research Connection:''' CCMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

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=== Series vs Parallel circuits ===
[[Image:Pv_parallel.jpg|thumb|300px|3 solar cells wired in Parallel ]]

[[Image:Series_parallel.png|thumb|300px|Two arrangements for solar cells.]]

a. Explain the difference between voltage and current. Show that the large panel produces a higher voltage (because it has several cell areas wired in series).
Measure the voltage and current produced from each cell using the digital meter. The wood test frame provides a convenient support and visual explanation of the circuit.

[[Image:Testcellholder.jpg|thumb|300px|]]

Note that the red lead must be moved and the selector switch set to mA to get the ammeter mode. Each cell has a characteristic voltage. Silicon cells produce between .5 -.6 V oc *(volts open circuit), OPVs are usually around .4 Voc. Use the clip leads and the three small panels to demonstrate that in a series circuit the voltage is added. In a parallel circuit the voltage does not change but the current (amperage) is increased.’

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=== Measuring Power Output===

'''The power from a solar cell depends on the current and voltage.''' To measure the power record the voltage and amperage of a solar cell across a load. The ammeter has builtin precision resistors in its circuit. If you only had a voltmeter you could place a known resistor in the circuit and calculate current in amps as voltage divided by ohms. The peak power depends on specific load which affects the current and voltage. ( see voltage current graph below) For this activity you measure the voltage and current in a simple circuit without a load.

[[Image:Volt_amp.png|thumb|300px|Circuit for measuring voltage and current through a solar cell]]
P= V x I
Power (watts) = Volts x Amps

Sample calculation:
Volts = .4 V
Amp = 50ma= .05 amp
Power = .02 Watts

a. Compare the power for a 3 x 4 cm area for the crystalline solar cell compared to the same area of amorphous silicon cell.

b. The amorphous panel provided is 7.2 V and 200 ma. How many of these panels would be needed to in what configuration to generate 100 Watts?

c. Experiment with different sources of light, sunlight, or diffuse vs. direct light

d. Experiment with the effect of temperature on cell power.

*'''Research Connection:''' CMDITR Engineers and scientists test their OPV cells in a similar manner by measuring voltage and current under different loads and light conditions to calculate the maximum efficiency. With a reliable way of comparing cells then it is possible to fine-tune the systems and methods to improve efficiency and longevity.<br clear='all'>

=== Power : area relationship ===

'''The larger the cross sectional area of the light beam that is trapped, the greater the power generated.'''

a. Cover portions of the panel to show decreasing current and voltage. Solar cells measured with the meter are under no load so you get the open circuit voltage (Voc). You should notice that the current responds quickly with decreasing light while the voltage stays somewhat stable, finally the voltage drops too. To measure the power from the panel you have to measure both voltage and amperage produced.

b. Plot the power versus area for the amorphous silicon panel. Complete the table and graph from BLM 1- Power vs Area Experiment

c. Repeat the measurement with a different pattern of shading (block the left, right top or bottom) You may get different results because of the wiring of cells within the array. Once a parallel section of panel is partially shaded it tends to knock out the whole section. Panels can also be equipped with bypass diodes which reroute current around underperforming cells.

[http://www.electroiq.com/index/display/article-display.articles.Photovoltaics-World.bos-components.inverters.2009.03.shade-happens__installation.QP129867.dcmp=rss.page=1.html Shading / Power loss diagram]

*'''Research Connection:''' OPVs could be less expensive even if they are less efficient which means a larger area could be deployed.

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=== Power : distance relationship ===
'''Energy from a radiant light source drops off with distance.'''
[[Image:479px-Inverse_square_law.svg.png|thumb|300px|]]

As you move away from a diffuse light source the same amount of light is spread over a large area so the solar panel only intercepts part of the energy. This called the inverse square law. It relates I intensity with r the distance.

:<math>I \propto \frac{1}{r^2} \,</math>

If you use a focused light source up close this relationship will not hold. At the distance we are from the sun it does not make any measurable difference how close (for example sea level versus on mountain top) we place solar cells to the sun. There is some variation in power available from the sun as we as the Earth’s orbit reaches perihelion. Currently this occurs in January when the Earth is 5million km (3 million miles) closer to the sun. This results in about 7% more solar energy striking the earth at perihelion.

a. Use the electric meter to measure the current produced by the sample silicon cell as you move away from a light source. Collect data and graph the experiment using BLM 2 – Power vs Distance Experiment

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=== Power : Angle of Incidence relationship ===
[[Image:Seasons.too.png|thumb|300px|Effect of sun angle on insolation]]
'''The angle with respect to the sun influences the energy output.'''
:<math>I = S cos Z\,\!</math>

a. Set up the solar panel on its inclined support with protractor. Change the angle of the solar panel and measure the current. Changing the angle has the effect of decreasing the cross section of light that is intercepted. You can see this by measuring the shadow of the panel as it is tilted. In addition low angle sun on the Earth must pass through more atmosphere so some energy is absorbed.

b. Plot the current versus the angle. Complete the data and graph on BLM 3 Power vs Angle Experiment

c. Use this information to create a bar chart showing the total power generated by a cell during the course of day if the cell were fixed on a roof with an angle of 30 degrees. The peak angle of the sun on the spring or autumn equinox is 90- your latitude. At mid summer it is 90 – latitude -23.45 degrees. At mid winter it is 90 – latitude + 23.45 degrees

[[Image:Pv angle.jpg|thumb|300px|PV panel with battery charger and protractor]]

*'''Research Connection:''' Engineers have designed tracking systems that keep PV panels facing perpendicular to sun all day long. Others have explored using concentrators to reflect light to a smaller area where the cell is.

=== Measuring Absorption Spectrum ===

'''Photovoltaics absorb light at specific wavelengths.'''

a. Use the red, green and blue filters to show that certain colors when filtered out reduce the power more than other colors.

b. Plot the current versus wavelength when different colors are placed in front of the solar cell. You can use the large filter sheets or the filter sample booklets. Be sure to pick filters with approximately the same optical density. Use the attached transmission spectra tabs to pick colors that represent an even array across the spectrum. Complete BLM 4 Power vs Wavelength Experiment

c. Compare the amorphous silicon, the polycrystalline silicon cell, and the dye densitized solar cell.

*'''Research Connection:''' When we design chemicals to use in organic photovoltaics we measure the absorption spectra of the chromophores. Ideally we want dyes that absorb across the entire visible spectrum.

=== Measuring Efficiency ===

'''Efficiency is a measure of how much of the available energy is captured by a cell.''' It is the amount of electricity produced divided by the amount shining on the solar cell. To measure efficiency we have to know how much light energy is hitting the cell and how much electricity it is producing. It’s difficult to measure the incident light. Direct sunlight is between 250 and 1,000 W/m2.

a. In full sunlight measure the power of your solar cell and calculate the efficiency. In this example the cell has an area of 2.4 x 10-3 m2 , measuring .6 Volts and .5 amps in full sun

Pi = A * Ps = 2.4 x 10<sup>-3</sup> * 1000 = 2.4 watts

Po = V x I = 0.6 x 0.5 = 0.3 W

e = Po/Pi = 0.3/2.4 = 0.12 = 12%

b. Repeat this measurement for various cells.
=== PV Cost estimation ===

'''Solar cells are still somewhat expensive.''' Several factors have to be considered in sizing a solar system. Calculate how much area is needed to power a house, how much would it cost?

a. Solar cells currently run about $5-$9 per peak watt.

b. A house might require 2kW peak power

c. If the silicon cells are 15% efficient and the

d. Incoming energy is 1000 W/m2 assume 5 hours (5 kWh/m2) per day of useful sunlight or use the “Photovoltaics Solar Resource” map from NREL to identify the available solar resource for your area.

e. If you aren’t connected to the grid you will need batteries which cost $1 amp hour

*'''Research Connection:''' Materials and manufacturing process determines the cost. Organic photovoltaics have a potential of being low cost because they can be manufactured with roll printing methods. Further research is needed to get higher efficiency, better durability (through encapusulation and decreased photobleaching) New organic solar cells may be much cheaper in the future.

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=== PV characterization ===

'''Solar cells are characterized using a voltage- current curve.'''

a. Place the test PV cell in the wood test holder. Place an ammeter and a volt meter at the two pegs labeled A and V. Gradually change the series load in the circuit by sliding the variable resistor. Adjust the load to get an even series of voltage readings such as every .1 volts and record the amps for each voltage. Plot the data. The goal is to get a curve that is closer to a right angle (with a minimum fill factor). There is a certain combination of voltage and current that delivers peak power.

b. Complete BLM 5 Current vs wavelength experiment

*'''Research Connection:''' CMDITR researcher do this same measurement with much finer accuracy.

[[Image:Opv powercurve.jpg|thumb|300px|]]

=== Dye Sensitized Solar Cell ===

'''Organic pigments can be used to capture light to power electrochemical processes.''' Demonstrate the dye sensitized solar cell.Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Then apply iodide solution as an electrolyte and then pinch this together with the carbon black coated slide.

*'''Research Connection:''' Dye sensitized cells have begun commercial production as research continues.
[[Nanocrystalline_-_Dye_Solar_Cell_Kit| Build the complete dye sensitized solar cell activity for high school]]
==Posters==
Courtesy of Ginger Research Group - UW- by Kristina Knesting, Brad MacLeod and Kevin Noone

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/Plastic_Solar_Cells.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Plastic_Solar_Cells.pdf Download PowerPoint of Plastic Solar Cell Poster]

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/OPVefficiency.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/OPVefficiency.ppt Download PowerPoint of OPV Efficiency Poster]

== Links ==
[http://www.nrel.gov/learning/re_photovoltaics.html NREL]

[http://www.powernaturally.org/Programs/SchoolPowerNaturally/InTheClassroom/kitlessons.asp?i=9#Lesson14 Solar Cell lessons]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://www.infinitepower.org/pdf/No19%2096-828B.pdf Photovoltaic measurements Lesson]

[http://www.nrel.gov/midc/unlv/ live insolation data for Las Vegas NREL Solar Data]

[http://en.wikipedia.org/wiki/Solar_cell Wikipedia on solar cells]

[http://depts.washington.edu/cmditr/media/PlasticPV.ppt Plastic Solar Cell Poster]

[http://www.nanosense.org/activities/cleanenergy/solarcellanimation.html Solar Cell Animations]

[http://www.iop.org/EJ/article/0031-9120/41/5/005/pe6_5_005.pdf?request-id=e7503f0f-68f9-4217-bfe8-24c174c90fa5 Other chemicals for photovoltaics demo]

[http://www.teachersdomain.org/asset/hew06_int_ohmslaw/ Ohms Law Simulation from the Teachers Domain]

[http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/watcir.html Water analogy to circuits- Hyperphysics]

== Materials in the kit ==
*Sunzoom Lite car kit
*4 AA battery PV battery charger
*4 AA recharable NiCAD or LI ion batteries
*Solar mini car
*Digital Electric meter
*Protractor
*Ruler
== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/Photovoltaics.docx Cover art for Photovoltaics Kit]

[http://depts.washington.edu/cmditr/media/PVcelldisplay.docx Photovoltaic cell display boards]

http://shop.pitsco.com/store/detail.aspx?CategoryID=115&by=9&ID=2647&c=1&t=0&l=0 $8. 95 sunzoom lite car

http://store.sundancesolar.com/subusobachki6.html 4 AA battery charger $39.95

http://store.sundancesolar.com/misorokitsus.html mini solar car $9.95

http://store.sundancesolar.com/multi-meter.html Electric Meter 2 a $12.95

Light Source for indoor use- quartz desk lamp

http://scientificsonline.com/product.asp?pn=3039810 Individual silicon cells 3 @ $5.95

http://scientificsonline.com/product.asp?pn=3085037 CIS Solar Panel 3 @ $2.95

Color Filter pack for testing cells

Rechargeable Batteries

Basic Optics - Outreach Kit

2010-03-30T18:49:19Z

128.95.39.187: /* Basic Light Poster */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Photovoltaics- Outreach Kit|Next Topic]]</td>
</tr>
</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

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[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

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'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]
<br clear='all'>

=== Color filters ===

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[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color.

a. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through. The deluxe filter paddle also has a polarizing filter and a diffraction grating.

b. Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.If an organic solar cell appears red colored what does tell you about its absorption spectrum? The color of reflected light from a material represents the color of light that is not absorbed.

c. Print out the “red reveal” hidden message sheets. As student to find a filter that reveals the hidden message. The red filter will mask all the colors that are similar to close to red in the picture. This leaves only the cyan layer that shows up as black.

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal.pdf</embed_document>
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal2.pdf</embed_document>

*Reseach Connection Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

<br clear='all'>
'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source.

a. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb.

b. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum. Try using other filters to isolated different lines. What rule can you come up with about what color filters do to the full color spectrum of light? ( A color filter blocks all colors except for the color it appears to be. Similarly reflective colors absorb all light except for the color they can be observed to reflect)

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.

*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
<br clear='all'>

=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===
[[Image:Glowpaper.png|thumb|300px|Phosphorescent paper is only excited by certain colors of light.]]

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Laser pointer ===

<br clear='all'>
'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

<br clear='all'>
[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

<br clear='all'>
'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
<br clear='all'>

Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
<br clear='all'>
*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

<br clear='all'>
[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

<br clear='all'>
[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

== Basic Light Poster ==

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/Basiclight_poster.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Basiclight_poster.pptx Download PowerPoint file]

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7
* LED Flashlights with color filters

Basic Optics - Outreach Kit

2010-03-30T18:47:51Z

128.95.39.187: /* Lasers and diffraction grating */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Photovoltaics- Outreach Kit|Next Topic]]</td>
</tr>
</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

<br clear='all'>
[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

<br clear='all'>
'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]
<br clear='all'>

=== Color filters ===

<br clear='all'>
[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color.

a. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through. The deluxe filter paddle also has a polarizing filter and a diffraction grating.

b. Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.If an organic solar cell appears red colored what does tell you about its absorption spectrum? The color of reflected light from a material represents the color of light that is not absorbed.

c. Print out the “red reveal” hidden message sheets. As student to find a filter that reveals the hidden message. The red filter will mask all the colors that are similar to close to red in the picture. This leaves only the cyan layer that shows up as black.

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal.pdf</embed_document>
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal2.pdf</embed_document>

*Reseach Connection Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

<br clear='all'>
'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source.

a. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb.

b. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum. Try using other filters to isolated different lines. What rule can you come up with about what color filters do to the full color spectrum of light? ( A color filter blocks all colors except for the color it appears to be. Similarly reflective colors absorb all light except for the color they can be observed to reflect)

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.

*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
<br clear='all'>

=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===
[[Image:Glowpaper.png|thumb|300px|Phosphorescent paper is only excited by certain colors of light.]]

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Laser pointer ===

<br clear='all'>
'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

<br clear='all'>
[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

<br clear='all'>
'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
<br clear='all'>

Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
<br clear='all'>
*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

<br clear='all'>
[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

<br clear='all'>
[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

=== Basic Light Poster ===

<embed_document width="100%" height="600">http://depts.washington.edu/cmditr/media/Basiclight_poster.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Basiclight_poster.pptx Download PowerPoint file]

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7
* LED Flashlights with color filters

Basic Optics - Outreach Kit

2010-03-30T18:46:17Z

128.95.39.187: /* Lasers and diffraction grating */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Photovoltaics- Outreach Kit|Next Topic]]</td>
</tr>
</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

<br clear='all'>
[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

<br clear='all'>
'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]
<br clear='all'>

=== Color filters ===

<br clear='all'>
[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color.

a. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through. The deluxe filter paddle also has a polarizing filter and a diffraction grating.

b. Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.If an organic solar cell appears red colored what does tell you about its absorption spectrum? The color of reflected light from a material represents the color of light that is not absorbed.

c. Print out the “red reveal” hidden message sheets. As student to find a filter that reveals the hidden message. The red filter will mask all the colors that are similar to close to red in the picture. This leaves only the cyan layer that shows up as black.

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal.pdf</embed_document>
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/redreveal2.pdf</embed_document>

*Reseach Connection Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

<br clear='all'>
'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source.

a. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb.

b. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum. Try using other filters to isolated different lines. What rule can you come up with about what color filters do to the full color spectrum of light? ( A color filter blocks all colors except for the color it appears to be. Similarly reflective colors absorb all light except for the color they can be observed to reflect)

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.

*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
<br clear='all'>

=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===
[[Image:Glowpaper.png|thumb|300px|Phosphorescent paper is only excited by certain colors of light.]]

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Laser pointer ===

<br clear='all'>
'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

<br clear='all'>
[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

<br clear='all'>
'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
<br clear='all'>

Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
<br clear='all'>
*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

<br clear='all'>
[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

<br clear='all'>
[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

*Basic Light Poster

<embed_document width="100%" height="600">http://depts.washington.edu/cmditr/media/Basiclight_poster.pdf</embed_document>

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7
* LED Flashlights with color filters

Materials Processing and Fabrication

2010-03-24T16:48:08Z

128.95.39.187:

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>
A great amount of research effort is devoted to developing new ways to apply materials to substrates in extremely thin organized layers so as to improve performance and to make the large scale manufacturing of devices economical. Some techniques that are practical for developing a single device with record breaking efficiency would not work for making millions of devices in a production line. Also engineers must be concerned with the durability of devices under real world conditions of heat, moisture and oxygen. At the same time new nanotechniques and self assembly make it possible to build novel structures virtually one molecule at a time.

See Wikipedia [http://en.wikipedia.org/wiki/MEMS Microelectromechanical systems]

==Microfabrication Overview==
Much microfabrication is done in cleanroom facilities such as that at the Washington Technology Center

{{#ev:youtube|Ltj3tlpDy2M}}

==Crystallization and Deposition Techniques==

=== Spin Coating ===
see Wikipedia [http://en.wikipedia.org/wiki/Spin_coating Spin Coating]

===Physical ===

=== Bulk Crystal growth ===

=== Evaporation ===

=== Sputtering ===

=== doping ===

=== Micro-printing ===

===Chemical- epitaxial growth techniques===
Liquid phase epitaxy
Molecular Beam Epitaxy MBE

Chemical vapor depostion MOCVD

CBE

=== Self Assembly ===
Current research into [[Self Assembled Materials]] is pointing to ways that thin layers can be built up in a highly organized manner. This provides more control of the dipole moment of applied surfaces.

==Patterning - Lithography==

=== Spin Coating ===

=== Photolithography ===

=== negative process ===

=== positive process ===

=== soft lithography ===

=== Lift - off process ===

=== Resist processing ===

Exposure
Nanoimprinting

=== [[E-beam Lithography]]===

=== X-ray lithography ===

=== Soft Lithography ===

=== Thermomechanical nanolithography ===

== Metallization ==

=== Ohmic contact ===

=== Schottky contacts ===

=== Annealing ===

==Etching==

=== wet etching ===

=== dry etching ===

=== plasma etching ===

=== Rapid thermal processing ===
and annealing

== Holography ==

== Passivation and packaging ==

==Poling==

=== Optically assisted poling ===
=== Electric Field poling ===
== Optoelectronics Fabrication ==

=== Polymer waveguide fab: RIE ===
[[Image:RIE.png|thumb|300px|Reactive Ion Etching of a polymer with applied mask]]

Reactive Ion Etching (RIE) is used to convert a slab waveguide into a channel waveguide.

#First a slab is prepared with a core layer (higher index of refraction) is placed on a polymer undercladding on a silicon substrate.
#A metallic photo mask is applied to protect the core material.
#A plasma of oxygen is used to eat away the unmasked portion of the polymer.
#The metalic mask is removed and the ribbon of core material is fully encased with overcladding.

=== Sol-gel waveguide fabrication ===
[[Image:Sol_gel_production.png|thumb|300px|Sol-gel waveguide fabrication (including gray scale masking)]]

This technique builds a complex sol-gel waveguide using completely wet techniques (no vacuum required). Direct illumination by UV through a mask is able to fix portions of the core in place, while unfixed portions are washed away. A series of steps like this can be used to build a complex device.

=== Polymer waveguide fab: Results ===
[[Image:Polymer_waveguide_SEM.png|thumb|300px|Etched polymer waveguide]]

The company Photon X has commercialized the polymer waveguide process. The SEM (5micron line shown) shows very smooth sidewalls from a high quality etching process. Walls can only have roughness of 40-50 nm before there is significant optical loss. The polymer waveguide shows excellent light transmission through a 4 mum x 4 mum waveguide core that has been designed to couple very well with an optical fiber.

See Yeniay <ref>Yeniay, et. al. J. Lightwave Tech. 22, 154</ref>
<br clear='all'>

=== Polymer waveguide fab UV curing ===
[[Image:Waveguide_uvcuring.png|thumb|300px|Two waveguides produced by UV photo curing process]]

This waveguide is created using the same UV curing process that is used with sol-gels. This shows two waveguides very close to each other. The channel is very difficult to control using photo etching process. The SEM shows a little cross striation but overall very good quality results.

See Viens 1999 <ref>Viens, et. al. Proc. SPIE (1999)</ref>
<br clear='all'>

=== Polymer athermal Array Waveguide Gradiant AWG filter ===
[[Image:Fibertofiber_transmission.png|thumb|300px| Measured fiber-to-fiber transmission spectra]]
An array waveguide gradiant is used to separate out wavelengths into separate ports. To characterize the device you shine a variety of wavelengths through the device simulating various information carriers and then measure the output from each port. The fluorinated polymer device was able to achieve these results:

*Insertion loss: 3 dB
*Adjacent crosstalk: -30dB
*Non-adjacent crosstalk: -28 dB

This passive polymer technology is being used to connect servers (interconnects) in server forms over very short distances with tremendous data rates.

<br clear='all'>

[[Image:Temperature_dependence.png|thumb|300px|]]

An athermal device performs equally well at different temperatures without temperature control.

Wavelength Temperature Dependence dλ/dt :
*without superstrate: 12pm/ °C
*with superstrate: - 0.5pm/ °C

See Gao 2002 <ref>Gao, et. al. European Conference on Optical Comm.2002</ref>

==References==
<references/>
[[category:materials processing and fabrication]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>

Materials Processing and Fabrication

2010-03-24T16:46:35Z

128.95.39.187: /* Physical */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>
A great amount of research effort is devoted to developing new ways to apply materials to substrates in extremely thin organized layers so as to improve performance and to make the large scale manufacturing of devices economical. Some techniques that are practical for developing a single device with record breaking efficiency would not work for making millions of devices in a production line. Also engineers must be concerned with the durability of devices under real world conditions of heat, moisture and oxygen. At the same time new nanotechniques and self assembly make it possible to build novel structures virtually one molecule at a time.

See Wikipedia [http://en.wikipedia.org/wiki/MEMS Microelectromechanical systems]

==Microfabrication Overview==
Much microfabrication is done in cleanroom facilities such as that at the Washington Technology Center

{{#ev:youtube|Ltj3tlpDy2M}}

==Crystallization and Deposition Techniques==

=== Spin Coating ===
see Wikipedia [http://en.wikipedia.org/wiki/Spin_coating Spin Coating]

===Physical ===

=== Bulk Crystal growth ===

=== Evaporation ===

=== Sputtering ===

=== doping ===

===
Micro-printing ===

===Chemical- epitaxial growth techniques===
Liquid phase epitaxy
Molecular Beam Epitaxy MBE

Chemical vapor depostion MOCVD

CBE

=== Self Assembly ===
Current research into [[Self Assembled Materials]] is pointing to ways that thin layers can be built up in a highly organized manner. This provides more control of the dipole moment of applied surfaces.

==Patterning - Lithography==
Spin Coating
=== Photolithography ===
negative process
positive process
soft lithography
Lift - off process
Resist processing
Exposure
Nanoimprinting

=== [[E-beam Lithography]]===

X-ray lithography
=== Soft Lithography ===

=== Thermomechanical nanolithography ===

== Metallization ==
Ohmic contact

Schottky contacts

Annealing

==Etching==

=== wet etching ===

=== dry etching ===

=== plasma etching ===

=== Rapid thermal processing ===
and annealing

== Holography ==

== Passivation and packaging ==

==Poling==

=== Optically assisted poling ===
=== Electric Field poling ===
== Optoelectronics Fabrication ==

=== Polymer waveguide fab: RIE ===
[[Image:RIE.png|thumb|300px|Reactive Ion Etching of a polymer with applied mask]]

Reactive Ion Etching (RIE) is used to convert a slab waveguide into a channel waveguide.

#First a slab is prepared with a core layer (higher index of refraction) is placed on a polymer undercladding on a silicon substrate.
#A metallic photo mask is applied to protect the core material.
#A plasma of oxygen is used to eat away the unmasked portion of the polymer.
#The metalic mask is removed and the ribbon of core material is fully encased with overcladding.

=== Sol-gel waveguide fabrication ===
[[Image:Sol_gel_production.png|thumb|300px|Sol-gel waveguide fabrication (including gray scale masking)]]

This technique builds a complex sol-gel waveguide using completely wet techniques (no vacuum required). Direct illumination by UV through a mask is able to fix portions of the core in place, while unfixed portions are washed away. A series of steps like this can be used to build a complex device.

=== Polymer waveguide fab: Results ===
[[Image:Polymer_waveguide_SEM.png|thumb|300px|Etched polymer waveguide]]

The company Photon X has commercialized the polymer waveguide process. The SEM (5micron line shown) shows very smooth sidewalls from a high quality etching process. Walls can only have roughness of 40-50 nm before there is significant optical loss. The polymer waveguide shows excellent light transmission through a 4 mum x 4 mum waveguide core that has been designed to couple very well with an optical fiber.

See Yeniay <ref>Yeniay, et. al. J. Lightwave Tech. 22, 154</ref>
<br clear='all'>

=== Polymer waveguide fab UV curing ===
[[Image:Waveguide_uvcuring.png|thumb|300px|Two waveguides produced by UV photo curing process]]

This waveguide is created using the same UV curing process that is used with sol-gels. This shows two waveguides very close to each other. The channel is very difficult to control using photo etching process. The SEM shows a little cross striation but overall very good quality results.

See Viens 1999 <ref>Viens, et. al. Proc. SPIE (1999)</ref>
<br clear='all'>

=== Polymer athermal Array Waveguide Gradiant AWG filter ===
[[Image:Fibertofiber_transmission.png|thumb|300px| Measured fiber-to-fiber transmission spectra]]
An array waveguide gradiant is used to separate out wavelengths into separate ports. To characterize the device you shine a variety of wavelengths through the device simulating various information carriers and then measure the output from each port. The fluorinated polymer device was able to achieve these results:

*Insertion loss: 3 dB
*Adjacent crosstalk: -30dB
*Non-adjacent crosstalk: -28 dB

This passive polymer technology is being used to connect servers (interconnects) in server forms over very short distances with tremendous data rates.

<br clear='all'>

[[Image:Temperature_dependence.png|thumb|300px|]]

An athermal device performs equally well at different temperatures without temperature control.

Wavelength Temperature Dependence dλ/dt :
*without superstrate: 12pm/ °C
*with superstrate: - 0.5pm/ °C

See Gao 2002 <ref>Gao, et. al. European Conference on Optical Comm.2002</ref>

==References==
<references/>
[[category:materials processing and fabrication]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>

Materials Processing and Fabrication

2010-03-24T16:46:02Z

128.95.39.187: /* Etching */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>
A great amount of research effort is devoted to developing new ways to apply materials to substrates in extremely thin organized layers so as to improve performance and to make the large scale manufacturing of devices economical. Some techniques that are practical for developing a single device with record breaking efficiency would not work for making millions of devices in a production line. Also engineers must be concerned with the durability of devices under real world conditions of heat, moisture and oxygen. At the same time new nanotechniques and self assembly make it possible to build novel structures virtually one molecule at a time.

See Wikipedia [http://en.wikipedia.org/wiki/MEMS Microelectromechanical systems]

==Microfabrication Overview==
Much microfabrication is done in cleanroom facilities such as that at the Washington Technology Center

{{#ev:youtube|Ltj3tlpDy2M}}

==Crystallization and Deposition Techniques==

=== Spin Coating ===
see Wikipedia [http://en.wikipedia.org/wiki/Spin_coating Spin Coating]

===Physical ===
Bulk Crystal growth

Evaporation

Sputtering

doping

Micro-printing
===Chemical- epitaxial growth techniques===
Liquid phase epitaxy
Molecular Beam Epitaxy MBE

Chemical vapor depostion MOCVD

CBE

=== Self Assembly ===
Current research into [[Self Assembled Materials]] is pointing to ways that thin layers can be built up in a highly organized manner. This provides more control of the dipole moment of applied surfaces.

==Patterning - Lithography==
Spin Coating
=== Photolithography ===
negative process
positive process
soft lithography
Lift - off process
Resist processing
Exposure
Nanoimprinting

=== [[E-beam Lithography]]===

X-ray lithography
=== Soft Lithography ===

=== Thermomechanical nanolithography ===

== Metallization ==
Ohmic contact

Schottky contacts

Annealing

==Etching==

=== wet etching ===

=== dry etching ===

=== plasma etching ===

=== Rapid thermal processing ===
and annealing

== Holography ==

== Passivation and packaging ==

==Poling==

=== Optically assisted poling ===
=== Electric Field poling ===
== Optoelectronics Fabrication ==

=== Polymer waveguide fab: RIE ===
[[Image:RIE.png|thumb|300px|Reactive Ion Etching of a polymer with applied mask]]

Reactive Ion Etching (RIE) is used to convert a slab waveguide into a channel waveguide.

#First a slab is prepared with a core layer (higher index of refraction) is placed on a polymer undercladding on a silicon substrate.
#A metallic photo mask is applied to protect the core material.
#A plasma of oxygen is used to eat away the unmasked portion of the polymer.
#The metalic mask is removed and the ribbon of core material is fully encased with overcladding.

=== Sol-gel waveguide fabrication ===
[[Image:Sol_gel_production.png|thumb|300px|Sol-gel waveguide fabrication (including gray scale masking)]]

This technique builds a complex sol-gel waveguide using completely wet techniques (no vacuum required). Direct illumination by UV through a mask is able to fix portions of the core in place, while unfixed portions are washed away. A series of steps like this can be used to build a complex device.

=== Polymer waveguide fab: Results ===
[[Image:Polymer_waveguide_SEM.png|thumb|300px|Etched polymer waveguide]]

The company Photon X has commercialized the polymer waveguide process. The SEM (5micron line shown) shows very smooth sidewalls from a high quality etching process. Walls can only have roughness of 40-50 nm before there is significant optical loss. The polymer waveguide shows excellent light transmission through a 4 mum x 4 mum waveguide core that has been designed to couple very well with an optical fiber.

See Yeniay <ref>Yeniay, et. al. J. Lightwave Tech. 22, 154</ref>
<br clear='all'>

=== Polymer waveguide fab UV curing ===
[[Image:Waveguide_uvcuring.png|thumb|300px|Two waveguides produced by UV photo curing process]]

This waveguide is created using the same UV curing process that is used with sol-gels. This shows two waveguides very close to each other. The channel is very difficult to control using photo etching process. The SEM shows a little cross striation but overall very good quality results.

See Viens 1999 <ref>Viens, et. al. Proc. SPIE (1999)</ref>
<br clear='all'>

=== Polymer athermal Array Waveguide Gradiant AWG filter ===
[[Image:Fibertofiber_transmission.png|thumb|300px| Measured fiber-to-fiber transmission spectra]]
An array waveguide gradiant is used to separate out wavelengths into separate ports. To characterize the device you shine a variety of wavelengths through the device simulating various information carriers and then measure the output from each port. The fluorinated polymer device was able to achieve these results:

*Insertion loss: 3 dB
*Adjacent crosstalk: -30dB
*Non-adjacent crosstalk: -28 dB

This passive polymer technology is being used to connect servers (interconnects) in server forms over very short distances with tremendous data rates.

<br clear='all'>

[[Image:Temperature_dependence.png|thumb|300px|]]

An athermal device performs equally well at different temperatures without temperature control.

Wavelength Temperature Dependence dλ/dt :
*without superstrate: 12pm/ °C
*with superstrate: - 0.5pm/ °C

See Gao 2002 <ref>Gao, et. al. European Conference on Optical Comm.2002</ref>

==References==
<references/>
[[category:materials processing and fabrication]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>

Materials Processing and Fabrication

2010-03-24T16:21:06Z

128.95.39.187:

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>
A great amount of research effort is devoted to developing new ways to apply materials to substrates in extremely thin organized layers so as to improve performance and to make the large scale manufacturing of devices economical. Some techniques that are practical for developing a single device with record breaking efficiency would not work for making millions of devices in a production line. Also engineers must be concerned with the durability of devices under real world conditions of heat, moisture and oxygen. At the same time new nanotechniques and self assembly make it possible to build novel structures virtually one molecule at a time.

See Wikipedia [http://en.wikipedia.org/wiki/MEMS Microelectromechanical systems]

==Microfabrication Overview==
Much microfabrication is done in cleanroom facilities such as that at the Washington Technology Center

{{#ev:youtube|Ltj3tlpDy2M}}

==Crystallization and Deposition Techniques==

=== Spin Coating ===
see Wikipedia [http://en.wikipedia.org/wiki/Spin_coating Spin Coating]

===Physical ===
Bulk Crystal growth

Evaporation

Sputtering

doping

Micro-printing
===Chemical- epitaxial growth techniques===
Liquid phase epitaxy
Molecular Beam Epitaxy MBE

Chemical vapor depostion MOCVD

CBE

=== Self Assembly ===
Current research into [[Self Assembled Materials]] is pointing to ways that thin layers can be built up in a highly organized manner. This provides more control of the dipole moment of applied surfaces.

==Patterning - Lithography==
Spin Coating
=== Photolithography ===
negative process
positive process
soft lithography
Lift - off process
Resist processing
Exposure
Nanoimprinting

=== [[E-beam Lithography]]===

X-ray lithography
=== Soft Lithography ===

=== Thermomechanical nanolithography ===

== Metallization ==
Ohmic contact

Schottky contacts

Annealing

==Etching==
wet etching

dry etching

plasma etching
Rapid thermal processing and annealing

== Holography ==

== Passivation and packaging ==

==Poling==

=== Optically assisted poling ===
=== Electric Field poling ===
== Optoelectronics Fabrication ==

=== Polymer waveguide fab: RIE ===
[[Image:RIE.png|thumb|300px|Reactive Ion Etching of a polymer with applied mask]]

Reactive Ion Etching (RIE) is used to convert a slab waveguide into a channel waveguide.

#First a slab is prepared with a core layer (higher index of refraction) is placed on a polymer undercladding on a silicon substrate.
#A metallic photo mask is applied to protect the core material.
#A plasma of oxygen is used to eat away the unmasked portion of the polymer.
#The metalic mask is removed and the ribbon of core material is fully encased with overcladding.

=== Sol-gel waveguide fabrication ===
[[Image:Sol_gel_production.png|thumb|300px|Sol-gel waveguide fabrication (including gray scale masking)]]

This technique builds a complex sol-gel waveguide using completely wet techniques (no vacuum required). Direct illumination by UV through a mask is able to fix portions of the core in place, while unfixed portions are washed away. A series of steps like this can be used to build a complex device.

=== Polymer waveguide fab: Results ===
[[Image:Polymer_waveguide_SEM.png|thumb|300px|Etched polymer waveguide]]

The company Photon X has commercialized the polymer waveguide process. The SEM (5micron line shown) shows very smooth sidewalls from a high quality etching process. Walls can only have roughness of 40-50 nm before there is significant optical loss. The polymer waveguide shows excellent light transmission through a 4 mum x 4 mum waveguide core that has been designed to couple very well with an optical fiber.

See Yeniay <ref>Yeniay, et. al. J. Lightwave Tech. 22, 154</ref>
<br clear='all'>

=== Polymer waveguide fab UV curing ===
[[Image:Waveguide_uvcuring.png|thumb|300px|Two waveguides produced by UV photo curing process]]

This waveguide is created using the same UV curing process that is used with sol-gels. This shows two waveguides very close to each other. The channel is very difficult to control using photo etching process. The SEM shows a little cross striation but overall very good quality results.

See Viens 1999 <ref>Viens, et. al. Proc. SPIE (1999)</ref>
<br clear='all'>

=== Polymer athermal Array Waveguide Gradiant AWG filter ===
[[Image:Fibertofiber_transmission.png|thumb|300px| Measured fiber-to-fiber transmission spectra]]
An array waveguide gradiant is used to separate out wavelengths into separate ports. To characterize the device you shine a variety of wavelengths through the device simulating various information carriers and then measure the output from each port. The fluorinated polymer device was able to achieve these results:

*Insertion loss: 3 dB
*Adjacent crosstalk: -30dB
*Non-adjacent crosstalk: -28 dB

This passive polymer technology is being used to connect servers (interconnects) in server forms over very short distances with tremendous data rates.

<br clear='all'>

[[Image:Temperature_dependence.png|thumb|300px|]]

An athermal device performs equally well at different temperatures without temperature control.

Wavelength Temperature Dependence dλ/dt :
*without superstrate: 12pm/ °C
*with superstrate: - 0.5pm/ °C

See Gao 2002 <ref>Gao, et. al. European Conference on Optical Comm.2002</ref>

==References==
<references/>
[[category:materials processing and fabrication]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>

Materials Processing and Fabrication

2010-03-23T18:13:32Z

128.95.39.187: /* Deposition */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>
A great amount of research effort is devoted to developing new ways to apply materials to substrates in extremely thin organized layers so as to improve performance and to make the large scale manufacturing of devices economical. Some techniques that are practical for developing a single device with record breaking efficiency would not work for making millions of devices in a production line. Also engineers must be concerned with the durability of devices under real world conditions of heat, moisture and oxygen. At the same time new nanotechniques and self assembly make it possible to build novel structures virtually one molecule at a time.

See Wikipedia [http://en.wikipedia.org/wiki/MEMS Microelectromechanical systems]

==Microfabrication Overview==
Much microfabrication is done in cleanroom facilities such as that at the Washington Technology Center

{{#ev:youtube|Ltj3tlpDy2M}}

==Deposition==

=== Spin Coating ===
see Wikipedia [http://en.wikipedia.org/wiki/Spin_coating Spin Coating]

=== Crystal growth ===

=== Layer by layer deposition ===

=== Self Assembly ===
Current research into [[Self Assembled Materials]] is pointing to ways that thin layers can be built up in a highly organized manner. This provides more control of the dipole moment of applied surfaces.

==Poling==

=== Optically assisted poling ===
=== Electric Field poling ===

==Patterning==
=== [[E-beam Lithography]]===

=== Nanoimprinting ===

=== Soft Lithography ===

=== Thermomechanical nanolithography ===

==Etching==

=== Polymer waveguide fab: RIE ===
[[Image:RIE.png|thumb|300px|Reactive Ion Etching of a polymer with applied mask]]

Reactive Ion Etching (RIE) is used to convert a slab waveguide into a channel waveguide.

#First a slab is prepared with a core layer (higher index of refraction) is placed on a polymer undercladding on a silicon substrate.
#A metallic photo mask is applied to protect the core material.
#A plasma of oxygen is used to eat away the unmasked portion of the polymer.
#The metalic mask is removed and the ribbon of core material is fully encased with overcladding.

=== Sol-gel waveguide fabrication ===
[[Image:Sol_gel_production.png|thumb|300px|Sol-gel waveguide fabrication (including gray scale masking)]]

This technique builds a complex sol-gel waveguide using completely wet techniques (no vacuum required). Direct illumination by UV through a mask is able to fix portions of the core in place, while unfixed portions are washed away. A series of steps like this can be used to build a complex device.

=== Polymer waveguide fab: Results ===
[[Image:Polymer_waveguide_SEM.png|thumb|300px|Etched polymer waveguide]]

The company Photon X has commercialized the polymer waveguide process. The SEM (5micron line shown) shows very smooth sidewalls from a high quality etching process. Walls can only have roughness of 40-50 nm before there is significant optical loss. The polymer waveguide shows excellent light transmission through a 4 mum x 4 mum waveguide core that has been designed to couple very well with an optical fiber.

See Yeniay <ref>Yeniay, et. al. J. Lightwave Tech. 22, 154</ref>
<br clear='all'>

=== Polymer waveguide fab UV curing ===
[[Image:Waveguide_uvcuring.png|thumb|300px|Two waveguides produced by UV photo curing process]]

This waveguide is created using the same UV curing process that is used with sol-gels. This shows two waveguides very close to each other. The channel is very difficult to control using photo etching process. The SEM shows a little cross striation but overall very good quality results.

See Viens 1999 <ref>Viens, et. al. Proc. SPIE (1999)</ref>
<br clear='all'>

=== Polymer athermal Array Waveguide Gradiant AWG filter ===
[[Image:Fibertofiber_transmission.png|thumb|300px| Measured fiber-to-fiber transmission spectra]]
An array waveguide gradiant is used to separate out wavelengths into separate ports. To characterize the device you shine a variety of wavelengths through the device simulating various information carriers and then measure the output from each port. The fluorinated polymer device was able to achieve these results:

*Insertion loss: 3 dB
*Adjacent crosstalk: -30dB
*Non-adjacent crosstalk: -28 dB

This passive polymer technology is being used to connect servers (interconnects) in server forms over very short distances with tremendous data rates.

<br clear='all'>

[[Image:Temperature_dependence.png|thumb|300px|]]

An athermal device performs equally well at different temperatures without temperature control.

Wavelength Temperature Dependence dλ/dt :
*without superstrate: 12pm/ °C
*with superstrate: - 0.5pm/ °C

See Gao 2002 <ref>Gao, et. al. European Conference on Optical Comm.2002</ref>

==References==
<references/>
[[category:materials processing and fabrication]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>

Materials Processing and Fabrication

2010-03-23T18:07:19Z

128.95.39.187: /* E-beam Lithography */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>
A great amount of research effort is devoted to developing new ways to apply materials to substrates in extremely thin organized layers so as to improve performance and to make the large scale manufacturing of devices economical. Some techniques that are practical for developing a single device with record breaking efficiency would not work for making millions of devices in a production line. Also engineers must be concerned with the durability of devices under real world conditions of heat, moisture and oxygen. At the same time new nanotechniques and self assembly make it possible to build novel structures virtually one molecule at a time.

See Wikipedia [http://en.wikipedia.org/wiki/MEMS Microelectromechanical systems]

==Deposition==

=== Spin Coating ===
see Wikipedia [http://en.wikipedia.org/wiki/Spin_coating Spin Coating]

=== Crystal growth ===

=== Layer by layer deposition ===

=== Self Assembly ===
Current research into [[Self Assembled Materials]] is pointing to ways that thin layers can be built up in a highly organized manner. This provides more control of the dipole moment of applied surfaces.

==Poling==

=== Optically assisted poling ===
=== Electric Field poling ===

==Patterning==
=== [[E-beam Lithography]]===

=== Nanoimprinting ===

=== Soft Lithography ===

=== Thermomechanical nanolithography ===

==Etching==

=== Polymer waveguide fab: RIE ===
[[Image:RIE.png|thumb|300px|Reactive Ion Etching of a polymer with applied mask]]

Reactive Ion Etching (RIE) is used to convert a slab waveguide into a channel waveguide.

#First a slab is prepared with a core layer (higher index of refraction) is placed on a polymer undercladding on a silicon substrate.
#A metallic photo mask is applied to protect the core material.
#A plasma of oxygen is used to eat away the unmasked portion of the polymer.
#The metalic mask is removed and the ribbon of core material is fully encased with overcladding.

=== Sol-gel waveguide fabrication ===
[[Image:Sol_gel_production.png|thumb|300px|Sol-gel waveguide fabrication (including gray scale masking)]]

This technique builds a complex sol-gel waveguide using completely wet techniques (no vacuum required). Direct illumination by UV through a mask is able to fix portions of the core in place, while unfixed portions are washed away. A series of steps like this can be used to build a complex device.

=== Polymer waveguide fab: Results ===
[[Image:Polymer_waveguide_SEM.png|thumb|300px|Etched polymer waveguide]]

The company Photon X has commercialized the polymer waveguide process. The SEM (5micron line shown) shows very smooth sidewalls from a high quality etching process. Walls can only have roughness of 40-50 nm before there is significant optical loss. The polymer waveguide shows excellent light transmission through a 4 mum x 4 mum waveguide core that has been designed to couple very well with an optical fiber.

See Yeniay <ref>Yeniay, et. al. J. Lightwave Tech. 22, 154</ref>
<br clear='all'>

=== Polymer waveguide fab UV curing ===
[[Image:Waveguide_uvcuring.png|thumb|300px|Two waveguides produced by UV photo curing process]]

This waveguide is created using the same UV curing process that is used with sol-gels. This shows two waveguides very close to each other. The channel is very difficult to control using photo etching process. The SEM shows a little cross striation but overall very good quality results.

See Viens 1999 <ref>Viens, et. al. Proc. SPIE (1999)</ref>
<br clear='all'>

=== Polymer athermal Array Waveguide Gradiant AWG filter ===
[[Image:Fibertofiber_transmission.png|thumb|300px| Measured fiber-to-fiber transmission spectra]]
An array waveguide gradiant is used to separate out wavelengths into separate ports. To characterize the device you shine a variety of wavelengths through the device simulating various information carriers and then measure the output from each port. The fluorinated polymer device was able to achieve these results:

*Insertion loss: 3 dB
*Adjacent crosstalk: -30dB
*Non-adjacent crosstalk: -28 dB

This passive polymer technology is being used to connect servers (interconnects) in server forms over very short distances with tremendous data rates.

<br clear='all'>

[[Image:Temperature_dependence.png|thumb|300px|]]

An athermal device performs equally well at different temperatures without temperature control.

Wavelength Temperature Dependence dλ/dt :
*without superstrate: 12pm/ °C
*with superstrate: - 0.5pm/ °C

See Gao 2002 <ref>Gao, et. al. European Conference on Optical Comm.2002</ref>

==References==
<references/>
[[category:materials processing and fabrication]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>

Materials Processing and Fabrication

2010-03-23T18:06:54Z

128.95.39.187: /* Patterning */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>
A great amount of research effort is devoted to developing new ways to apply materials to substrates in extremely thin organized layers so as to improve performance and to make the large scale manufacturing of devices economical. Some techniques that are practical for developing a single device with record breaking efficiency would not work for making millions of devices in a production line. Also engineers must be concerned with the durability of devices under real world conditions of heat, moisture and oxygen. At the same time new nanotechniques and self assembly make it possible to build novel structures virtually one molecule at a time.

See Wikipedia [http://en.wikipedia.org/wiki/MEMS Microelectromechanical systems]

==Deposition==

=== Spin Coating ===
see Wikipedia [http://en.wikipedia.org/wiki/Spin_coating Spin Coating]

=== Crystal growth ===

=== Layer by layer deposition ===

=== Self Assembly ===
Current research into [[Self Assembled Materials]] is pointing to ways that thin layers can be built up in a highly organized manner. This provides more control of the dipole moment of applied surfaces.

==Poling==

=== Optically assisted poling ===
=== Electric Field poling ===

==Patterning==
=== E-beam Lithography===

=== Nanoimprinting ===

=== Soft Lithography ===

=== Thermomechanical nanolithography ===

==Etching==

=== Polymer waveguide fab: RIE ===
[[Image:RIE.png|thumb|300px|Reactive Ion Etching of a polymer with applied mask]]

Reactive Ion Etching (RIE) is used to convert a slab waveguide into a channel waveguide.

#First a slab is prepared with a core layer (higher index of refraction) is placed on a polymer undercladding on a silicon substrate.
#A metallic photo mask is applied to protect the core material.
#A plasma of oxygen is used to eat away the unmasked portion of the polymer.
#The metalic mask is removed and the ribbon of core material is fully encased with overcladding.

=== Sol-gel waveguide fabrication ===
[[Image:Sol_gel_production.png|thumb|300px|Sol-gel waveguide fabrication (including gray scale masking)]]

This technique builds a complex sol-gel waveguide using completely wet techniques (no vacuum required). Direct illumination by UV through a mask is able to fix portions of the core in place, while unfixed portions are washed away. A series of steps like this can be used to build a complex device.

=== Polymer waveguide fab: Results ===
[[Image:Polymer_waveguide_SEM.png|thumb|300px|Etched polymer waveguide]]

The company Photon X has commercialized the polymer waveguide process. The SEM (5micron line shown) shows very smooth sidewalls from a high quality etching process. Walls can only have roughness of 40-50 nm before there is significant optical loss. The polymer waveguide shows excellent light transmission through a 4 mum x 4 mum waveguide core that has been designed to couple very well with an optical fiber.

See Yeniay <ref>Yeniay, et. al. J. Lightwave Tech. 22, 154</ref>
<br clear='all'>

=== Polymer waveguide fab UV curing ===
[[Image:Waveguide_uvcuring.png|thumb|300px|Two waveguides produced by UV photo curing process]]

This waveguide is created using the same UV curing process that is used with sol-gels. This shows two waveguides very close to each other. The channel is very difficult to control using photo etching process. The SEM shows a little cross striation but overall very good quality results.

See Viens 1999 <ref>Viens, et. al. Proc. SPIE (1999)</ref>
<br clear='all'>

=== Polymer athermal Array Waveguide Gradiant AWG filter ===
[[Image:Fibertofiber_transmission.png|thumb|300px| Measured fiber-to-fiber transmission spectra]]
An array waveguide gradiant is used to separate out wavelengths into separate ports. To characterize the device you shine a variety of wavelengths through the device simulating various information carriers and then measure the output from each port. The fluorinated polymer device was able to achieve these results:

*Insertion loss: 3 dB
*Adjacent crosstalk: -30dB
*Non-adjacent crosstalk: -28 dB

This passive polymer technology is being used to connect servers (interconnects) in server forms over very short distances with tremendous data rates.

<br clear='all'>

[[Image:Temperature_dependence.png|thumb|300px|]]

An athermal device performs equally well at different temperatures without temperature control.

Wavelength Temperature Dependence dλ/dt :
*without superstrate: 12pm/ °C
*with superstrate: - 0.5pm/ °C

See Gao 2002 <ref>Gao, et. al. European Conference on Optical Comm.2002</ref>

==References==
<references/>
[[category:materials processing and fabrication]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Electro-optic Polymers and Devices|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Photonics Applications in Information Technology|Return to Organic Photonics Applications Menu]]</td>
</tr>
</table>

Scanning Electron Microscope

2010-03-23T18:04:32Z

128.95.39.187: /* Operation */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: center; width: 33%">[[Main_Page#Research Equipment, Devices and Techniques|Return to Research Tool Menu]]</td>

</tr>
</table>

=== Overview ===
[[Image:Sirion_sem.png|thumb|300px|]]
The scanning electron microscope is used to image the surface of a conducting sample by scanning it with a high energy beam of electrons. Some SEMs have additional software enhancements than enable them to focus the beam on a photomask for [[E-beam lithography]] or are equipped for focused ion beam (FIB) milling. The SEM is a useful tool for photonics research because it reveals nano-scale surface features and topography that is critical to the performance of multi-layer devices.

See Wikipedia on [http://en.wikipedia.org/wiki/Scanning_electron_microscope Scanning Electron Microscope]

=== Operation ===

Part 1 Tour and Sample Preparation
{{#ev:youtube|c7EVTnVHN-s}}

Part 2 Loading the Sample
{{#ev:youtube|SaaVaILUObg}}

Part 3 Setting the Working Distance
{{#ev:youtube|CNIrvGRXugU}}

Part 4 Lens Alignment and Stigmation
{{#ev:youtube|NP5VckJfv04}}

Part 5 Moving the Stage and Imaging
{{#ev:youtube|04Fvq5HWebA}}

Part 6 Changing the Sample and Shutdown
{{#ev:youtube|pu_pMYMYBlw}}

Training Manual for Sirion SEM[http://depts.washington.edu/cmditr/media/siriontraining_rev8_04223.pdf]

Training Video on [http://grover.mirc.gatech.edu/training/viewVideo.php?video=sem-high&size=0 Hitachi 3500H SEM at GT MiRC]

=== Significance ===
[[category:Research equipment]]

Photovoltaics- Outreach Kit

2010-03-23T16:18:07Z

128.95.39.187: /* Sources for Building your own kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Basic Optics - Outreach Kit|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Lasers and Telecommunication- Outreach Kit|Next Topic]]</td>
</tr>
</table>

== Overview ==
Photovoltaics (PV) or solar cells are one of the most promising sources for renewable electrical energy. The first generation cells were made from silicon crystals like those used computer semiconductor chips. These are efficient but very expensive. Silicon PV were first widely used where the cost of wiring to the grid was impractical such as in satellites or to power remote sensors along pipelines or railway tracks. Materials research and improved manufacturing techniques have brought the price down to where they are beginning to become practical for home energy systems. Plastic solar cells that use organic chemicals instead of silicon may be the next breakthrough. These demos show some basic devices and engage students in quantifying their performance and considering how basic science relates to engineering design.

== User Guide ==

=== Solar Car - Solar battery charger ===

'''Solar energy can be converted to electrical energy using a solar cell.''' Demonstrate the solar car, the motor and rotor, and solar battery charger. Place the solar car in the full sun. What happens when the car passes into the shade? Demonstrate that the small silicon cell doesn’t generate enough energy to power the single LED but the larger amorphous silicon panel can power the light, even in indirect sunlight. Compare the solar electricity to power from a battery. See if they know about batteries polarity. Predict what would happen to the motor if you switch the leads to the solar cell. Reverse the polarity and the disc on the motor will rotate in the opposite direction.

*'''Research Connection:''' CMDITR is building a new kind of solar cell that uses an organic chemical to trap light and then transfer electrons to conductive layers.

=== Three types of solar cells. ===

'''There are several kinds of solar cells which differ power, cost, durability, and preferred applications.'''
Demonstrate the various types of solar cells in the kit by connecting them to a motor, voltmeter or LED.
a. Single crystal and Multicrystaline cell. The smaller cells in the kit are rated .45 volts and 400ma. Crystalline silicon solar cells (c-Si) can have efficiencies from 10-12% . They are produced from ingots of solid silicon and are rigid. These are the cells that most often used in space station where power density and durability are most important.

b. Amorphous silicon battery charger. The panel is rated 7.2 volt / 200ma and has diode built into the circuit to prevent battery discharge into the panel when it is dark. Amorphous silicon is made by depositing an extremely thin layer of silicon on a conductive polymer. As a result the panel is flexible. (a-Si) Amorphous silicon has a comparatively low 6% efficiency because the silicon is poorly organized creating barriers to charge movement but it makes up for this with a lower cost and ease of manufacturing.

c. Copper indium selenide (CIS) CIS and Copper indium gallium selenide cells (CIGS) have 14-20% efficiency. These cells must be full encapsulated to prevent release of toxic selenium. These cells have an open circuit voltage of 5 volts and a short circuit current of 95ma. Max power output is 3.9 volts at 64mA.

d. Organic photovoltaics (OPV)- currently maximum is 5-6.5 %. The Konarka Power Plastic is one of the few commercially available OPV panel. The advantage of organic or plastic solar cells is that they have the potential of extremely low material and manufacturing cost and they are flexible. A disadvantage is that organic materials have a limited lifetime especially in full sun and exposed to water and oxygen.

e. Dye Sensitized Solar Cell (DSS)Demonstrate the dye sensitize solar cell. Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Lightly coat the other slide with the carbon soot from a candle slide. Pinch the slides together with the binder clips so that the slides are offset exposing the conductive ITO layer. Apply iodide solution as an electrolyte and then.

f. Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.
Research Connection: CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.

*'''Research Connection:''' CCMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

<br clear='all'>

<br clear='all'>
=== Series vs Parallel circuits ===
[[Image:Pv_parallel.jpg|thumb|300px|3 solar cells wired in Parallel ]]

[[Image:Series_parallel.png|thumb|300px|Two arrangements for solar cells.]]

a. Explain the difference between voltage and current. Show that the large panel produces a higher voltage (because it has several cell areas wired in series).
Measure the voltage and current produced from each cell using the digital meter. The wood test frame provides a convenient support and visual explanation of the circuit.

[[Image:Testcellholder.jpg|thumb|300px|]]

Note that the red lead must be moved and the selector switch set to mA to get the ammeter mode. Each cell has a characteristic voltage. Silicon cells produce between .5 -.6 V oc *(volts open circuit), OPVs are usually around .4 Voc. Use the clip leads and the three small panels to demonstrate that in a series circuit the voltage is added. In a parallel circuit the voltage does not change but the current (amperage) is increased.’

<br clear='all'>
=== Measuring Power Output===

'''The power from a solar cell depends on the current and voltage.''' To measure the power record the voltage and amperage of a solar cell across a load. The ammeter has builtin precision resistors in its circuit. If you only had a voltmeter you could place a known resistor in the circuit and calculate current in amps as voltage divided by ohms. The peak power depends on specific load which affects the current and voltage. ( see voltage current graph below) For this activity you measure the voltage and current in a simple circuit without a load.

[[Image:Volt_amp.png|thumb|300px|Circuit for measuring voltage and current through a solar cell]]
P= V x I
Power (watts) = Volts x Amps

Sample calculation:
Volts = .4 V
Amp = 50ma= .05 amp
Power = .02 Watts

a. Compare the power for a 3 x 4 cm area for the crystalline solar cell compared to the same area of amorphous silicon cell.

b. The amorphous panel provided is 7.2 V and 200 ma. How many of these panels would be needed to in what configuration to generate 100 Watts?

c. Experiment with different sources of light, sunlight, or diffuse vs. direct light

d. Experiment with the effect of temperature on cell power.

*'''Research Connection:''' CMDITR Engineers and scientists test their OPV cells in a similar manner by measuring voltage and current under different loads and light conditions to calculate the maximum efficiency. With a reliable way of comparing cells then it is possible to fine-tune the systems and methods to improve efficiency and longevity.<br clear='all'>

=== Power : area relationship ===

'''The larger the cross sectional area of the light beam that is trapped, the greater the power generated.'''

a. Cover portions of the panel to show decreasing current and voltage. Solar cells measured with the meter are under no load so you get the open circuit voltage (Voc). You should notice that the current responds quickly with decreasing light while the voltage stays somewhat stable, finally the voltage drops too. To measure the power from the panel you have to measure both voltage and amperage produced.

b. Plot the power versus area for the amorphous silicon panel. Complete the table and graph from BLM 1- Power vs Area Experiment

c. Repeat the measurement with a different pattern of shading (block the left, right top or bottom) You may get different results because of the wiring of cells within the array. Once a parallel section of panel is partially shaded it tends to knock out the whole section. Panels can also be equipped with bypass diodes which reroute current around underperforming cells.

[http://www.electroiq.com/index/display/article-display.articles.Photovoltaics-World.bos-components.inverters.2009.03.shade-happens__installation.QP129867.dcmp=rss.page=1.html Shading / Power loss diagram]

*'''Research Connection:''' OPVs could be less expensive even if they are less efficient which means a larger area could be deployed.

<br clear='all'>
=== Power : distance relationship ===
'''Energy from a radiant light source drops off with distance.'''
[[Image:479px-Inverse_square_law.svg.png|thumb|300px|]]

As you move away from a diffuse light source the same amount of light is spread over a large area so the solar panel only intercepts part of the energy. This called the inverse square law. It relates I intensity with r the distance.

:<math>I \propto \frac{1}{r^2} \,</math>

If you use a focused light source up close this relationship will not hold. At the distance we are from the sun it does not make any measurable difference how close (for example sea level versus on mountain top) we place solar cells to the sun. There is some variation in power available from the sun as we as the Earth’s orbit reaches perihelion. Currently this occurs in January when the Earth is 5million km (3 million miles) closer to the sun. This results in about 7% more solar energy striking the earth at perihelion.

a. Use the electric meter to measure the current produced by the sample silicon cell as you move away from a light source. Collect data and graph the experiment using BLM 2 – Power vs Distance Experiment

<br clear='all'>

=== Power : Angle of Incidence relationship ===
[[Image:Seasons.too.png|thumb|300px|Effect of sun angle on insolation]]
'''The angle with respect to the sun influences the energy output.'''
:<math>I = S cos Z\,\!</math>

a. Set up the solar panel on its inclined support with protractor. Change the angle of the solar panel and measure the current. Changing the angle has the effect of decreasing the cross section of light that is intercepted. You can see this by measuring the shadow of the panel as it is tilted. In addition low angle sun on the Earth must pass through more atmosphere so some energy is absorbed.

b. Plot the current versus the angle. Complete the data and graph on BLM 3 Power vs Angle Experiment

c. Use this information to create a bar chart showing the total power generated by a cell during the course of day if the cell were fixed on a roof with an angle of 30 degrees. The peak angle of the sun on the spring or autumn equinox is 90- your latitude. At mid summer it is 90 – latitude -23.45 degrees. At mid winter it is 90 – latitude + 23.45 degrees

[[Image:Pv angle.jpg|thumb|300px|PV panel with battery charger and protractor]]

*'''Research Connection:''' Engineers have designed tracking systems that keep PV panels facing perpendicular to sun all day long. Others have explored using concentrators to reflect light to a smaller area where the cell is.

=== Measuring Absorption Spectrum ===

'''Photovoltaics absorb light at specific wavelengths.'''

a. Use the red, green and blue filters to show that certain colors when filtered out reduce the power more than other colors.

b. Plot the current versus wavelength when different colors are placed in front of the solar cell. You can use the large filter sheets or the filter sample booklets. Be sure to pick filters with approximately the same optical density. Use the attached transmission spectra tabs to pick colors that represent an even array across the spectrum. Complete BLM 4 Power vs Wavelength Experiment

c. Compare the amorphous silicon, the polycrystalline silicon cell, and the dye densitized solar cell.

*'''Research Connection:''' When we design chemicals to use in organic photovoltaics we measure the absorption spectra of the chromophores. Ideally we want dyes that absorb across the entire visible spectrum.

=== Measuring Efficiency ===

'''Efficiency is a measure of how much of the available energy is captured by a cell.''' It is the amount of electricity produced divided by the amount shining on the solar cell. To measure efficiency we have to know how much light energy is hitting the cell and how much electricity it is producing. It’s difficult to measure the incident light. Direct sunlight is between 250 and 1,000 W/m2.

a. In full sunlight measure the power of your solar cell and calculate the efficiency. In this example the cell has an area of 2.4 x 10-3 m2 , measuring .6 Volts and .5 amps in full sun

Pi = A * Ps = 2.4 x 10<sup>-3</sup> * 1000 = 2.4 watts

Po = V x I = 0.6 x 0.5 = 0.3 W

e = Po/Pi = 0.3/2.4 = 0.12 = 12%

b. Repeat this measurement for various cells.
=== PV Cost estimation ===

'''Solar cells are still somewhat expensive.''' Several factors have to be considered in sizing a solar system. Calculate how much area is needed to power a house, how much would it cost?

a. Solar cells currently run about $5-$9 per peak watt.

b. A house might require 2kW peak power

c. If the silicon cells are 15% efficient and the

d. Incoming energy is 1000 W/m2 assume 5 hours (5 kWh/m2) per day of useful sunlight or use the “Photovoltaics Solar Resource” map from NREL to identify the available solar resource for your area.

e. If you aren’t connected to the grid you will need batteries which cost $1 amp hour

*'''Research Connection:''' Materials and manufacturing process determines the cost. Organic photovoltaics have a potential of being low cost because they can be manufactured with roll printing methods. Further research is needed to get higher efficiency, better durability (through encapusulation and decreased photobleaching) New organic solar cells may be much cheaper in the future.

<br clear='all'>
=== PV characterization ===

'''Solar cells are characterized using a voltage- current curve.'''

a. Place the test PV cell in the wood test holder. Place an ammeter and a volt meter at the two pegs labeled A and V. Gradually change the series load in the circuit by sliding the variable resistor. Adjust the load to get an even series of voltage readings such as every .1 volts and record the amps for each voltage. Plot the data. The goal is to get a curve that is closer to a right angle (with a minimum fill factor). There is a certain combination of voltage and current that delivers peak power.

b. Complete BLM 5 Current vs wavelength experiment

*'''Research Connection:''' CMDITR researcher do this same measurement with much finer accuracy.

[[Image:Opv powercurve.jpg|thumb|300px|]]

=== Dye Sensitized Solar Cell ===

'''Organic pigments can be used to capture light to power electrochemical processes.''' Demonstrate the dye sensitized solar cell.Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Then apply iodide solution as an electrolyte and then pinch this together with the carbon black coated slide.

*'''Research Connection:''' Dye sensitized cells have begun commercial production as research continues.
[[Nanocrystalline_-_Dye_Solar_Cell_Kit| Build the complete dye sensitized solar cell activity for high school]]
==Posters==
Courtesy of Ginger Research Group - UW- by Kristina Knesting, Brad MacLeod and Kevin Noone

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/Plastic_Solar_Cells.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/Plastic_Solar_Cells.pdf Download PowerPoint of Plastic Solar Cell Poster]

<embed_document width="100%" height="800">http://depts.washington.edu/cmditr/media/OPVefficiency.pdf</embed_document>

[http://depts.washington.edu/cmditr/media/OPVefficiency.ppt Download PowerPoint of OPV Efficiency Poster]

== Links ==
[http://www.nrel.gov/learning/re_photovoltaics.html NREL]

[http://www.powernaturally.org/Programs/SchoolPowerNaturally/InTheClassroom/kitlessons.asp?i=9#Lesson14 Solar Cell lessons]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://www.infinitepower.org/pdf/No19%2096-828B.pdf Photovoltaic measurements Lesson]

[http://www.nrel.gov/midc/unlv/ live insolation data for Las Vegas NREL Solar Data]

[http://en.wikipedia.org/wiki/Solar_cell Wikipedia on solar cells]

[http://depts.washington.edu/cmditr/media/PlasticPV.ppt Plastic Solar Cell Poster]

[http://www.nanosense.org/activities/cleanenergy/solarcellanimation.html Solar Cell Animations]

[http://www.iop.org/EJ/article/0031-9120/41/5/005/pe6_5_005.pdf?request-id=e7503f0f-68f9-4217-bfe8-24c174c90fa5 Other chemicals for photovoltaics demo]

[http://www.teachersdomain.org/asset/hew06_int_ohmslaw/ Ohms Law Simulation from the Teachers Domain]

[http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/watcir.html Water analogy to circuits- Hyperphysics]

== Materials in the kit ==
*Sunzoom Lite car kit
*4 AA battery PV battery charger
*4 AA recharable NiCAD or LI ion batteries
*Solar mini car
*Digital Electric meter
*Protractor
*Ruler
== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/Photovoltaics.docx Cover art for Photovoltaics Kit]

http://shop.pitsco.com/store/detail.aspx?CategoryID=115&by=9&ID=2647&c=1&t=0&l=0 $8. 95 sunzoom lite car

http://store.sundancesolar.com/subusobachki6.html 4 AA battery charger $39.95

http://store.sundancesolar.com/misorokitsus.html mini solar car $9.95

http://store.sundancesolar.com/multi-meter.html Electric Meter 2 a $12.95

Light Source for indoor use- quartz desk lamp

http://scientificsonline.com/product.asp?pn=3039810 Individual silicon cells 3 @ $5.95

http://scientificsonline.com/product.asp?pn=3085037 CIS Solar Panel 3 @ $2.95

Color Filter pack for testing cells

Rechargeable Batteries

Transmission Electron Microscope

2010-03-22T16:29:54Z

128.95.39.187:

The transmission electron microscope (TEM) is used in photonics research as a way of visualizing and measuring extremely thin layers. It is well suited for this research because the devices and prototypes are often conductive, are extremely thin, and can withstand high vacuum.

See wikipedia on [http://en.wikipedia.org/wiki/Transmission_electron_microscope TEM]

[http://www.youtube.com/watch?v=fToTFjwUc5M&feature=related Brief Youtube intro]

Transmission Electron Microscope

2010-03-22T16:27:22Z

128.95.39.187: New page: The transmission electron microscope (TEM) is used in photonics research as a way of visualizing and measuring extremely thin layers. It is well suited for this research because the device...

Main Page

2010-03-22T16:19:29Z

128.95.39.187: /* Research Equipment, Devices and Techniques */

<big>'''Center for Materials and Devices for Information Technology Research (CMDITR) Wiki'''</big><br>
This wiki is a reference collection on photonics. Most of the text has been captured from a series of lectures recorded in 2005-2008 by Center faculty Jean-Luc Bredas (Georgia Tech), Neal Armstrong (University of Arizona) and Seth Marder (Georgia Tech). You may also want to search the
[http://depts.washington.edu/cmditr/cwis/SPT--Home.php CMDITR Photonics Digital Libary] for individual learning objects.

(The sections below with ** asterisks are currently in development, the rest are in draft form)

[http://depts.washington.edu/cmditr/media/Photonics.html Concept Map CMDITR]

== Photonics Core Concepts and Applications ==
[[Image:Wordle3.png|thumb|center|600px|This graphic was created by processing the CMDITR 2009 annual report in the Wordle program. The larger the word the more times it appeared in the text.]]
<br clear='all'>

===Basics of Light ===
[[Image:Snells_law_wavefronts.gif|thumb|150px|]]
*[[Propagation, Reflection and Refraction]]
*[[Dispersion and Scattering of Light]]
*[[Diffraction of Light]]
*[[Electromagnetic Radiation]]
*[[Luminescence Phenomena]]
*[[Color and Chromaticity]]

<br clear='all'>

=== Optical Fibers, Waveguides, and Lasers ===
[[Image:800px-Military_laser_experiment.jpg|thumb|200px|]]

*[[Optical Fibers]]
*[[Total Internal Reflection]]
*[[Planar Dielectric Waveguides]]
*[[Optical Fiber Waveguides]]
*[[Dispersion and Attenuation Phenomena]]
*[[Lasers]]

===Molecular Orbitals===
[[Image:HAtomOrbitals.png|thumb|150px|]]
*[[Atomic Orbitals and Nodes]]
*[[Electronegativity and Bonding Between Atoms]]
*[[Sigma and pi Orbitals|Sigma and Pi Orbitals]]
*[[Polarization and Polarizability]]
*[[Electronic Coupling Between Orbitals]]
*[[Donors and Acceptors]]
<br clear='all'>

===Electronic Band Structure of Organic Materials===
[[Image:Ethylene.JPG|thumb|200px|]]
*[[Introduction to Band Structure]]
*[[Electronic Structure of Hydrogen]]
*[[The Polyene Series]]
*[[Bloch's Theorem]]
*[[Electrical Properties]]
*[[Electronic States vs Molecular Levels]]
<br clear='all'>

===Absorption and Emission of Light===
[[Image:Abs Emis stokes.png|thumb|200px|]]
*[[Introduction to Absorption]]
*[[Changes in Absorption Spectra]]
*[[Jablonksi Diagram]]
*[[Fluorescence Process]]
*[[Transition Dipole Moment]]
*[[Absorption and Emission]]
*[[Photochromism]]
*[[Interchain Interactions]]

<br clear='all'>

===Transport Properties===
[[Image:rubrene.png|thumb|150px|]]
*[[Charge Carrier Mobility]]
*[[Band Regime versus Hopping Regime]]
*[[Electronic Coupling]]
*[[Model Calculations of Electronic Coupling]]
*[[Marcus Theory and Reorganization Energy]]
*[[Electron-Phonon Coupling]]

<br clear='all'>

===Liquid Crystals and Displays===
[[Image:smectic_C.jpg|thumb|200px|]]
*[[Liquid Crystals]]
*[[Double Refraction and Birefringence]]
*[[Director – Degrees of Order in Liquid Crystals]]
*[[Classification and Examples of Liquid Crystals]]
*[[Alignment]]
*[[Freederickz Transition and Dielectric Anisotropy]]
*[[Liquid Crystal Displays]]

<br clear='all'>

===Organic Light Emitting Diodes===
[[Image:PNNL_Light_Lab_041.jpg|thumb|200px|Blue phosphorescent OLED developed by Pacific Northwest National Laboratory.]]
*[[OLED Device Applications]]
*[[Light Emitting Electrochemical Processes]]
*[[The OLED Test Cell]]
*[[What is a Light Emitting Diode?]]
*[[The First OLEDs]]
*[[Organic/Organic Heterojunctions in OLEDs]]
*[[OLED Charge Mobilities]]
*[[Organic Heterojunctions]]
*[[Fluorescent/Phosphorescent Dopants]]
*[[Metal Complex Dopants]]
<br clear='all'>

===Organic Solar Cells===
[[Image:Opvtestcells.png|thumb|200px|OPV Test Cells]]
*[[Organic Solar Cells|OPV Introduction]]
*[[Solar Technologies]]
*[[Major Processes in Organic Solar Cells]]
*[[Organic Heterojunctions in Solar Cells]]
*[[Physics of Solar Cells]]
*[[Energy vs Charge Transfer at Heterojunctions]]
*[[Current OPV Research Directions]]
<br clear='all'>

===Organic Electronics===
*[[Organic Electronics Overview]]
*[[Synthesis of Organic Semiconductors]](In progress)
*[[Organic Field Effect Transistors]]
*Design of n-type Semiconductors for Organic Electronic Applications

==Non linear Optics and Devices==

===Quantum Mechanical and Perturbation Theory of Polarizability===
*[[Quantum-Mechanical Theory of Molecular Polarizabilities]]
*[[Perturbation Theory]]

===Second-order Processes, Materials & Characterization ===
[[Image:MachZehnder.gif|thumb|200px]]
*[[Second-order Processes]]
*[[Structure-Property Relationships]]
*[[Second-order NLO Materials]]
*[[Second-order Material Design]]
*[[Terahertz Radiation]]
*[[Second-order Material Characterization]]

<br clear='all'>

===Third-order Processes, Materials & Characterization ===
[[Image:Tpa_concentrated.png|thumb|100px|]]
*[[Introduction to Third-order Processes and Materials]]
*[[Two Photon Absorption]]
*Advanced Concepts in Third-order Processes
*Characterization of Third-order Materials (Perry)
<br clear='all'>

===Organic Photonics Applications in Information Technology ===
[[Image:Dualmz packaged.png|thumb|200px|]]
*[[Optical Networks]]
*[[Passive Optical Polymers]]
*[[Electro-optic Polymers and Devices]]
*[[Materials Processing and Fabrication]]
<br clear='all'>

===Photonics Integration===
[[Image:Si_waveguide_em.jpg‎|thumb|200px|]]
*[[The Need for Photonic Integration]]
*[[Photonics Integration]]
<br clear='all'>

== Research Equipment, Devices and Techniques ==
<br clear='all'>
[[Image:PES.jpg|thumb|200px|]]
'''Characterization'''
*[[Photoelectron Spectrometer XPS and UPS]]
*[[Conducting Tip Atomic Force Microscopy]]
*[[Organic Photovoltaic Fabrication and Test Apparatus]]
*[[Two-Photon Spectroscopy]]
*[[Hyper Rayleigh Scattering]]
*[[Scanning Electron Microscope]]
*[[External quantum efficiency]]
*[[Teng-Mann Method]]
*[[UV/VIS/NIR spectrometer]]
*[[Attenuated Total Reflectance]]

'''In Development'''
*[[Profilometer]]
*[[Ellipsometer]]
*Fluorometer
*NMR spectrometer

*[[Transmission Electron Microscope]]
*SPM
*Raman microscope
*[[confocal microsope]]

'''Fabrication'''
*[[E-beam Lithography]]
*Reactive ion etcher
*Plasma etcher
*Atomic layer deposition
*[[Spin coater]]
*Sputter coater

==Acronyms and Unit Abbreviations==
*[[Acronyms]]
*[[Variables and Constants]]
*[[Units]]

== General Research Best Practices ==
*[[How to Keep a Lab Notebook]]
*[[How to Give a Research Presentation]]
*[[Writing a Scientific Paper]]
*[[Writing a Successful Proposal]]
*[[Mentoring]]

==[[External Photonics Education Links]]==

==K-12 Outreach Kits==
[[Image:AssembledCell_small.JPG|thumb|200px|]]
*[[K-12 Outreach Introduction]]
*[[Basic Optics - Outreach Kit]]
*[[Photovoltaics- Outreach Kit]]
*[[Lasers and Telecommunication- Outreach Kit]]
*[[Nanocrystalline - Dye Solar Cell Kit]]
<br clear='all'>

==[[Credits and Reviewers]]==

==[[Suggested Wiki Sequence By Audience]]==

== [[Photonics Wiki Showcase]] ==

== [[Concept Map]] ==

Organic Field Effect Transistors

2010-03-17T15:56:55Z

128.95.39.187: /* Organic Field Effect Transistors */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Synthesis of Organic Semiconductors|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Electronics|Return to Organic Electronics Menu]]</td>
<td style="text-align: right; width: 33%">[[Organic Field Effect Transistors|Next Topic]]</td>

</tr>
</table>

===Organic Field Effect Transistors===
[[Image:Field_effect_transistor.png|thumb|300px]]
A field effect transistor (FET) uses an electric field to change the conductivity of an semiconductor material. An organic field effect transistor (OFET) uses an electrically active organic compound as the switching component.

There are three major processes involved with organic field-effect transistors; charge injection, charge transport, and charge collection.

The first one is the injection of charges into the semi-conductor. In the case of light-emitting diode and photovoltaic cell there are only two electrodes. However, in a field-effect transistor, the charge injection is modulated through a third electrode called a gate. Now all is needed are the electrons and the holes. Let’s suppose you inject electrons. Those electrons must migrate and be collected. The first electrode will be referred to as a gate. Next there is a thin insulator called a dielectric. You have two other electrodes referred to as the source and the drain. The organic semi-conductor sits between these. This is one of the configurations possible.

When there is a voltage difference between the source and drain, the amount of charges that will be injected into the semi-conductor will be modulated by the voltage at the gate. The gate will modulate the injection and produce a switching effect. For a given voltage between the source and drain, the voltage of the gate can either be decreased such that there is a small injection or current or it can be increased to have a very large injection of charges into the semi-conductor and a large current. These are the components that make a transistor also called a three terminal device because there are 3 electrodes.

Following injection of charges into the organic semi-conductor, those charges will travel and be collected at the other electrodes.

:<math>I_{DS} = \frac {WC_i} {2L} \mu ( V_{GS} - V_T) ^2\,\!</math>

where
:<math>I_{DS}\,\!</math> is the current between the drain and source

:<math>I_{GS}\,\!</math> is the Voltage between gate and source

:<math>\mu\,\!</math> is the mobility

furthermore
:<math>
\sqrt{\mu} \propto \frac {\sqrt {I_{DS}}}{V_{GS}}\,\!</math>

=== <div id="Flash">OFET Simulation</div> ===

Use this simulation to explore N-type, P-type and ambipolar semiconductor polymers in an organic field effect transistor.

You can control the gate voltage and the voltage across the circuit.

<swf width="600" height="500">http://depts.washington.edu/cmditr/media/ofet.swf</swf>

See Wikipedia on [http://en.wikipedia.org/wiki/Field_effect_transistor field Effect transistor]

Organic Field Effect Transistors

2010-03-17T15:53:29Z

128.95.39.187: /* OFET Simulation */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Synthesis of Organic Semiconductors|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Electronics|Return to Organic Electronics Menu]]</td>
<td style="text-align: right; width: 33%">[[Organic Field Effect Transistors|Next Topic]]</td>

</tr>
</table>

===Organic Field Effect Transistors===
[[Image:Field_effect_transistor.png|thumb|300px]]
A field effect transistor (FET) uses an electric field to change the conductivity of an semiconductor material. An organic field effect transistor (OFET) uses an electrically active organic compound as the switching component.

There are three major processes involved with organic field-effect transistors; charge injection, charge transport, and charge collection.

The first one is the injection of charges into the semi-conductor. In the case of light-emitting diode and photovoltaic cell there are only two electrodes. However, in a field-effect transistor, the charge injection is modulated through a third electrode called a gate. Now all is needed are the electrons and the holes. Let’s suppose you inject electrons. Those electrons must migrate and be collected. The first electrode will be referred to as a gate. Next there is a thin insulator called a dielectric. You have two other electrodes referred to as the source and the drain. The organic semi-conductor sits between these. This is one of the configurations possible.

When there is a voltage difference between the source and drain, the amount of charges that will be injected into the semi-conductor will be modulated by the voltage at the gate. The gate will modulate the injection and produce a switching effect. For a given voltage between the source and drain, the voltage of the gate can either be decreased such that there is a small injection or current or it can be increased to have a very large injection of charges into the semi-conductor and a large current. These are the components that make a transistor also called a three terminal device because there are 3 electrodes.

Following injection of charges into the organic semi-conductor, those charges will travel and be collected at the other electrodes.

:<math>I_{DS} = \frac {WC_i} {2L} \mu ( V_{GS} - V_T) ^2\,\!</math>

where
:<math>I_{DS}\,\!</math> is the current between the drain and source

:<math>I_{GS}\,\!</math> is the Voltage between gate and source

:<math>\mu\,\!</math> is the mobility

furthermore
:<math>
\sqrt{\mu} \propto \frac {\sqrt {I_{DS}}}{V_{GS}}\,\!</math>

<div id="Flash">OFET Simulation</div>

Use this simulation to explore N-type, P-type and ambipolar semiconductor polymers in an organic field effect transistor.

You can control the gate voltage and the voltage across the circuit.

<swf width="600" height="500">http://depts.washington.edu/cmditr/media/ofet.swf</swf>

See Wikipedia on [http://en.wikipedia.org/wiki/Field_effect_transistor field Effect transistor]

Synthesis of Organic Semiconductors

2010-03-17T15:44:06Z

128.95.39.187: /* Fluorinated pentacene */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Organic Electronics Overview|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Electronics|Return to Organic Electronics Menu]]</td>
<td style="text-align: right; width: 33%">[[Organic Field Effect Transistors|Next Topic]]</td>

</tr>
</table>

== Design criteria ==

*HOMO/LUMO levels and bandgap
-Controlled by type of conjugated system, electron donating/electron withdrawing groups

*Solid state packing/self-assembly
-Presence and position of substituents

*Solubility
-Introduction of substituents

*Volatility

*Ease of synthesis

=== HOMO/LUMO level control ===
[[Image:Homocontrol.png|thumb|500px|The conjugation length determines homo lumo levels.]]

*The HOMO increases in energy with increasing conjugation length.
*The LUMO decreases in energy with increasing conjugation length.
*The band gap (Eg) is decreases with increasing conjugation length.
*Polymer is more susceptible to electrophiles because of its higher HOMO. ie. more reactive.

==== Effect of electron donating and electron withdrawing substituents ====

Electron donating groups increase the energy levels.

Electron withdrawing groups decrease the energy levels.

==== Effect of polymer structure ====

Twists in the structure generally decrease the effective conjugation length and therefore increase the bandgap.

=== Substituents ===

Bulky substituents will increase solubility making the material easier to process.

However, in the solid state, bulky substituents will disrupt the packing of molecules/polymers therefore decreasing charge mobility through materials.

The substituent often has to be altered through trial and error to obtain material with the appropriate HOMO/LUMO levels, solubility, and optoelectronic performance.

== P-type small molecule/oligomer synthesis ==

=== Examples of p-type molecules: Pentacene ===
[[Image:Pentacene.png|thumb|400px|]]
Excellent TFT performance
Best TFTs give > 5 cm2/(V s), ION/IOFF = 106

Insoluble: Devices fabricated by vacuum sublimation

Pentacene is oxygen and light-sensitive

<br clear='all'>

=== Efforts to solubilize pentacene: Silyl modified pentacene ===
[[Image:Silyl_pentacene.png|thumb|500px|Silyl modified pentacene]]

[[Image:Silyl_pentacene2.png|thumb|500px|]]
Solution processed TFTs: > 5 cm2/(V s)

see Anthony 2001<ref>J. E. Anthony; J. S. Brooks; D. L. Eaton; S. R. Parkin; J. Am. Chem. Soc. 2001, 123, 9482-9483.</ref>

see Park 2006 <ref>S. J. Park; C. C. Kuo; J. E. Anthony; T. N. Jackson; Tech. Dig. − Int. Electron Devices Meet. 2006, 113.</ref>
<br clear='all'>

=== Soluble precursor approach ===
[[Image:Soluble_precursor.png|thumb|500px|Soluble precursor approach]]
Combines best of both worlds by providing material that is soluble, but has good packing once solubilizing group is removed.

OTFTs

μ = 0.1 cm2 / V⋄s

I<sub>ON</sub> / I<sub>OFF</sub> = 2 x 10<sup>5</sup>

see Weidkamp 2004 <ref>Weidkamp, K. P.; Afzali, A.; Tromp, R. M.; and Hamers, R. J. J. Am. Chem. Soc., 2004, 126, 12740.</ref>
see Afzali 2002 <ref>Afzali, A.; Dimitrakopoulos, C. D.; Breen, T. L. J. Am. Chem. Soc., 2002, 124, 8812.</ref>

=== Examples of p-type molecules: Oligothiophenes ===
[[Image:Oligothiophene_solubility.png|thumb|300px|Introduce substituents to * position to provide solubility
]]
<br clear='all'>
[[Image:Dihexylsexithiophene.jpg|thumb|300px|Dihexylsexithiophene]]

Packing aided by liquid crystalline-like behavior of alkyl chains
Sparingly soluble in hot organic solvents

see Lovinger 1998<ref>A. J. Lovinger; H. E. Katz; A. Dodabalapur Chem. Mater., 1998, 10, 3275.</ref>
<br clear='all'>

=== Soluble precursor route ===
[[Image:Soluble_precursor_oligo.png|thumb|500px|]]
*Precursor is highly soluble in organic solvents
*Heating burns off the solubilizing groups, anneals thiophenes into terraced structures

OTFTs: μ= 0.05 cm2 / V⋄s; I<sub>ON</sub> / I<sub>OFF</sub> = 10<sup>5</sup> after thermal treatment

see Murphy 2004 <ref>A. R. Murphy; J. M. J. Fréchet; P. Chang; J. Lee; V. Subramanian J. Am. Chem. Soc., 2004, 126, 1596.</ref>

== N-type small molecule/oligomer synthesis ==

=== N-type materials ===
Most organic materials are p-type.

Two procedures are generally used to make a material n-type.
<br clear='all'>
-Decrease LUMO level of material by introducing electron withdrawing groups eg. naphthalene derivatives

[[Image:Napthalene_derivatives.png|thumb|300px|naphthalene derivatives]]

-Decrease LUMO level by introducing strain eg. C60 derivatives

[[Image:C60.png|thumb|300px|C60]]
<br clear='all'>

=== Examples of n-type molecules===

==== Aromatic bis-imides ====
[[Image: Aromaticbisamide.png|thumb|200px|]]
One of the early organic n-FET successes.

see Katz 2000 <ref>Katz, H. E.; Lovinger, A. J.; Johnson, J.; Kloc, C.; Slegrist, T.; Li, W.; Lin, Y. Y.; Dodabalapur, A. Nature 2000, 404, 478</ref>
<br clear='all'>
[[Image:Aromaticbisamide2.png|thumb|300px|]]
see Würthner 2004 <ref>F. Würthner; V. Stepanenko; Z. Chen; C. R. Saha-Möller; N. Kocher; D. Stalke J. Org. Chem. 2004, 69, 7933.</ref>

====Fluorinated pentacene ====

[[Image:Fluorinated_pentacene.png|thumb|500px|Fluorinated pentacene synthesis]]

μ = 0.22 cm<sup>2</sup>/Vs and I<sub>on</sub>/I<sub>off</sub> =10<sup>5</sup>

see Sakamoto 2004 <ref>Y. Sakamoto; T. Suzukil; M. Kobayashi; Y. Gao; Y. Fukai; Y. Inoue; F. Sato; S. Tokito J. Am. Chem. Soc., 2004, 126, 8138–8140</ref>.

<br clear='all'>

==== C60 derivatives ====
[[Image:PCBM.png|thumb|300px|PCBM]]
Phenyl C60 Butyric Acid Methyl Ester
(PCBM)
<br clear='all'>
[[Image:ThCMBM.png|thumb|300px|ThCBM]]
Thienyl CBM (ThCBM)

See Lacramioara 2006 <ref>Lacramioara M. Popescu, Patrick van 't Hof, Alexander B. Sieval, Harry T. Jonkman, and Jan C. Hummelen
Appl. Phys. Lett. 89 213507 (2006)
</ref>

=== Single precursor p & n-type material ===
[[Image:Precursor_p&n.png|thumb|300px|]]

N-type OTFT μ = 0.08 cm<sup>2</sup>/Vs and Ion/I<sub>off</sub> =10<sup>6</sup>

P-type OTFT μ = 2 × 10<sup>-4</sup> cm2/Vs and I<sub>on</sub>/I<sub>off</sub> =10<sup>4</sup>

see Yoon 2007 <ref>M.-H. Yoon; S. A. DiBenedetto; M. T. Russell; A. Facchetti; T. J. Marks Chem. Mater., 2007, 19, 4864–4881.</ref>

== Review of polymers ==

=== Step growth vs. Chain growth polymerizations ===
<br clear='all'>
Step growth
[[Image:Stepgrowth.gif|thumb|200px|Step growth ]]
Broad molecular weights

*Molecular weight is heavily dependent on the purity of the monomer
*Leads to batch-to-batch variability
*Optoelectronic properties vary which means fluctuating electronic device performance
<br clear='all'>
Chain growth
[[Image:Chaingrowth.gif|thumb|200px|Chain growth ]]

*One monomer at a time adds to the growing polymer chain.
*Under certain conditions, the polymerization can be controlled to produce specific molecular weights with narrow polydispersities (living polymerization)

=== Molecular weights of polymers ===
[[Image:Polymer_mw.png|thumb|300px|]]

The Number average molecular weight:
:<math>M_n = \frac {\sum_i N_i M_i} {\sum_i N_i}\,\!</math>

The Weight average molecular weight:

:<math>M_w = \frac {\sum_i N_i M_i^2} {\sum_i N_i M_i}\,\!</math>

The Polydispersity Index:

:<math>PDI = \frac {M_w} {M_n}\,\!</math>

<br clear='all'>

=== Small molecule vs. Polymer semiconductors ===

*Small molecules have well-defined molecular weights which lends itself better to provide crystalline packing.

*Polymers generally contain amorphous domains which reduces charge transport.

*Polymers are more amenable to room temperature solution processing. Although both small molecules and polymers can be solubilized, polymers tend to make smoother, more continuous films.

=== Semiconducting polymers ===
Semiconductivity in polymers can be achieved in two ways:
[[Image:Semeconduct_backbone.png|thumb|200px|]]
1) By having pendant small molecule semiconductors attached onto an insulating polymer backbone.
<br clear='all'>
[[Image:Conjugated_polymer.png|thumb|300px|]]
2) By having a conjugated polymer.

*Polymers with pendant groups tend to show poorer charge mobility because it is difficult to organize the polymer such that the pendant groups stack well.

*But, easier to perform a controlled polymer synthesis on polymers with pendant groups using, for example, ATRP, ROMP, and NMRP.
<br clear='all'>

=== Common conjugated polymers ===
[[Image:Conjugated_polymer_common.png|500px|]]
<br clear='all'>

== P-type polymer synthesis ==

=== Polythiophenes ===
[[Image:Polythiophenes_history.png|thumb|center|600px|]]
Historical progression of polythiophenes

For comprehensive review on polythiophenes: <ref>R. D. McCullough, Adv. Mater. 1998, 10, 93</ref>

<br clear='all'>

Initially, conjugated polymers were synthesized by oxidative coupling reactions.
[[Image:Polythiophene_coupling.png|thumb|500px|]]

But oxidative coupling can lead to defects. Eg. instead of the required 2,2 coupling, 2,3 coupling can also take place.
[[Image:Polythiophene_coupling_defect.png|thumb|300px|]]
<br clear='all'>

Dehalogenation routes were also attempted.
[[Image:Polythiophene_dehalogenation.png|thumb|300px|]]
<br clear='all'>

Better than oxidative coupling because 2,3 coupling can be avoided.

However, both routes still suffer when solubilizing groups are added.

Regiorandom polymers end up being synthesized when a regioregular HT-HT polymer is desirable.
[[Image:Regiorandom_polymer.png|thumb|500px|]]
<br clear='all'>
By differentiating the two ends of the substituted thiophene, which can be done cleanly, it is possible to do a cross coupling reaction and thereby synthesize truly regioregular polyalkylthiophenes.

[[Image:Regioregular.png|thumb|500px|]]

[[Image:Regioregular2.png|thumb|400px|]]

see McCullough method: <ref>J. Chem. Soc. Chem. Commun. 1992, 70-72</ref>

see Rieke method: <ref>J. Am. Chem. Soc. 1992, 114, 10087</ref>

=== Improving on regioregular poly(3-hexylthiophene) (P3HT)===
[[Image:P3ht_unit.png|thumb|200px|]]
Poor TFT performance when devices are fabricated in air.
(I<sub>OFF</sub> high due to O<sub>2</sub> doping)

[[Image:P3ht_lamellar.png|thumb|500px|]]

μ = 0.15 cm<sup>2</sup> / V⋅s

I<sub>ON</sub>/I<sub>OFF</sub> = 10<sup>7</sup>

Stable in air for >30d

see Ong 2004 <ref>B. S. Ong; Y. Wu.; P. Liu; S. Gardner, J. Am. Chem. Soc., 2004, 126, 3378.
</ref>
<br clear='all'>

=== Fused ring polythiophenes ===
[[Image:Fusedring.png|thumb|center|500px|]]
see Heeney 2005 <ref>M. Heeney; C. Bailey; K. Genevicius; M. Shkunov; D. Sparrowe; S. Tierney; I. McCulloch J. Am. Chem. Soc., 2005, 127, 1078-1079.</ref>

=== More p-type polymers: Polyphenylenevinylenes (PPV) ===
[[Image:Ppv.png|thumb|500px|]]

Synthesized via soluble precursor route

see Wessling 1985 <ref>Wessling, J. Polym. Sci. Polym. Symp. 1985, 72, 55</ref>

see Wessling 1972 <br clear='all'>Wessling, 1968 (?!), US Patent 3,401,152 and 1972, US Patent 3,706,677

=== Soluble PPV ===

[[Image:Ppv_soluble.png|thumb|500px|a) 3-(bromomethyl)heptane, KOH, C2H5OH, reflux

b) formaldehyde, conc. HCl, dioxane

c) KOC(CH3)3, THF]]

a) 3-(bromomethyl)heptane, KOH, C2H5OH, reflux

b) formaldehyde, conc. HCl, dioxane

c) KOC(CH3)3, THF

See Wudl 1991 <ref>Wudl et al. ACS Symp. Ser, 1991, 455; US Patent 1990, 5,189,136</ref>
<br clear='all'>
=== More p-type polymers: Polyfluorenes ===
[[Image:Polyfluorene.jpg|thumb|300px|]]
Polyfluorene: Originally synthesized in 1989
see Fukuda 1989 <ref>Fukuda et al. Jpn. J. Appl. Phys. 28, L1433, 1989</ref>

[[Image:Polyfluorene_all.jpg|thumb|500px|]]

see <ref>Adv. Funct. Mater. 15, 981, 2005</ref>
<br clear='all'>

=== Polyfluorenes: obtained blue polymer for LEDs ===
[[Image:Polyfluorene_synth.jpg|thumb|500px|]]
Originally, the emission at approx. 550 nm was thought to be a results of aggregation.

Bulky substituents were added to polyfluorene to reduce green emission and create “blue” polymer.

[[Image:Polyfluorene_spec.jpg|thumb|400px|]]

see JACS <ref>J. Am. Chem. Soc., 123, 6965, 2001</ref>

[[Image:Polyfluorene_synth2.jpg|thumb|400px|]]

see List and Scherf <ref>List and Scherf et al. Adv. Mater. 14, 374, 2002</ref>

[[Image:Polyfluorene_synth3.jpg|thumb|400px|]]
But it was realized that the red-shifted emission was due to keto defects within the polymer.

[[Image:Polyfluorene_synth4.jpg|thumb|400px|]]

Polymer design was altered so that there would be a silicon bridge rather than a carbon bridge to prevent keto defects from forming.

[[Image:Polyfluorene_spec2.jpg|thumb|300px|]]
see Chan and Holmes <ref>Chan and Holmes et al. J. Am. Chem. Soc. 127, 7662, 2005.</ref>
<br clear='all'>

== N-type polymer synthesis ==

=== N-type polymers ===
This is rare but growing area of research.
[[Image:N-type.png|thumb|500px|Highly ordered Lamellar packing]]

μ = 0.10−0.16 cm<sup>2</sup>/(V s), Ion/I<sub>off</sub> = 10<sup>7</sup>
Devices stable in air for >5 months

[[Image:Ladder.png|thumb|500px|]]

see Usta 2008<ref>H. Usta; A. Facchetti; T. J. MarksJ. Am. Chem. Soc., 2008, 130, 8580.</ref>

see Babel and Jenekhe 2003 <ref>A. Babel and S. A. Jenekhe J. Am. Chem. Soc., 2003, 125, 13656.</ref>
<br clear='all'>
=== Napthalene based polymers ===

[[Image:Napthalene_polymer_synth.png|thumb|500px|μ = 0.01 cm<sup>2</sup>/VS]]

see JACS <ref>JACS, 2009, 8-9.</ref>
<br clear='all'>

=== Ambipolar polymers ===

[[Image:Ambipolar.png|thumb|500px|]]

μh = 10-3 cm2/(V s)
μe = 10-2 cm2/(V s)

see Kim and Jenekhe 2009 <ref>F. S. Kim and S. A. Jenekhe et al. Adv. Mater., Vol. 21, P. 1-5, 2009</ref>
<br clear='all'>

== Controlled polymer synthesis ==

=== Metal catalyzed cross-coupling polymerizations ===
[[Image:Crosscoupling.png|thumb|400px|]]
The majority of conjugated polymers are synthesized via metal catalyzed cross-coupling reactions eg. Ni mediated reactions is shown.

=== P3HT synthesis ===
[[Image:P3ht_synth.png|thumb|500px|P3HT synthesis]]
P3HT synthesis was originally thought to occur via a step-growth polymerization.

When Ni(0) reductively eliminates, it can in theory reinsert into any Ar-Br bond. If this were to occur, this would be a step-growth polymerization

But McCullough and Yokozawa found that the resulting polymer had a narrow PDI and controlled molecular weight, which means that it is likely to be a chain-growth polymerization.
[[Image:P3ht_synth2.png|thumb|500px|P3HT synthesis]]

dppp>dppe>dppf>PPh3

Polymerization is heavily ligand dependent and works best if dppp is used as the ligand.
*Narrow PDI
*MW proportional to Ni loading

Associated pair

Key step: Ni(0) only adds into the same growing polymer chain resulting in chain-growth polymerization

see McCullough <ref>McCullough, Macromolecules 2004, 37, 3526</ref>

see Miyakoshi <ref>Miyakoshi and Yokozawa et al., J. Am. Chem. Soc. 2005, 127, 17542</ref>
<br clear='all'>

=== Externally initiated P3HT synthesis ===
[[Image:P3ht_synth_ext.png|thumb|500px|]]

[[Image:P3ht_synth_ext2.png|thumb|500px|]]
<br clear='all'>
TM = transmetallation
RE = reductive elimination
OA = oxidative addition

Restricted to only being able to use PPh3 as a ligand. dppp gives H/Br polymer.

see Doubina and Luscombe 2009 <ref>Doubina and Luscombe, Macromolecules, 2009, 42, 7670</ref>

<br clear='all'>
[[Image:P3ht_synth_ext_ligand.png|thumb|300px|]]

see van Leeuwen 2000 <ref>van Leeuwen et al. Chem. Rev. 2000, 100, 2741</ref>
<br clear='all'>

=== Adapting to ligands other than PPh3 ===
[[Image:P3ht_synth_regioregular.png|thumb|500px|]]

A novel method for the external initiated polymerizations of P3HT has developed by CMDITR researchers. The method produces a polymer with a well-defined molecular weight, narrow polydispersity index (PDI), 100% initiation efficiency, 100% regioregularity. This work represents the most control achieved for the synthesis of P3HT.

see Bronstein and Luscombe 2009 <ref>H. Bronstein, C. K. Luscombe, J. Am. Chem. Soc., 2009, 131, 12894</ref>

== References ==
<references/>

Photonics Wiki Showcase

2010-03-16T23:56:47Z

128.95.39.187: /* Flash Simulations */

Here are some examples from the Photonics Wiki that are useful for a quick tour.

=== Basic Features ===

*[[Main Page | Table of contents show structure of information on the page.]]

*[[Acronyms and Unit Abbreviations]]

*[[Organic Heterojunctions in Solar Cells | Adobe Acrobat for slide sequences]]

*[[Electromagnetic_Radiation | Latex for Math Formulas - (go to page and edit to see the source)]]

*[[Solar_Technologies#External_Links | External Links and References]]

*[[Organic Photovoltaic Fabrication and Test Apparatus | Flash Video for Lab Training]]

*[[How to Give a Research Presentation]]

*[[Electromagnetic_Spectrum#Knowledge_Check | Knowledge Check - Wiki Quiz]]

=== Flash Simulations ===

*[[Color and Chromaticity#Flash | RGB Color Mixing Simulation]]

*[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]

*[[Second-order_NLO_Materials#Flash | Poling Simulation]]

*[[Second-order_NLO_Materials#Flash2 | Interactions]]

*[[Second-order_Processes#Flash | Electro-optical effect animation]]

*[[Introduction_to_Third-order_Processes_and_Materials#Flash |Phase Conjugate Mirror]]

*[[Attenuated Total Reflectance#Flash |Attenuated Total Reflectance]]

*[[Polarization_and_Polarizability#Flash | Four types of polarization animation]]

*[[Organic Field Effect Transistors#Flash | Organic Field Effect Transistor Simulation]]

Color and Chromaticity

2010-03-16T23:55:31Z

128.95.39.187: /* RGB Color Mixing Schema */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Luminescence Phenomena|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Basics of Light|Return to Basics of Light Menu]]</td>

</tr>
</table>

There are many terms that describe color. In addition to descriptive terms there are corresponding quantitative terms.

== Light absorption ==
[[Image:Excitation.jpg|thumb|300px|Electron configuration after absorption]]
When a molecule interacts with light and energy is absorbed, the molecule is said be excited and a transition occurs which can take the molecule from an initial state to a higher energy state

Within the one-electron approximation, this is described by the promotion of an electron from a filled orbital to an unfilled orbital (in the case of diamagnetic materials).
The difference in energy between those levels, (the excited state and the ground state), gives the energy of the photons that can be absorbed.

Several parameters can be used to characterize this transition, including the energy of the incident radiation required for the efficient absorption of the light and the inherent ability of the molecules to absorb radiation of the appropriate energy
by the Planck relation:

:<math>\Delta E_{ge} = E_{excited state}-E_{ground state} = h\nu\,\!</math>

where hv is the energy of the photon corresponding to the energy gap between the states.
The energy is reported in several units; the following is helpful for translating between some common units one comes across in the literature:

'''1 eV = 23.06 kcal/mol = 8065 cm<sup>-1</sup> = 1240 nm'''

== Common Color Description==

Our perception of color is determined by what wavelengths of radiation reach our eye and the sensitivity of the receptors in our eye to various colors
The eye has rods and cones containing chromophores which convert light into electrical impulse that the brain uses to perceive images. This the opposite of what you see in light emitting diodes in which electricity causes emission of light.

The rods function under low intensity conditions and provide images in shades of black, grey, and white
This is referred to as scotopic vision

The cones process images of high intensity in color which is referred to as photopic vision.
Cones come in three varieties which correspond roughly to blue, green, and red sensitivities; if all three cones are simultaneously excited, then the image will appear white.

See also Wikipedia [http://en.wikipedia.org/wiki/Color Color]

See also [http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/lighttoc.html Physics Classroom tutorial]
<br clear='all'>

=== Complementary Colors ===

[[Image:Complementarycolors.png|thumb|400px|This graphic shows what color will be perceived when a material absorbs in certain regions of the visible spectrum.]]
If wavelengths of light from a certain region of the spectrum are absorbed by a material, then the material will appear to be the complementary color. Thus, for instance, if violet light with wavelength of 400nm is absorbed, the material will look yellow. If the material absorbs blue you will see the color orange.
{| class="wikitable"
|-
! Color absorbed
! Color seen

|-
| Violet
| Yellow

|-
| Blue
| Orange
|-
| Green
| Red
|-
| Yellow
| Violet
|-
| Orange
| Blue
|}

Note that green is not indicated in the figure; this is because materials that appear green actually absorb in the red and the blue (i.e., about 650 nm and 425 nm)
band shape and color

Our ability to perceive very small differences in color is rather extraordinary; for instance, two solutions which appear to have virtually identical absorption spectra, with minute differences in their tails, can be recognized as clearly different hues. Very small changes in the shape of an absorption band (not only the position) will cause materials to appear different shades

=== Bright and Dull ===

[[Image:Brightanddull.jpg|thumb|300px|A sharp absorption peak results in the perception of a saturated color.]]
In general, colors that we perceive as brilliant and bright have strong narrow absorption bands whereas dull colors tend to have weaker and broader absorption bands.

<br clear='all'>

=== Hue and Saturation ===

The '''hue''' is that aspect of color usually associated with terms such as red, orange, yellow, and so forth.Hue distinguishes the color purity of the dominant color (i.e. red from yellow). The position of absorption maxima largely determines this property.

'''saturation''' (also known as chroma, or tone) refers to relative purity; when a pure, vivid, strong shade of red is mixed with a variable amount of white, weaker or paler reds are produced, each having the same hue but a different saturation; such paler colors are called unsaturated colors. You can define the amount of saturation of a given using a chromaticity diagram. For example, suppose you had a red color and you slowly increased the amount of blue and green light reaching the eye, then the mixture of the red, blue and green would contribute to the perception of white. White plus red would give pink. The hue would not have been altered, but the saturation would be lower

Light of any given combination of hue and saturation can have a variable '''brightness''' (also called intensity, lightness, or value), which depends on the total amount of light energy present. Lightness of a color is changed by varying the intensity of all three primary colors by the same amount. For example, if the intensity of a red were increased it would appear brown.

=== RGB Color Mixing Schema===
All colors can be create by the addition of the primary colors. Use this Flash application to explore color mixing.

<div id="Flash">RBB Color Mixing Simulation</div>
  <swf width="400" height="300">http://depts.washington.edu/cmditr/media/colorbox.swf</swf>

Engineers and designers have very specific requirements for light emitting and light absorbing materials. They frequently use a color measurement system called tristimulus to precisely specify any possible color, even those that can not be described with a simple wavelength.

== Tristimulus measurement and chromaticity diagrams ==

The tristimulus color measurement system is based on visually matching a color under standardized conditions against the three primary colors, red, green, and blue; the three results are expressed as X, Y, and Z, respectively, and are called '''tristimulus''' values

These values specify not only color but also visually perceived reflectance, since they are calculated in such a way that the Y value equals a sample's reflectivity (39.1 percent in this example) when visually compared to a standard white surface by a standard (average) viewer under average daylight.

The tristimulus values of the emerald-green pigment of Figure 6 are X = 22.7, Y = 39.1, and Z = 31.0[[Image:Emeraldabsorb.jpg|thumb|200px|Reflectance of emerald green color]]

The tristimulus values can also be used to determine the visually perceived dominant spectral wavelength (which is related to the hue) of a given sample; the dominant wavelength of the emerald-green pigment is 511.9 nm:

it is based on the values x, y, and z,

Where

'''x = X/(X + Y + Z)'''

'''y = Y/(X + Y + Z)'''

'''z = Z/(X + Y + Z)'''

<br clear='all'>
[[Image:Cie_chromaticity_diagram_wavelength.png|thumb|300px|]]
Note that x + y + z = 1; thus if two values are known, the third can always be calculated and the z value is usually omitted thus, the x and y values together constitute the chromaticity of a sample light and dark colors that have the same chromaticity (and are therefore plotted at the same point on the two-dimensional chromaticity diagram) can be distinguished in a third dimension (by their luminance or visually perceived brightness).

White light is x= 1/3, y = 1/3 and z= 1/3. This is achromatic point. Pure grays and black are the same hue as white light but vary only in the magnitude of their luminance. Occasionally colors will be also be described using luminance as well.

So for the goal of LED makers is to make a white light with x and y values close to 1/3.

Around the horseshoe shaped periphery are the pure saturated colors , beginning with 400nm (violet) and going around to 700 nm (red). Those are the colors of the visible spectrum. The straight line across the bottom are colors that come from the non-spectral mixing of violet and red, they do not correspond to a single wavelength.
<br clear='all'>
[[Image:300px-CIExy1931_twocolors.png|thumb|300px|]]

=== Plotting CIE values ===

By plotting the calculated x = 0.245 and y = 0.421 of the emerald-green pigment at point E on the chromaticity diagram and extending a line through it from the achromatic point W to the saturated spectral boundary, it is possible to determine the dominant wavelength of the pigment color, 511.9 nm. Emerald green is not a pure color. But it can be made by mixing the pure color with wavelength 511.9nm with white light.

The color of the pigment is the visual equivalent of adding white light and light of 511.9 nm in amounts proportional to the lengths '''n''' (the distance between points '''E''' and '''W''') and '''m''' (the distance between '''E''' and the point of the dominant wavelength) in the figure. The saturation or purity equals 100n/(m + n) percent - in this case, 22.8 percent. A purity of 100 percent corresponds to a pure saturated spectral color and 0 percent to the achromatic colors (white, gray, and black)

Another example, a red apple marked '''R''' on the diagram. If you connect the line through '''w''' and '''R''' it intersects the bottom line which are not pure spectral colors. In this case this shade of red must be defined in terms of the complementary color on the opposite side of the achromatic point.

The dominant color designation is then obtained by extrapolating the line in the opposite direction to a saturated spectral color it is given as "complementary dominant wavelength 495 nm" or 495c. The color of this apple is therefore the visual equivalent of a mixture of white light and the 495c saturated purple-red in the intensity ratio of the distances p to q shown in the figure with a purity of 100p/(p + q) percent.

<br clear='all'>
=== Incandescent light sources ===

[[Image:533px-PlanckianLocus.png|thumb|300px|]]
Light from incandescent sources falls on the solid curve marked with temperatures in this figure, following the sequence saturated red to saturated orange to unsaturated yellow to white to unsaturated bluish white for an infinite temperature.

The points A, B, and C on the curve are CIE standard illuminants that approximate, respectively, a 100-watt incandescent filament lamp at a color temperature of about 2,850 K, noon sunlight (about 4,800 K), and average daylight (about 6,500 K)

The color of daylight changes over the course of a day. LED designers could make the color of their devices change during the day to better match the daylight experience. Some white lights feel “warmer “ or “colder “depending on the color balance. LEDs will have the same descriptives.

== External Links ==

[http://hyperphysics.phy-astr.gsu.edu/hbase/vision/colper.html#c2 Hyperphysics materials about chromaticity]
[[category:Light]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Luminescence Phenomena|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Basics of Light|Return to Basics of Light Menu]]</td>

</tr>
</table>

Photonics Wiki Showcase

2010-03-16T20:15:38Z

128.95.39.187: /* Flash Simulations */

Here are some examples from the Photonics Wiki that are useful for a quick tour.

=== Basic Features ===

*[[Main Page | Table of contents show structure of information on the page.]]

*[[Acronyms and Unit Abbreviations]]

*[[Organic Heterojunctions in Solar Cells | Adobe Acrobat for slide sequences]]

*[[Electromagnetic_Radiation | Latex for Math Formulas - (go to page and edit to see the source)]]

*[[Solar_Technologies#External_Links | External Links and References]]

*[[Organic Photovoltaic Fabrication and Test Apparatus | Flash Video for Lab Training]]

*[[How to Give a Research Presentation]]

*[[Electromagnetic_Spectrum#Knowledge_Check | Knowledge Check - Wiki Quiz]]

=== Flash Simulations ===

*[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]

*[[Second-order_NLO_Materials#Flash | Poling Simulation]]

*[[Second-order_NLO_Materials#Flash2 | Interactions]]

*[[Second-order_Processes#Flash | Electro-optical effect animation]]

*[[Introduction_to_Third-order_Processes_and_Materials#Flash |Phase Conjugate Mirror]]

*[[Attenuated Total Reflectance#Flash |Attenuated Total Reflectance]]

*[[Polarization_and_Polarizability#Flash | Four types of polarization animation]]

*[[Organic Field Effect Transistors#Flash | Organic Field Effect Transistor Simulation]]

Photonics Wiki Showcase

2010-03-16T20:14:47Z

128.95.39.187: /* Flash Simulations */

Here are some examples from the Photonics Wiki that are useful for a quick tour.

=== Basic Features ===

*[[Main Page | Table of contents show structure of information on the page.]]

*[[Acronyms and Unit Abbreviations]]

*[[Organic Heterojunctions in Solar Cells | Adobe Acrobat for slide sequences]]

*[[Electromagnetic_Radiation | Latex for Math Formulas - (go to page and edit to see the source)]]

*[[Solar_Technologies#External_Links | External Links and References]]

*[[Organic Photovoltaic Fabrication and Test Apparatus | Flash Video for Lab Training]]

*[[How to Give a Research Presentation]]

*[[Electromagnetic_Spectrum#Knowledge_Check | Knowledge Check - Wiki Quiz]]

=== Flash Simulations ===

*[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]

*[[Second-order_NLO_Materials#Flash | Poling Simulation]]

*[[Second-order_NLO_Materials#Flash2 | Interactions]]

*[[Second-order_Processes#Flash | Electro-optical effect animation]]

*[[Introduction_to_Third-order_Processes_and_Materials#Flash |Phase Conjugate Mirror]]

*[[Attenuated Total Reflectance#Flash |Attenuated Total Reflectance]]

*[[Polarization_and_Polarizability#Flash | Four types of polarization animation]]

*[[Organic Field Effect Transistor#Flash | Organic Field Effect Transistor Simulation]]

Organic Field Effect Transistors

2010-03-16T20:13:23Z

128.95.39.187: /* OFET SimulationSimulation */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Synthesis of Organic Semiconductors|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Electronics|Return to Organic Electronics Menu]]</td>
<td style="text-align: right; width: 33%">[[Organic Field Effect Transistors|Next Topic]]</td>

</tr>
</table>

===Organic Field Effect Transistors===
[[Image:Field_effect_transistor.png|thumb|300px]]
A field effect transistor (FET) uses an electric field to change the conductivity of an semiconductor material. An organic field effect transistor (OFET) uses an electrically active organic compound as the switching component.

There are three major processes involved with organic field-effect transistors; charge injection, charge transport, and charge collection.

The first one is the injection of charges into the semi-conductor. In the case of light-emitting diode and photovoltaic cell there are only two electrodes. However, in a field-effect transistor, the charge injection is modulated through a third electrode called a gate. Now all is needed are the electrons and the holes. Let’s suppose you inject electrons. Those electrons must migrate and be collected. The first electrode will be referred to as a gate. Next there is a thin insulator called a dielectric. You have two other electrodes referred to as the source and the drain. The organic semi-conductor sits between these. This is one of the configurations possible.

When there is a voltage difference between the source and drain, the amount of charges that will be injected into the semi-conductor will be modulated by the voltage at the gate. The gate will modulate the injection and produce a switching effect. For a given voltage between the source and drain, the voltage of the gate can either be decreased such that there is a small injection or current or it can be increased to have a very large injection of charges into the semi-conductor and a large current. These are the components that make a transistor also called a three terminal device because there are 3 electrodes.

Following injection of charges into the organic semi-conductor, those charges will travel and be collected at the other electrodes.

:<math>I_{DS} = \frac {WC_i} {2L} \mu ( V_{GS} - V_T) ^2\,\!</math>

where
:<math>I_{DS}\,\!</math> is the current between the drain and source

:<math>I_{GS}\,\!</math> is the Voltage between gate and source

:<math>\mu\,\!</math> is the mobility

furthermore
:<math>
\sqrt{\mu} \propto \frac {\sqrt {I_{DS}}}{V_{GS}}\,\!</math>

=== <div id="Flash">OFET Simulation</div> ===
Use this simulation to explore N-type, P-type and ambipolar semiconductor polymers in an organic field effect transistor.

You can control the gate voltage and the voltage across the circuit.

<swf width="600" height="500">http://depts.washington.edu/cmditr/media/ofet.swf</swf>

See Wikipedia on [http://en.wikipedia.org/wiki/Field_effect_transistor field Effect transistor]

Organic Field Effect Transistors

2010-03-16T20:13:11Z

128.95.39.187: /* Simulation */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Synthesis of Organic Semiconductors|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Electronics|Return to Organic Electronics Menu]]</td>
<td style="text-align: right; width: 33%">[[Organic Field Effect Transistors|Next Topic]]</td>

</tr>
</table>

===Organic Field Effect Transistors===
[[Image:Field_effect_transistor.png|thumb|300px]]
A field effect transistor (FET) uses an electric field to change the conductivity of an semiconductor material. An organic field effect transistor (OFET) uses an electrically active organic compound as the switching component.

There are three major processes involved with organic field-effect transistors; charge injection, charge transport, and charge collection.

The first one is the injection of charges into the semi-conductor. In the case of light-emitting diode and photovoltaic cell there are only two electrodes. However, in a field-effect transistor, the charge injection is modulated through a third electrode called a gate. Now all is needed are the electrons and the holes. Let’s suppose you inject electrons. Those electrons must migrate and be collected. The first electrode will be referred to as a gate. Next there is a thin insulator called a dielectric. You have two other electrodes referred to as the source and the drain. The organic semi-conductor sits between these. This is one of the configurations possible.

When there is a voltage difference between the source and drain, the amount of charges that will be injected into the semi-conductor will be modulated by the voltage at the gate. The gate will modulate the injection and produce a switching effect. For a given voltage between the source and drain, the voltage of the gate can either be decreased such that there is a small injection or current or it can be increased to have a very large injection of charges into the semi-conductor and a large current. These are the components that make a transistor also called a three terminal device because there are 3 electrodes.

Following injection of charges into the organic semi-conductor, those charges will travel and be collected at the other electrodes.

:<math>I_{DS} = \frac {WC_i} {2L} \mu ( V_{GS} - V_T) ^2\,\!</math>

where
:<math>I_{DS}\,\!</math> is the current between the drain and source

:<math>I_{GS}\,\!</math> is the Voltage between gate and source

:<math>\mu\,\!</math> is the mobility

furthermore
:<math>
\sqrt{\mu} \propto \frac {\sqrt {I_{DS}}}{V_{GS}}\,\!</math>

=== <div id="Flash">OFET Simulation</div>Simulation ===
Use this simulation to explore N-type, P-type and ambipolar semiconductor polymers in an organic field effect transistor.

You can control the gate voltage and the voltage across the circuit.

<swf width="600" height="500">http://depts.washington.edu/cmditr/media/ofet.swf</swf>

See Wikipedia on [http://en.wikipedia.org/wiki/Field_effect_transistor field Effect transistor]

Organic Field Effect Transistors

2010-03-16T20:12:54Z

128.95.39.187: /* Simulation */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Synthesis of Organic Semiconductors|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Organic Electronics|Return to Organic Electronics Menu]]</td>
<td style="text-align: right; width: 33%">[[Organic Field Effect Transistors|Next Topic]]</td>

</tr>
</table>

===Organic Field Effect Transistors===
[[Image:Field_effect_transistor.png|thumb|300px]]
A field effect transistor (FET) uses an electric field to change the conductivity of an semiconductor material. An organic field effect transistor (OFET) uses an electrically active organic compound as the switching component.

There are three major processes involved with organic field-effect transistors; charge injection, charge transport, and charge collection.

The first one is the injection of charges into the semi-conductor. In the case of light-emitting diode and photovoltaic cell there are only two electrodes. However, in a field-effect transistor, the charge injection is modulated through a third electrode called a gate. Now all is needed are the electrons and the holes. Let’s suppose you inject electrons. Those electrons must migrate and be collected. The first electrode will be referred to as a gate. Next there is a thin insulator called a dielectric. You have two other electrodes referred to as the source and the drain. The organic semi-conductor sits between these. This is one of the configurations possible.

When there is a voltage difference between the source and drain, the amount of charges that will be injected into the semi-conductor will be modulated by the voltage at the gate. The gate will modulate the injection and produce a switching effect. For a given voltage between the source and drain, the voltage of the gate can either be decreased such that there is a small injection or current or it can be increased to have a very large injection of charges into the semi-conductor and a large current. These are the components that make a transistor also called a three terminal device because there are 3 electrodes.

Following injection of charges into the organic semi-conductor, those charges will travel and be collected at the other electrodes.

:<math>I_{DS} = \frac {WC_i} {2L} \mu ( V_{GS} - V_T) ^2\,\!</math>

where
:<math>I_{DS}\,\!</math> is the current between the drain and source

:<math>I_{GS}\,\!</math> is the Voltage between gate and source

:<math>\mu\,\!</math> is the mobility

furthermore
:<math>
\sqrt{\mu} \propto \frac {\sqrt {I_{DS}}}{V_{GS}}\,\!</math>

=== Simulation ===
Use this simulation to explore N-type, P-type and ambipolar semiconductor polymers in an organic field effect transistor.

You can control the gate voltage and the voltage across the circuit.
<div id="Flash">OFET Simulation</div>

<swf width="600" height="500">http://depts.washington.edu/cmditr/media/ofet.swf</swf>

See Wikipedia on [http://en.wikipedia.org/wiki/Field_effect_transistor field Effect transistor]

Help:Contents

2010-03-16T20:12:05Z

128.95.39.187:

== Photonics Wiki Important Links ==

[http://en.wikipedia.org/wiki/How_to_edit Main Wikipedia How to Edit page]

[[Photonics Wiki Stylesheet]]

[[Photonics Wiki Showcase]]

[[Photonics Digital Library]]

[[User_talk:Smhunter | Note to Suzy for graphics suggestions]]

[[User_talk:Cmditradmin | Note to Shaun for editorial or flash suggestions]]

== Wiki Formatting Quick Guide ==

=== To enforce a break so picture stays with a text block ===

<nowiki><br clear="all">
</nowiki>

=== To embed an acrobat pdf file for slide series ===

<nowiki><embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/OLED2_ecl_redoxpairs.pdf</embed_document>
</nowiki>

=== Wiki Table ===

<nowiki>{| class="wikitable"
|-
! header 1
! header 2
! header 3
|-
| row 1, cell 1
| row 1, cell 2
| row 1, cell 3
|-
| row 2, cell 1
| row 2, cell 2
| row 2, cell 3
|}</nowiki>

=== To make a heading that automatically gets assembled as table of contents when there are more than 3 such headings. ===

<nowiki>

===Heading===
</nowiki>

=== Page Bookmarks and Links ===

To put in an anchor so you can point to place ("Flash" in sample below) in a pages

<nowiki><div id="Flash">Text that is displayed </div></nowiki>

And use this construction to link to this bookmark, using the page and the # to denote the id.

<nowiki>[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]</nowiki>

=== TO have a gallery of images with individual captions ===
<gallery widths=300px heights=200px perrow=3>
Image:Oled1_3_eclredox.png‎|First the loss of an electron by this conjugated aromatic system to form a cation radical species.
Image:Oled1_4_eclredox.png‎‎|Comment for second image
</gallery>

<nowiki><gallery widths=300px heights=200px perrow=3>
Image:Oled1_3_eclredox.png‎|First the loss of an electron by this conjugated aromatic system to form a cation radical species.
Image:Oled1_4_eclredox.png‎‎|Comment for sec
</gallery></nowiki>

=== Embed Latex formula and force png rendering ===

<nowiki>:<math>\eta _\mathrm{ext} = \eta_\mathrm{ph} \eta_\mathrm{int} = \eta_\mathrm{ph} \gamma \phi \eta_\mathrm{ext}\,\!</math></nowiki>

:<math>\eta _\mathrm{ext} = \eta_\mathrm{ph} \eta_\mathrm{int} = \eta_\mathrm{ph} \gamma \phi \eta_\mathrm{ext}\,\!</math>

[http://www.sitmo.com/latex/ Online Latex formula editor]

=== To put mid size picture in the scene with caption ===

<nowiki>[[Image:OLED5-organic_heterojunction.jpg |thumb||400px | Organic Heterojunction]]
</nowiki>

=== Category ===
This creates a category so that articles can belong to more than one classification

<nowiki>[[category:organic solar cell]]</nowiki>

=== Embed Flash in page ===

<nowiki>
<div id="Flash">Four kinds of polarization animation</div>

<swf width="500" height="400">http://depts.washington.edu/cmditr/media/opvanim.swf</swf>
</nowiki>

The div id makes it possible to point to the flash at a particular place on page in another link.

=== References ===
see this <ref>put your citation in text and it copies it below.</ref>

<nowiki>
== References ==

<references/></nowiki>
<references/>

=== Knowledge Check ===
Try your hand at these problems about basic paratmeters of light.
<quiz display=simple>
{Which part of the electromagnetic spectrum has the most energy?
|type="()"}
- Violet light.
|| Feedback for correct answer.
+ X-rays.
|| Feedback for distractor.
- Infrared.
|| Feedback for distractor.
- Radiowaves.
|| Radiowaves have very long wavelengths .

</quiz>
[[main_alt]]

=== Latex for formulas ===

[ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf Latex math guide]

[http://authors.ck12.org/wiki/index.php/Math_Symbols Latex lookup]

=== Embed Youtube video ===

<nowiki>{{#ev:youtube|M3no-TFORpQ}}</nowiki>

Help:Contents

2010-03-16T20:09:20Z

128.95.39.187: /* Embed Flash in page */

== Photonics Wiki Important Links ==

[http://en.wikipedia.org/wiki/How_to_edit Main Wikipedia How to Edit page]

[[Photonics Wiki Stylesheet]]

[[Photonics Wiki Showcase]]

[[Photonics Digital Library]]

[[User_talk:Smhunter | Note to Suzy for graphics suggestions]]

[[User_talk:Cmditradmin | Note to Shaun for editorial or flash suggestions]]

== Wiki Formatting Quick Guide ==

=== To enforce a break so picture stays with a text block ===

<nowiki><br clear="all">
</nowiki>

=== To embed an acrobat pdf file for slide series ===

<nowiki><embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/OLED2_ecl_redoxpairs.pdf</embed_document>
</nowiki>

=== Wiki Table ===

<nowiki>{| class="wikitable"
|-
! header 1
! header 2
! header 3
|-
| row 1, cell 1
| row 1, cell 2
| row 1, cell 3
|-
| row 2, cell 1
| row 2, cell 2
| row 2, cell 3
|}</nowiki>

=== To make a heading that automatically gets assembled as table of contents when there are more than 3 such headings. ===

<nowiki>

===Heading===
</nowiki>

=== Page Bookmarks and Links ===

To put in an anchor so you can point to place ("Flash" in sample below) in a pages

<nowiki><div id="Flash">Text that is displayed </div></nowiki>

And use this construction to link to this bookmark, using the page and the # to denote the id.

<nowiki>[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]</nowiki>

=== TO have a gallery of images with individual captions ===
<gallery widths=300px heights=200px perrow=3>
Image:Oled1_3_eclredox.png‎|First the loss of an electron by this conjugated aromatic system to form a cation radical species.
Image:Oled1_4_eclredox.png‎‎|Comment for second image
</gallery>

<nowiki><gallery widths=300px heights=200px perrow=3>
Image:Oled1_3_eclredox.png‎|First the loss of an electron by this conjugated aromatic system to form a cation radical species.
Image:Oled1_4_eclredox.png‎‎|Comment for sec
</gallery></nowiki>

=== Embed Latex formula and force png rendering ===

<nowiki>:<math>\eta _\mathrm{ext} = \eta_\mathrm{ph} \eta_\mathrm{int} = \eta_\mathrm{ph} \gamma \phi \eta_\mathrm{ext}\,\!</math></nowiki>

:<math>\eta _\mathrm{ext} = \eta_\mathrm{ph} \eta_\mathrm{int} = \eta_\mathrm{ph} \gamma \phi \eta_\mathrm{ext}\,\!</math>

[http://www.sitmo.com/latex/ Online Latex formula editor]

=== To put mid size picture in the scene with caption ===

<nowiki>[[Image:OLED5-organic_heterojunction.jpg |thumb||400px | Organic Heterojunction]]
</nowiki>

=== Category ===
This creates a category so that articles can belong to more than one classification

<nowiki>[[category:organic solar cell]]</nowiki>

=== Embed Flash in page ===

<nowiki>
<div id="Flash">Four kinds of polarization animation</div>

<swf width="500" height="400">http://depts.washington.edu/cmditr/media/opvanim.swf</swf>
</nowiki>

see this <ref>put your citation in text and it copies it below.</ref>

=== References ===
<nowiki>
== References ==

<references/></nowiki>
<references/>

=== Knowledge Check ===
Try your hand at these problems about basic paratmeters of light.
<quiz display=simple>
{Which part of the electromagnetic spectrum has the most energy?
|type="()"}
- Violet light.
|| Feedback for correct answer.
+ X-rays.
|| Feedback for distractor.
- Infrared.
|| Feedback for distractor.
- Radiowaves.
|| Radiowaves have very long wavelengths .

</quiz>
[[main_alt]]

=== Latex for formulas ===

[ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf Latex math guide]

[http://authors.ck12.org/wiki/index.php/Math_Symbols Latex lookup]

=== Embed Youtube video ===

<nowiki>{{#ev:youtube|M3no-TFORpQ}}</nowiki>

Photonics Wiki Showcase

2010-03-16T20:08:21Z

128.95.39.187: /* Flash Simulations */

Here are some examples from the Photonics Wiki that are useful for a quick tour.

=== Basic Features ===

*[[Main Page | Table of contents show structure of information on the page.]]

*[[Acronyms and Unit Abbreviations]]

*[[Organic Heterojunctions in Solar Cells | Adobe Acrobat for slide sequences]]

*[[Electromagnetic_Radiation | Latex for Math Formulas - (go to page and edit to see the source)]]

*[[Solar_Technologies#External_Links | External Links and References]]

*[[Organic Photovoltaic Fabrication and Test Apparatus | Flash Video for Lab Training]]

*[[How to Give a Research Presentation]]

*[[Electromagnetic_Spectrum#Knowledge_Check | Knowledge Check - Wiki Quiz]]

=== Flash Simulations ===

*[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]

*[[Second-order_NLO_Materials#Flash | Poling Simulation]]

*[[Second-order_NLO_Materials#Flash2 | Interactions]]

*[[Second-order_Processes#Flash | Electro-optical effect animation]]

*[[Introduction_to_Third-order_Processes_and_Materials#Flash |Phase Conjugate Mirror]]

*[[Attenuated Total Reflectance#Flash |Attenuated Total Reflectance]]

*[[Polarization_and_Polarizability#Flash | Four types of polarization animation]]

*[[Organic Electronics#Flash | Organic Field Effect Transistor Simulation]]

K-12 Outreach Introduction

2010-03-15T17:32:43Z

128.95.39.187: /* More Hands On Demos and Activity Ideas */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Basic Optics - Outreach Kit|Next Topic]]</td>
</tr>
</table>

=== Outreach Overview ===

These kits are being assembled for loan to CMDITR members to enhance their outreach activities. Each kit contains materials for several demonstrations and in some cases hands-on materials that are suitable for various grade levels. There is one kit for one general interest area.

[http://depts.washington.edu/cmditr/media/Outreach_kits.docx Download complete manuals for 3 kits]

As a scientist who is deeply immersed in your research it is easy to overestimate the sophistication and content background of children. Even common events that you might consider everyday students may have not encountered. One of the reason of doing hands-on demos is to give students a shared concrete experience on which to build understanding and connections.

The table below suggests the topics that might be appropriate for each audience. Note: sometimes the materials in a kit might be quite impressive to kids even when the scientific explanation is inappropriate at lower levels. We assume you will be adjusting your presentation to make it fit the audience and venue.

=== Outreach Kits Topic Matrix ===

{| class="wikitable" border = "1"
|-
! Kit
! Elementary Topics
! Middle School / Public Topics
! High School Topics
|-
| [[Basic Optics - Outreach Kit]]
| Light goes straight, Color mixing
| Lenses, optics, refraction, reflection, absorption
| Polarization, Diffraction, emission spectra, dye sensitized solar cell
|-
| [[Photovoltaics- Outreach Kit]]
| Solar car, Batteries
| Angle /area dependence, Types of PV cells
| Total efficiency, measuring VC curves, color absorption

|-
| [[Lasers and Telecommunication- Outreach Kit]]
| Optical fiber, water stream demo,
| Total internal reflection, Tyndal effect
| Polarization, Interferometer, Index of refraction, optical networks
|-
| [[Nanocrystalline - Dye Solar Cell Kit]]
|
|
| Total efficiency, measuring VC curves, color absorption, oxidation-reduction,
|}

=== The Kits ===

[[Image:AssembledCell_small.JPG|thumb|200px|]]

*[[Basic Optics - Outreach Kit]]
*[[Lasers and Telecommunication- Outreach Kit]]
*[[Photovoltaics- Outreach Kit]]
*[[Nanocrystalline - Dye Solar Cell Kit]]
<br clear='all'>

=== Assembling the Kits ===
#To build your own kits start by ordering the components listed at the end of the wiki for each kit. Most of the materials in the original kits are provided in quantities for a table top demo (1-2 copies). If you know that you are going to want to do a larger group where everyone needs a polarizing filter for example then order enough for a class. Be warned that that if you pass out something cool to everyone in a class you are probably not going to get them all back!
#Print the manual with a color printer and assemble with a 1 1/2" three ring binder with separators for each activity.
#Place materials for each activity in three ring, zip lock binder bags so they are organized with each activity. You may want to keep the additional product info and lessons that come with each component at the end of the binder.
#Keep all the materials and binder in a plastic snap case from Storables. The box needs to be 17"x13"x6".

[http://www.storables.com/Shop/Office/Hobby-Cases--Photo-Storage/?launch_pg=itemPage&launch_sel=1001905&launch_pg_sp=true&title=Large+Snap+Case Storables- Large Snap Case $7.95]

===Education Standards===
Science classroom time is packed full and teachers have many specific educational objective that are dictated by their districts and states. One key to being welcomed to the classroom is to relate your presentation to specific content they have to cover anyway. Even if your specific science is not covered you can switch the activity format to address general process skills such as observation, hypothesing, designing an experiment and interpreting results. Careers and the connect between science, technology and society are also hooks that tie into must curricula.

To learn what is taught at various grade levels check the National Science Education Standards, AAAS Project 2061 and the links to state Science below.

[http://www.nap.edu/openbook.php?record_id=4962&page=104 National Science Education Standards - Grade level Content]

[http://www.project2061.org/publications/bsl/online/index.php?chapter=4 AAAS 2061 Benchmarks - The Physical Setting]

[http://www.education-world.com/standards/state/toc/index.shtml Education World State Standards Links]

[http://www.mcrel.org/compendium/SubjectTopics.asp?SubjectID=2 McREL Content Knowledge]

[http://dev.nsta.org/ssc/ National Science Teachers Association- Science Scope and Coordination]

=== More Hands On Demos and Activity Ideas ===
[http://depts.washington.edu/cmditr/media/Educ_demo_suppliers.docx List of suppliers for education kit materials]

[http://www.hands-on-optics.org/resources/ HANDS ON OPTICS- (from OSA, SPIE and NOA0]

[http://projectsol.aps.com/inside/inside_pv.asp APS Project Sol- Animation explains silicon solar solar cells]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://ice.chem.wisc.edu/Catalog/SciKits.htm#Anchor-Optical-13405 Institute for Chemical Education- Source for kits]

[http://mrsec.wisc.edu/Edetc/nanolab/index.html Video labs in Nanotechnology from Univ. Wisconsin MRSEC]

[http://www.optics.rochester.edu/workgroups/berger/EDay/EDay_Writeups.html Rochester Optics demonstrations for Eday]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.tryscience.org/experiments/experiments_home.html Try science demonstrations ]

'''Lab Interfacing'''

Using a computer to connect to measurement probes is very common in research. In demonstrations it gives you the chance to generated a data display on the fly while you are doing a demo to get students more engaged. Voltage, current, light and temperature probes are available and there are simple analog to digital converters that can plug into your USB interface.

[http://k8.vernier.com/products/interfaces/ Vernier Go!Link USB interface and voltage/current probe]

[http://store.pasco.com/pascostore/showdetl.cfm?did=9&partnumber=PS-2100A&detail=1 Pasco USBlink]

[http://sites.google.com/a/flosscience.com/probeware/Home/build-your-own Audacity Oscilloscope using sound card]

[http://depts.washington.edu/cmditr/media/voltmetercs3.swf Experimental Flash Voltmeter using microphone input- .5 volts or less]

=== Resources for Informal Science Education ===
[http://www.informalscience.org/research/resources Informal Science Education - Good resource to see what museums are doing with outreach activities.]

[http://www.astc.org/ Association of Science and Technology Centers- Main clearinghouse for museum exhibit and demo technologies.]

Lasers and Telecommunication- Outreach Kit

2010-03-15T17:31:48Z

128.95.39.187:

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Photovoltaics- Outreach Kit|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>

</tr>
</table>
== Overview ==
One of the major research thrusts of CMDITR is organic electronics that can be used in information technology and telecommunications. At the heart of this is the modulation of light using new organic electro-optical materials. Students need to understand how the system currently uses light and optics to carry information. Electro-optic materials can change their index of refraction in the presence of an electric field. This property combined with wave interference makes high speed switching possible. Finally, electro-optical and all optical switches can be miniaturized to the nano-scale to take advantage of other unique properties in device design.

== User Guide ==

=== Analog vs Digital Signals ===

[[Image:120px-Digital.signal.png|thumb|300px|]]
'''Information can be carried by modulating electrical signals either analog (continuously changing) or digital (discrete values- coded in timed pulses either on or off).''' Show or draw pictures of waveforms of analog and digital signals.

=== Light as a signal carrier ===

'''Information can be carried by light.''' Bounce a laser off of mirror attached to a balloon stretched on a can. Tap the rubber membrane or speak into it. Brainstorm the advantages of using light as carrier for information?

*CMDITR is working on ways to modulate light by controlling the optical properties of the materials it passes through. This may lead to improved efficiency of switching light in communication systems. It also may lead to all-optical switching (AOS) in which light from one channel controls light in another channel.

=== Fiber optics explanation ===

'''Optic fiber transmits light due to total internal reflection.''' Demonstrate light reflecting inside of plastic hose filled with water. Fill the plastic chamber with water and add a pinch of dry milk powder to reveal the light rays. Demonstrate the critical angle where there is total internal reflection. Place a wood plug in the hole in the plastic bottle and fill the bottle with water, place it on top of the plastic case. Position the laser in the support so that it points directly at the end of the plug. Place the larger plastic tub below the stream path. Turn on the laser and pull the plug. Use a white card to interrupt the stream and demonstrate that light is internally reflected in the stream.

[[Image:Colladon's Lightfountain.JPG|thumb|300px|The light fountain was first demonstrated by Daniel Colladon in 1842]]

=== Index of refraction demo ===

'''Light is refracted and reflected when it encounters a material with a different index of refraction.''' Place a straw in the plastic tub with water (add a little milk to visualize laser) and observe that it appears to bend when placed at an angle. Repeat the demonstration this time with a laser pointed down from above. Index of refraction is the ratio of the speed of light in a vacuum over to that in the material. Air and water have very different indexes of refraction.

=== Comparing index of refraction of substances ===

'''Solids and liquids can have different indexes of refraction.''' Carefully pour a layer of 80% sugar solution or corn syrup into the bottom of the plastic container. Tell students that sugar water has index of refraction of 1.49 and pure water is 1.33. Repeat the refraction demo. The light should bend a second time when it reaches the sugar water layer. Another variation is to carefully mix a series of sugar solutions and layer them so the solution is progressively more dense. This will result in a smoothly bending straw or light beam.

*This property is used in optic fiber in which the core and cladding have different IOR. Some fibers use the graded index fiber with special glass or polymers with progressively higher IOR. This decreases the dispersion of light that is caused by light at different angles passing through the fiber at different speeds (modal dispersion).

=== Optic Fiber Network Demo ===
[[Image:Optic_Fiber_Network.jpg|thumb|500px|]]
'''Fiber optics are used to transmit signals over long distances''' for phone and computer networks, or short distances between computer servers where high speed connections are needed. This usually involves transferring from electrical to optical and back to electrical signals. The optical fiber communications demonstration kit includes a transmitter and a receiver. Apply the 5V power supply to the demonstration device. This demo shows one way communication. (for two way communication the system would have a receiver and transmitter at both ends). The transmitter has a simple oscillator that controls an LED at the point where the optical fiber enters the device. Light passes along the fiber to the receiver where a photo detector senses the light and the circuitry coverts the light back into electricity at the Data output lines. Connect EN and EXT on the transmitter to the +5V positive terminal. An LED will flash on the Data lines on the receiver, proving that the signal has made it all the way back to electricity again. Disconnect the optical fiber from the receiver end and show that that the fiber end is flashing, the LED on the data will stop flashing when it stops getting its optical signal. As you bring the fiber back into the receiver the LED will begin flashing again.

The circuit is controlled with the following logic on the transmitter side. 0 means the line is connected to the ground, 1 means it is connected to the +5V line. This table explains the logic conditions that can be use to configure the circuit:

{| class="wikitable" border = "1"
|-
! Mode
! EN
! EXT
! LED State
|-
| 1
| 0
| 1
| ON
|-
| 2
| 0
| 0
| OFF
|-
| 3
| 1
| 1
| OSCILLATING
|-
| 4
| 1
| 0
| OFF
|}

*CMDITR researchers are concerned with various aspects of the optical network. An electro-optical switch can built using polymers. A key problem is switching speed. New organic molecules may be able to operate at higher speeds than current materials.

=== Polarizing Filter with Laser ===

<br clear='all'>
'''Telecommunications depend on the ability to turn light on and off quickly (modulation).''' Show how the polarizing filter can pass or block light from the laser pointer.

=== Michelson Interferometer ===

<br clear='all'>
[[Image:MachZehnder.gif|thumb|400px|]]

'''Coherent light can be modulated by using interference of light waves.''' The Mach-Zehnder (MZ) interferometer is a device used to modulate light. In the MZ device a light beam is divided into two paths and one path goes through some electro-optic material. Changing the electric field on the EO material changes its index of refraction. When the two paths converge again destructive interference cancel the output light creating a signal.

<br clear='all'>
[[Image:600px-Interferometre Michelson pattern.png|thumb|300px|The Michelson Interferometer Light Path- A-light source, B-beam splitting mirror, CD-first surface mirrors ]]
The Michelson Interferometer demonstrates this kind of interference with a more complicated path. One path of the split beam goes through the beam splitter, reflects off a mirror, then reflects off the back side of the image splitter and finally reflect off a second mirror before exiting the beam splitter along the original path. The two beams then pass through a diverging lens to spread the beam out into a wider area to reveal a series of bands or circles where there has been interference. This device is extremely sensitive to distance (for visible light it is 1/100th the thickness of human hair. This makes it sensitive to minute vibrations and minute changes in the index of refraction of material placed in the path.
<br clear='all'>

[[Image:Interferometer_labeled.jpg|thumb|400px|Michelson Interferometer Demo]]
Follow the manufacturer’s instructions for arranging the pieces for the interferometer demo. Once you get a somewhat stable interference pattern then experiment with placing glass in the path. By turning the glass slightly you will alter its effective index of refraction and cause a shift in the interference pattern. Similarly, when an electro-optical material is placed in the beam path it will alter the interference pattern. A variation on this setup can be used to measure the electro-optic coefficient of materials.

*CMDITR research is building materials that can be used in telecom and all optical switching.

=== Silicon Integration Photos ===

<br clear='all'>
'''New materials can be fashioned into extremely small nano-scale devices integrated right on to the chip.''' Show photos, discuss micro-electronic trends, fabrication and scale.
<br clear='all'>

== Links ==
[http://en.wikipedia.org/wiki/Interferometer Wikipedia on interferometry]

[http://depts.washington.edu/cmditr/mediawiki/index.php?title=Dispersion_and_Attenuation_Phenomena Fiber optic materials]

[http://depts.washington.edu/cmditr/mediawiki/index.php?title=Optical_Networks Optical Networks]

== Sources for Building Your Own Kit ==
[http://depts.washington.edu/cmditr/media/TL-kit.docx Cover art for Telecommunications Kit]
*laser pointer
*plastic tub
*plastic tubing
*Optic fiber receiver and transmitter
*Michelson interferometer
[http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2110 Michelson interferometer with pointer $109]

[http://www.i-fiberoptics.com/educational-detail.php?id=14200 Educational Communication Kit $18 includes fiber, LED photodetector]

[http://i-fiberoptics.com/educational-detail.php?id=13700&cat=kits-projects Adventures in Fiber Optics Kit $42]

Photovoltaics- Outreach Kit

2010-03-15T17:31:05Z

128.95.39.187: /* Sources for Building your own kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Basic Optics - Outreach Kit|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Lasers and Telecommunication- Outreach Kit|Next Topic]]</td>
</tr>
</table>

== Overview ==
Photovoltaics (PV) or solar cells are one of the most promising sources for renewable electrical energy. The first generation cells were made from silicon crystals like those used computer semiconductor chips. These are efficient but very expensive. Silicon PV were first widely used where the cost of wiring to the grid was impractical such as in satellites or to power remote sensors along pipelines or railway tracks. Materials research and improved manufacturing techniques have brought the price down to where they are beginning to become practical for home energy systems. Plastic solar cells that use organic chemicals instead of silicon may be the next breakthrough. These demos show some basic devices and engage students in quantifying their performance and considering how basic science relates to engineering design.

== User Guide ==

=== Solar Car - Solar battery charger ===

'''Solar energy can be converted to electrical energy using a solar cell.''' Demonstrate the solar car, the motor and rotor, and solar battery charger. Place the solar car in the full sun. What happens when the car passes into the shade? Demonstrate that the small silicon cell doesn’t generate enough energy to power the single LED but the larger amorphous silicon panel can power the light, even in indirect sunlight. Compare the solar electricity to power from a battery. See if they know about batteries polarity. Predict what would happen to the motor if you switch the leads to the solar cell. Reverse the polarity and the disc on the motor will rotate in the opposite direction.

*'''Research Connection:''' CMDITR is building a new kind of solar cell that uses an organic chemical to trap light and then transfer electrons to conductive layers.

=== Three types of solar cells. ===

'''There are several kinds of solar cells which differ power, cost, durability, and preferred applications.'''
Demonstrate the various types of solar cells in the kit by connecting them to a motor, voltmeter or LED.
a. Single crystal and Multicrystaline cell. The smaller cells in the kit are rated .45 volts and 400ma. Crystalline silicon solar cells (c-Si) can have efficiencies from 10-12% . They are produced from ingots of solid silicon and are rigid. These are the cells that most often used in space station where power density and durability are most important.

b. Amorphous silicon battery charger. The panel is rated 7.2 volt / 200ma and has diode built into the circuit to prevent battery discharge into the panel when it is dark. Amorphous silicon is made by depositing an extremely thin layer of silicon on a conductive polymer. As a result the panel is flexible. (a-Si) Amorphous silicon has a comparatively low 6% efficiency because the silicon is poorly organized creating barriers to charge movement but it makes up for this with a lower cost and ease of manufacturing.

c. Copper indium selenide (CIS) CIS and Copper indium gallium selenide cells (CIGS) have 14-20% efficiency. These cells must be full encapsulated to prevent release of toxic selenium. These cells have an open circuit voltage of 5 volts and a short circuit current of 95ma. Max power output is 3.9 volts at 64mA.

d. Organic photovoltaics (OPV)- currently maximum is 5-6.5 %. The Konarka Power Plastic is one of the few commercially available OPV panel. The advantage of organic or plastic solar cells is that they have the potential of extremely low material and manufacturing cost and they are flexible. A disadvantage is that organic materials have a limited lifetime especially in full sun and exposed to water and oxygen.

e. Dye Sensitized Solar Cell (DSS)Demonstrate the dye sensitize solar cell. Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Lightly coat the other slide with the carbon soot from a candle slide. Pinch the slides together with the binder clips so that the slides are offset exposing the conductive ITO layer. Apply iodide solution as an electrolyte and then.

f. Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.
Research Connection: CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.

*'''Research Connection:''' CCMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

<br clear='all'>

=== Series vs Parallel circuits ===
[[Image:Pv_parallel.jpg|thumb|300px|3 solar cells wired in Parallel ]]

a. Explain the difference between voltage and current. Show that the large panel produces a higher voltage (because it has several cell areas wired in series).
Measure the voltage and current produced from each cell using the digital meter. The wood test frame provides a convenient support and visual explanation of the circuit.

[[Image:Testcellholder.jpg|thumb|300px|]]

Note that the red lead must be moved and the selector switch set to mA to get the ammeter mode. Each cell has a characteristic voltage. Silicon cells produce between .5 -.6 V oc *(volts open circuit), OPVs are usually around .4 Voc. Use the clip leads and the three small panels to demonstrate that in a series circuit the voltage is added. In a parallel circuit the voltage does not change but the current (amperage) is increased.’

b. Compare the power for a 2 x 2 cm area for the crystalline solar cell compared to the same area of amorphous silicon cell.

P= V x I
Power (watts) = Volts x Amps

Sample calculation:
Volts = .4 V
Amp = 50ma= .05 amp
Power = .02 Watts

c. The amorphous panel provided is 7.2 V and 200 ma. How many of these panels would be needed to in what configuration to generate 100 Watts?

d. Experiment with different sources of light, sunlight, or diffuse vs. direct light

*'''Research Connection:''' CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The advantage of these is that they can be produced cheaply, they can put printed on plastic, and materials are available.

=== Power : area relationship ===

'''The larger the cross sectional area of the light beam that is trapped, the greater the power generated.'''

a. Cover portions of the panel to show decreasing current and voltage. Solar cells measured with the meter are under no load so you get the open circuit voltage (Voc). You should notice that the current responds quickly with decreasing light while the voltage stays somewhat stable, finally the voltage drops too. To measure the power from the panel you have to measure both voltage and amperage produced.

b. Plot the power versus area for the amorphous silicon panel. Complete the table and graph from BLM 1- Power vs Area Experiment

*'''Research Connection:''' OPVs could be less expensive even if they are less efficient which means a larger area could be deployed.

=== Power : distance relationship ===

<br clear='all'>
[[Image:479px-Inverse_square_law.svg.png|thumb|300px|]]
'''Energy from a radiant light source drops off with distance.'''

a. Use the electric meter to measure the current produced by the sample silicon cell as you move away from a light source. As you move away from a diffuse light source the same amount of light is spread over a large area so the solar panel only intercepts part of the energy. This called the inverse square law. If you use a focused light source this relationship will not hold. At the distance we are from the sun it does not make any measurable difference how close (for example sea level versus on mountain top) we place solar cells to the sun.

b. Collect data and graph the experiment using BLM 2 – Power vs Distance Experiment

=== Power : Incidence Angle relationship ===

<br clear='all'>
[[Image:Seasons.too.png|thumb|300px|Effect of sun angle on insolation]]
'''The angle with respect to the sun influences the energy output.'''

a. Set up the solar panel on its inclined support with protractor. Change the angle of the solar panel and measure the current. Changing the angle has the effect of decreasing the cross section of light that is intercepted. You can see this by measuring the shadow of the panel as it is tilted. In addition low angle sun on the Earth must pass through more atmosphere so some energy is absorbed.

b. Plot the current versus the angle. Complete the data and graph on BLM 3 Power vs Angle Experiment

c. Use this information to create a bar chart showing the total power generated by a cell during the course of day if the cell were fixed on a roof with an angle of 30 degrees. The peak angle of the sun on the spring or autumn equinox is 90- your latitude. At mid summer it is 90 – latitude -23.45 degrees. At mid winter it is 90 – latitude + 23.45 degrees

[[Image:Pv angle.jpg|thumb|300px|PV panel with battery charger and protractor]]

*'''Research Connection:''' Engineers have designed tracking systems that keep PV panels facing perpendicular to sun all day long. Others have explored using concentrators to reflect light to a smaller area where the cell is.

=== Measuring Absorption Spectrum ===

'''Photovoltaics absorb light at specific wavelengths.'''

a. Use the red, green and blue filters to show that certain colors when filtered out reduce the power more than other colors.

b. Plot the current versus wavelength when different colors are placed in front of the solar cell. You can use the large filter sheets or the filter sample booklets. Be sure to pick filters with approximately the same optical density. Use the attached transmission spectra tabs to pick colors that represent an even array across the spectrum. Complete BLM 4 Power vs Wavelength Experiment

c. Compare the amorphous silicon, the polycrystalline silicon cell, and the dye densitized solar cell.

*'''Research Connection:''' When we design chemicals to use in organic photovoltaics we measure the absorption spectra of the chromophores. Ideally we want dyes that absorb across the entire visible spectrum.

=== Measuring Efficiency ===

'''Efficiency is a measure of how much of the available energy is captured by a cell.''' It is the amount of electricity produced divided by the amount shining on the solar cell. To measure efficiency we have to know how much light energy is hitting the cell and how much electricity it is producing. It’s difficult to measure the incident light. Direct sunlight is between 250 and 1,000 W/m2.

a. In full sunlight measure the power of your solar cell and calculate the efficiency. In this example the cell has an area of 2.4 x 10-3 m2 , measuring .6 Volts and .5 amps in full sun

Pi = A * Ps = 2.4 x 10<sup>-3</sup> * 1000 = 2.4 watts

Po = V x I = 0.6 x 0.5 = 0.3 W

e = Po/Pi = 0.3/2.4 = 0.12 = 12%

b. Repeat this measurement for various cells.
=== PV Cost estimation ===

'''Solar cells are still somewhat expensive.''' Several factors have to be considered in sizing a solar system. Calculate how much area is needed to power a house, how much would it cost?

a. Solar cells currently run about $5-$9 per peak watt.

b. A house might require 2kW peak power

c. If the silicon cells are 15% efficient and the

d. Incoming energy is 1000 W/m2 assume 5 hours (5 kWh/m2) per day of useful sunlight or use the “Photovoltaics Solar Resource” map from NREL to identify the available solar resource for your area.

e. If you aren’t connected to the grid you will need batteries which cost $1 amp hour

*'''Research Connection:''' Materials and manufacturing process determines the cost. Organic photovoltaics have a potential of being low cost because they can be manufactured with roll printing methods. Further research is needed to get higher efficiency, better durability (through encapusulation and decreased photobleaching) New organic solar cells may be much cheaper in the future.

<br clear='all'>
=== PV characterization ===

'''Solar cells are characterized using a voltage- current curve.'''

a. Place the test PV cell in the wood test holder. Place an ammeter and a volt meter at the two pegs labeled A and V. Gradually change the series load in the circuit by sliding the variable resistor. Adjust the load to get an even series of voltage readings such as every .1 volts and record the amps for each voltage. Plot the data. The goal is to get a curve that is closer to a right angle (with a minimum fill factor). There is a certain combination of voltage and current that delivers peak power.

b. Complete BLM 5 Current vs wavelength experiment

*'''Research Connection:''' CMDITR researcher do this same measurement with much finer accuracy.

[[Image:Opv powercurve.jpg|thumb|300px|]]

=== Dye Sensitized Solar Cell ===

'''Organic pigments can be used to capture light to power electrochemical processes.''' Demonstrate the dye sensitized solar cell.Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Then apply iodide solution as an electrolyte and then pinch this together with the carbon black coated slide.

*'''Research Connection:''' Dye sensitized cells have begun commercial production as research continues.
[[Nanocrystalline_-_Dye_Solar_Cell_Kit| Build the complete dye sensitized solar cell activity for high school]]

== Links ==
[http://www.nrel.gov/learning/re_photovoltaics.html NREL]

[http://www.powernaturally.org/Programs/SchoolPowerNaturally/InTheClassroom/kitlessons.asp?i=9#Lesson14 Solar Cell lessons]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://www.infinitepower.org/pdf/No19%2096-828B.pdf Photovoltaic measurements Lesson]

[http://www.nrel.gov/midc/unlv/ live insolation data for Las Vegas NREL Solar Data]

[http://en.wikipedia.org/wiki/Solar_cell Wikipedia on solar cells]

[http://depts.washington.edu/cmditr/media/PlasticPV.ppt Plastic Solar Cell Poster]

[http://www.nanosense.org/activities/cleanenergy/solarcellanimation.html Solar Cell Animations]

[http://www.iop.org/EJ/article/0031-9120/41/5/005/pe6_5_005.pdf?request-id=e7503f0f-68f9-4217-bfe8-24c174c90fa5 Other chemicals for photovoltaics demo]

[http://www.teachersdomain.org/asset/hew06_int_ohmslaw/ Ohms Law Simulation from the Teachers Domain]

[http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/watcir.html Water analogy to circuits- Hyperphysics]

== Materials in the kit ==
*Sunzoom Lite car kit
*4 AA battery PV battery charger
*4 AA recharable NiCAD or LI ion batteries
*Solar mini car
*Digital Electric meter
*Protractor
*Ruler
== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/Photovoltaics.docx Cover art for Photovoltaics Kit]

http://shop.pitsco.com/store/detail.aspx?CategoryID=115&by=9&ID=2647&c=1&t=0&l=0 $8. 95 sunzoom lite car

http://store.sundancesolar.com/subusobachki6.html 4 AA battery charger $39.95

http://store.sundancesolar.com/misorokitsus.html mini solar car $9.95

http://store.sundancesolar.com/ecdimu.html Electric Meter 2 a $12.95

Light Source for indoor use- quartz desk lamp

http://scientificsonline.com/product.asp?pn=3039810 Individual silicon cells 3 @ $5.95

http://scientificsonline.com/product.asp?pn=3085037 CIS Solar Panel 3 @ $2.95

Color Filter pack for testing cells

Rechargeable Batteries

Lasers and Telecommunication- Outreach Kit

2010-03-15T17:30:29Z

128.95.39.187: /* Materials in the kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Photovoltaics- Outreach Kit|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>

</tr>
</table>
== Overview ==
One of the major research thrusts of CMDITR is organic electronics that can be used in information technology and telecommunications. At the heart of this is the modulation of light using new organic electro-optical materials. Students need to understand how the system currently uses light and optics to carry information. Electro-optic materials can change their index of refraction in the presence of an electric field. This property combined with wave interference makes high speed switching possible. Finally, electro-optical and all optical switches can be miniaturized to the nano-scale to take advantage of other unique properties in device design.

== User Guide ==

=== Analog vs Digital Signals ===

[[Image:120px-Digital.signal.png|thumb|300px|]]
'''Information can be carried by modulating electrical signals either analog (continuously changing) or digital (discrete values- coded in timed pulses either on or off).''' Show or draw pictures of waveforms of analog and digital signals.

=== Light as a signal carrier ===

'''Information can be carried by light.''' Bounce a laser off of mirror attached to a balloon stretched on a can. Tap the rubber membrane or speak into it. Brainstorm the advantages of using light as carrier for information?

*CMDITR is working on ways to modulate light by controlling the optical properties of the materials it passes through. This may lead to improved efficiency of switching light in communication systems. It also may lead to all-optical switching (AOS) in which light from one channel controls light in another channel.

=== Fiber optics explanation ===

'''Optic fiber transmits light due to total internal reflection.''' Demonstrate light reflecting inside of plastic hose filled with water. Fill the plastic chamber with water and add a pinch of dry milk powder to reveal the light rays. Demonstrate the critical angle where there is total internal reflection. Place a wood plug in the hole in the plastic bottle and fill the bottle with water, place it on top of the plastic case. Position the laser in the support so that it points directly at the end of the plug. Place the larger plastic tub below the stream path. Turn on the laser and pull the plug. Use a white card to interrupt the stream and demonstrate that light is internally reflected in the stream.

[[Image:Colladon's Lightfountain.JPG|thumb|300px|The light fountain was first demonstrated by Daniel Colladon in 1842]]

=== Index of refraction demo ===

'''Light is refracted and reflected when it encounters a material with a different index of refraction.''' Place a straw in the plastic tub with water (add a little milk to visualize laser) and observe that it appears to bend when placed at an angle. Repeat the demonstration this time with a laser pointed down from above. Index of refraction is the ratio of the speed of light in a vacuum over to that in the material. Air and water have very different indexes of refraction.

=== Comparing index of refraction of substances ===

'''Solids and liquids can have different indexes of refraction.''' Carefully pour a layer of 80% sugar solution or corn syrup into the bottom of the plastic container. Tell students that sugar water has index of refraction of 1.49 and pure water is 1.33. Repeat the refraction demo. The light should bend a second time when it reaches the sugar water layer. Another variation is to carefully mix a series of sugar solutions and layer them so the solution is progressively more dense. This will result in a smoothly bending straw or light beam.

*This property is used in optic fiber in which the core and cladding have different IOR. Some fibers use the graded index fiber with special glass or polymers with progressively higher IOR. This decreases the dispersion of light that is caused by light at different angles passing through the fiber at different speeds (modal dispersion).

=== Optic Fiber Network Demo ===
[[Image:Optic_Fiber_Network.jpg|thumb|500px|]]
'''Fiber optics are used to transmit signals over long distances''' for phone and computer networks, or short distances between computer servers where high speed connections are needed. This usually involves transferring from electrical to optical and back to electrical signals. The optical fiber communications demonstration kit includes a transmitter and a receiver. Apply the 5V power supply to the demonstration device. This demo shows one way communication. (for two way communication the system would have a receiver and transmitter at both ends). The transmitter has a simple oscillator that controls an LED at the point where the optical fiber enters the device. Light passes along the fiber to the receiver where a photo detector senses the light and the circuitry coverts the light back into electricity at the Data output lines. Connect EN and EXT on the transmitter to the +5V positive terminal. An LED will flash on the Data lines on the receiver, proving that the signal has made it all the way back to electricity again. Disconnect the optical fiber from the receiver end and show that that the fiber end is flashing, the LED on the data will stop flashing when it stops getting its optical signal. As you bring the fiber back into the receiver the LED will begin flashing again.

The circuit is controlled with the following logic on the transmitter side. 0 means the line is connected to the ground, 1 means it is connected to the +5V line. This table explains the logic conditions that can be use to configure the circuit:

{| class="wikitable" border = "1"
|-
! Mode
! EN
! EXT
! LED State
|-
| 1
| 0
| 1
| ON
|-
| 2
| 0
| 0
| OFF
|-
| 3
| 1
| 1
| OSCILLATING
|-
| 4
| 1
| 0
| OFF
|}

*CMDITR researchers are concerned with various aspects of the optical network. An electro-optical switch can built using polymers. A key problem is switching speed. New organic molecules may be able to operate at higher speeds than current materials.

=== Polarizing Filter with Laser ===

<br clear='all'>
'''Telecommunications depend on the ability to turn light on and off quickly (modulation).''' Show how the polarizing filter can pass or block light from the laser pointer.

=== Michelson Interferometer ===

<br clear='all'>
[[Image:MachZehnder.gif|thumb|400px|]]

'''Coherent light can be modulated by using interference of light waves.''' The Mach-Zehnder (MZ) interferometer is a device used to modulate light. In the MZ device a light beam is divided into two paths and one path goes through some electro-optic material. Changing the electric field on the EO material changes its index of refraction. When the two paths converge again destructive interference cancel the output light creating a signal.

<br clear='all'>
[[Image:600px-Interferometre Michelson pattern.png|thumb|300px|The Michelson Interferometer Light Path- A-light source, B-beam splitting mirror, CD-first surface mirrors ]]
The Michelson Interferometer demonstrates this kind of interference with a more complicated path. One path of the split beam goes through the beam splitter, reflects off a mirror, then reflects off the back side of the image splitter and finally reflect off a second mirror before exiting the beam splitter along the original path. The two beams then pass through a diverging lens to spread the beam out into a wider area to reveal a series of bands or circles where there has been interference. This device is extremely sensitive to distance (for visible light it is 1/100th the thickness of human hair. This makes it sensitive to minute vibrations and minute changes in the index of refraction of material placed in the path.
<br clear='all'>

[[Image:Interferometer_labeled.jpg|thumb|400px|Michelson Interferometer Demo]]
Follow the manufacturer’s instructions for arranging the pieces for the interferometer demo. Once you get a somewhat stable interference pattern then experiment with placing glass in the path. By turning the glass slightly you will alter its effective index of refraction and cause a shift in the interference pattern. Similarly, when an electro-optical material is placed in the beam path it will alter the interference pattern. A variation on this setup can be used to measure the electro-optic coefficient of materials.

*CMDITR research is building materials that can be used in telecom and all optical switching.

=== Silicon Integration Photos ===

<br clear='all'>
'''New materials can be fashioned into extremely small nano-scale devices integrated right on to the chip.''' Show photos, discuss micro-electronic trends, fabrication and scale.
<br clear='all'>

== Links ==
[http://en.wikipedia.org/wiki/Interferometer Wikipedia on interferometry]

[http://depts.washington.edu/cmditr/mediawiki/index.php?title=Dispersion_and_Attenuation_Phenomena Fiber optic materials]

[http://depts.washington.edu/cmditr/mediawiki/index.php?title=Optical_Networks Optical Networks]

== Materials in the kit ==
[http://depts.washington.edu/cmditr/media/TL-kit.docx Cover art for Telecommunications Kit]
*laser pointer
*plastic tub
*plastic tubing
*Optic fiber receiver and transmitter
*Michelson interferometer
[http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2110 Michelson interferometer with pointer $109]

[http://www.i-fiberoptics.com/educational-detail.php?id=14200 Educational Communication Kit $18 includes fiber, LED photodetector]

[http://i-fiberoptics.com/educational-detail.php?id=13700&cat=kits-projects Adventures in Fiber Optics Kit $42]

Photovoltaics- Outreach Kit

2010-03-15T17:29:33Z

128.95.39.187: /* Sources for Building your own kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Basic Optics - Outreach Kit|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Lasers and Telecommunication- Outreach Kit|Next Topic]]</td>
</tr>
</table>

== Overview ==
Photovoltaics (PV) or solar cells are one of the most promising sources for renewable electrical energy. The first generation cells were made from silicon crystals like those used computer semiconductor chips. These are efficient but very expensive. Silicon PV were first widely used where the cost of wiring to the grid was impractical such as in satellites or to power remote sensors along pipelines or railway tracks. Materials research and improved manufacturing techniques have brought the price down to where they are beginning to become practical for home energy systems. Plastic solar cells that use organic chemicals instead of silicon may be the next breakthrough. These demos show some basic devices and engage students in quantifying their performance and considering how basic science relates to engineering design.

== User Guide ==

=== Solar Car - Solar battery charger ===

'''Solar energy can be converted to electrical energy using a solar cell.''' Demonstrate the solar car, the motor and rotor, and solar battery charger. Place the solar car in the full sun. What happens when the car passes into the shade? Demonstrate that the small silicon cell doesn’t generate enough energy to power the single LED but the larger amorphous silicon panel can power the light, even in indirect sunlight. Compare the solar electricity to power from a battery. See if they know about batteries polarity. Predict what would happen to the motor if you switch the leads to the solar cell. Reverse the polarity and the disc on the motor will rotate in the opposite direction.

*'''Research Connection:''' CMDITR is building a new kind of solar cell that uses an organic chemical to trap light and then transfer electrons to conductive layers.

=== Three types of solar cells. ===

'''There are several kinds of solar cells which differ power, cost, durability, and preferred applications.'''
Demonstrate the various types of solar cells in the kit by connecting them to a motor, voltmeter or LED.
a. Single crystal and Multicrystaline cell. The smaller cells in the kit are rated .45 volts and 400ma. Crystalline silicon solar cells (c-Si) can have efficiencies from 10-12% . They are produced from ingots of solid silicon and are rigid. These are the cells that most often used in space station where power density and durability are most important.

b. Amorphous silicon battery charger. The panel is rated 7.2 volt / 200ma and has diode built into the circuit to prevent battery discharge into the panel when it is dark. Amorphous silicon is made by depositing an extremely thin layer of silicon on a conductive polymer. As a result the panel is flexible. (a-Si) Amorphous silicon has a comparatively low 6% efficiency because the silicon is poorly organized creating barriers to charge movement but it makes up for this with a lower cost and ease of manufacturing.

c. Copper indium selenide (CIS) CIS and Copper indium gallium selenide cells (CIGS) have 14-20% efficiency. These cells must be full encapsulated to prevent release of toxic selenium. These cells have an open circuit voltage of 5 volts and a short circuit current of 95ma. Max power output is 3.9 volts at 64mA.

d. Organic photovoltaics (OPV)- currently maximum is 5-6.5 %. The Konarka Power Plastic is one of the few commercially available OPV panel. The advantage of organic or plastic solar cells is that they have the potential of extremely low material and manufacturing cost and they are flexible. A disadvantage is that organic materials have a limited lifetime especially in full sun and exposed to water and oxygen.

e. Dye Sensitized Solar Cell (DSS)Demonstrate the dye sensitize solar cell. Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Lightly coat the other slide with the carbon soot from a candle slide. Pinch the slides together with the binder clips so that the slides are offset exposing the conductive ITO layer. Apply iodide solution as an electrolyte and then.

f. Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.
Research Connection: CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.

*'''Research Connection:''' CCMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

<br clear='all'>

=== Series vs Parallel circuits ===
[[Image:Pv_parallel.jpg|thumb|300px|3 solar cells wired in Parallel ]]

a. Explain the difference between voltage and current. Show that the large panel produces a higher voltage (because it has several cell areas wired in series).
Measure the voltage and current produced from each cell using the digital meter. The wood test frame provides a convenient support and visual explanation of the circuit.

[[Image:Testcellholder.jpg|thumb|300px|]]

Note that the red lead must be moved and the selector switch set to mA to get the ammeter mode. Each cell has a characteristic voltage. Silicon cells produce between .5 -.6 V oc *(volts open circuit), OPVs are usually around .4 Voc. Use the clip leads and the three small panels to demonstrate that in a series circuit the voltage is added. In a parallel circuit the voltage does not change but the current (amperage) is increased.’

b. Compare the power for a 2 x 2 cm area for the crystalline solar cell compared to the same area of amorphous silicon cell.

P= V x I
Power (watts) = Volts x Amps

Sample calculation:
Volts = .4 V
Amp = 50ma= .05 amp
Power = .02 Watts

c. The amorphous panel provided is 7.2 V and 200 ma. How many of these panels would be needed to in what configuration to generate 100 Watts?

d. Experiment with different sources of light, sunlight, or diffuse vs. direct light

*'''Research Connection:''' CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The advantage of these is that they can be produced cheaply, they can put printed on plastic, and materials are available.

=== Power : area relationship ===

'''The larger the cross sectional area of the light beam that is trapped, the greater the power generated.'''

a. Cover portions of the panel to show decreasing current and voltage. Solar cells measured with the meter are under no load so you get the open circuit voltage (Voc). You should notice that the current responds quickly with decreasing light while the voltage stays somewhat stable, finally the voltage drops too. To measure the power from the panel you have to measure both voltage and amperage produced.

b. Plot the power versus area for the amorphous silicon panel. Complete the table and graph from BLM 1- Power vs Area Experiment

*'''Research Connection:''' OPVs could be less expensive even if they are less efficient which means a larger area could be deployed.

=== Power : distance relationship ===

<br clear='all'>
[[Image:479px-Inverse_square_law.svg.png|thumb|300px|]]
'''Energy from a radiant light source drops off with distance.'''

a. Use the electric meter to measure the current produced by the sample silicon cell as you move away from a light source. As you move away from a diffuse light source the same amount of light is spread over a large area so the solar panel only intercepts part of the energy. This called the inverse square law. If you use a focused light source this relationship will not hold. At the distance we are from the sun it does not make any measurable difference how close (for example sea level versus on mountain top) we place solar cells to the sun.

b. Collect data and graph the experiment using BLM 2 – Power vs Distance Experiment

=== Power : Incidence Angle relationship ===

<br clear='all'>
[[Image:Seasons.too.png|thumb|300px|Effect of sun angle on insolation]]
'''The angle with respect to the sun influences the energy output.'''

a. Set up the solar panel on its inclined support with protractor. Change the angle of the solar panel and measure the current. Changing the angle has the effect of decreasing the cross section of light that is intercepted. You can see this by measuring the shadow of the panel as it is tilted. In addition low angle sun on the Earth must pass through more atmosphere so some energy is absorbed.

b. Plot the current versus the angle. Complete the data and graph on BLM 3 Power vs Angle Experiment

c. Use this information to create a bar chart showing the total power generated by a cell during the course of day if the cell were fixed on a roof with an angle of 30 degrees. The peak angle of the sun on the spring or autumn equinox is 90- your latitude. At mid summer it is 90 – latitude -23.45 degrees. At mid winter it is 90 – latitude + 23.45 degrees

[[Image:Pv angle.jpg|thumb|300px|PV panel with battery charger and protractor]]

*'''Research Connection:''' Engineers have designed tracking systems that keep PV panels facing perpendicular to sun all day long. Others have explored using concentrators to reflect light to a smaller area where the cell is.

=== Measuring Absorption Spectrum ===

'''Photovoltaics absorb light at specific wavelengths.'''

a. Use the red, green and blue filters to show that certain colors when filtered out reduce the power more than other colors.

b. Plot the current versus wavelength when different colors are placed in front of the solar cell. You can use the large filter sheets or the filter sample booklets. Be sure to pick filters with approximately the same optical density. Use the attached transmission spectra tabs to pick colors that represent an even array across the spectrum. Complete BLM 4 Power vs Wavelength Experiment

c. Compare the amorphous silicon, the polycrystalline silicon cell, and the dye densitized solar cell.

*'''Research Connection:''' When we design chemicals to use in organic photovoltaics we measure the absorption spectra of the chromophores. Ideally we want dyes that absorb across the entire visible spectrum.

=== Measuring Efficiency ===

'''Efficiency is a measure of how much of the available energy is captured by a cell.''' It is the amount of electricity produced divided by the amount shining on the solar cell. To measure efficiency we have to know how much light energy is hitting the cell and how much electricity it is producing. It’s difficult to measure the incident light. Direct sunlight is between 250 and 1,000 W/m2.

a. In full sunlight measure the power of your solar cell and calculate the efficiency. In this example the cell has an area of 2.4 x 10-3 m2 , measuring .6 Volts and .5 amps in full sun

Pi = A * Ps = 2.4 x 10<sup>-3</sup> * 1000 = 2.4 watts

Po = V x I = 0.6 x 0.5 = 0.3 W

e = Po/Pi = 0.3/2.4 = 0.12 = 12%

b. Repeat this measurement for various cells.
=== PV Cost estimation ===

'''Solar cells are still somewhat expensive.''' Several factors have to be considered in sizing a solar system. Calculate how much area is needed to power a house, how much would it cost?

a. Solar cells currently run about $5-$9 per peak watt.

b. A house might require 2kW peak power

c. If the silicon cells are 15% efficient and the

d. Incoming energy is 1000 W/m2 assume 5 hours (5 kWh/m2) per day of useful sunlight or use the “Photovoltaics Solar Resource” map from NREL to identify the available solar resource for your area.

e. If you aren’t connected to the grid you will need batteries which cost $1 amp hour

*'''Research Connection:''' Materials and manufacturing process determines the cost. Organic photovoltaics have a potential of being low cost because they can be manufactured with roll printing methods. Further research is needed to get higher efficiency, better durability (through encapusulation and decreased photobleaching) New organic solar cells may be much cheaper in the future.

<br clear='all'>
=== PV characterization ===

'''Solar cells are characterized using a voltage- current curve.'''

a. Place the test PV cell in the wood test holder. Place an ammeter and a volt meter at the two pegs labeled A and V. Gradually change the series load in the circuit by sliding the variable resistor. Adjust the load to get an even series of voltage readings such as every .1 volts and record the amps for each voltage. Plot the data. The goal is to get a curve that is closer to a right angle (with a minimum fill factor). There is a certain combination of voltage and current that delivers peak power.

b. Complete BLM 5 Current vs wavelength experiment

*'''Research Connection:''' CMDITR researcher do this same measurement with much finer accuracy.

[[Image:Opv powercurve.jpg|thumb|300px|]]

=== Dye Sensitized Solar Cell ===

'''Organic pigments can be used to capture light to power electrochemical processes.''' Demonstrate the dye sensitized solar cell.Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Then apply iodide solution as an electrolyte and then pinch this together with the carbon black coated slide.

*'''Research Connection:''' Dye sensitized cells have begun commercial production as research continues.
[[Nanocrystalline_-_Dye_Solar_Cell_Kit| Build the complete dye sensitized solar cell activity for high school]]

== Links ==
[http://www.nrel.gov/learning/re_photovoltaics.html NREL]

[http://www.powernaturally.org/Programs/SchoolPowerNaturally/InTheClassroom/kitlessons.asp?i=9#Lesson14 Solar Cell lessons]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://www.infinitepower.org/pdf/No19%2096-828B.pdf Photovoltaic measurements Lesson]

[http://www.nrel.gov/midc/unlv/ live insolation data for Las Vegas NREL Solar Data]

[http://en.wikipedia.org/wiki/Solar_cell Wikipedia on solar cells]

[http://depts.washington.edu/cmditr/media/PlasticPV.ppt Plastic Solar Cell Poster]

[http://www.nanosense.org/activities/cleanenergy/solarcellanimation.html Solar Cell Animations]

[http://www.iop.org/EJ/article/0031-9120/41/5/005/pe6_5_005.pdf?request-id=e7503f0f-68f9-4217-bfe8-24c174c90fa5 Other chemicals for photovoltaics demo]

[http://www.teachersdomain.org/asset/hew06_int_ohmslaw/ Ohms Law Simulation from the Teachers Domain]

[http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/watcir.html Water analogy to circuits- Hyperphysics]

== Materials in the kit ==
*Sunzoom Lite car kit
*4 AA battery PV battery charger
*4 AA recharable NiCAD or LI ion batteries
*Solar mini car
*Digital Electric meter
*Protractor
*Ruler
== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/Photovoltaics.docx Cover art for Optics Kit]

http://shop.pitsco.com/store/detail.aspx?CategoryID=115&by=9&ID=2647&c=1&t=0&l=0 $8. 95 sunzoom lite car

http://store.sundancesolar.com/subusobachki6.html 4 AA battery charger $39.95

http://store.sundancesolar.com/misorokitsus.html mini solar car $9.95

http://store.sundancesolar.com/ecdimu.html Electric Meter 2 a $12.95

Light Source for indoor use- quartz desk lamp

http://scientificsonline.com/product.asp?pn=3039810 Individual silicon cells 3 @ $5.95

http://scientificsonline.com/product.asp?pn=3085037 CIS Solar Panel 3 @ $2.95

Color Filter pack for testing cells

Rechargeable Batteries

Photovoltaics- Outreach Kit

2010-03-15T17:29:08Z

128.95.39.187: /* Sources for Building your own kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Basic Optics - Outreach Kit|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Lasers and Telecommunication- Outreach Kit|Next Topic]]</td>
</tr>
</table>

== Overview ==
Photovoltaics (PV) or solar cells are one of the most promising sources for renewable electrical energy. The first generation cells were made from silicon crystals like those used computer semiconductor chips. These are efficient but very expensive. Silicon PV were first widely used where the cost of wiring to the grid was impractical such as in satellites or to power remote sensors along pipelines or railway tracks. Materials research and improved manufacturing techniques have brought the price down to where they are beginning to become practical for home energy systems. Plastic solar cells that use organic chemicals instead of silicon may be the next breakthrough. These demos show some basic devices and engage students in quantifying their performance and considering how basic science relates to engineering design.

== User Guide ==

=== Solar Car - Solar battery charger ===

'''Solar energy can be converted to electrical energy using a solar cell.''' Demonstrate the solar car, the motor and rotor, and solar battery charger. Place the solar car in the full sun. What happens when the car passes into the shade? Demonstrate that the small silicon cell doesn’t generate enough energy to power the single LED but the larger amorphous silicon panel can power the light, even in indirect sunlight. Compare the solar electricity to power from a battery. See if they know about batteries polarity. Predict what would happen to the motor if you switch the leads to the solar cell. Reverse the polarity and the disc on the motor will rotate in the opposite direction.

*'''Research Connection:''' CMDITR is building a new kind of solar cell that uses an organic chemical to trap light and then transfer electrons to conductive layers.

=== Three types of solar cells. ===

'''There are several kinds of solar cells which differ power, cost, durability, and preferred applications.'''
Demonstrate the various types of solar cells in the kit by connecting them to a motor, voltmeter or LED.
a. Single crystal and Multicrystaline cell. The smaller cells in the kit are rated .45 volts and 400ma. Crystalline silicon solar cells (c-Si) can have efficiencies from 10-12% . They are produced from ingots of solid silicon and are rigid. These are the cells that most often used in space station where power density and durability are most important.

b. Amorphous silicon battery charger. The panel is rated 7.2 volt / 200ma and has diode built into the circuit to prevent battery discharge into the panel when it is dark. Amorphous silicon is made by depositing an extremely thin layer of silicon on a conductive polymer. As a result the panel is flexible. (a-Si) Amorphous silicon has a comparatively low 6% efficiency because the silicon is poorly organized creating barriers to charge movement but it makes up for this with a lower cost and ease of manufacturing.

c. Copper indium selenide (CIS) CIS and Copper indium gallium selenide cells (CIGS) have 14-20% efficiency. These cells must be full encapsulated to prevent release of toxic selenium. These cells have an open circuit voltage of 5 volts and a short circuit current of 95ma. Max power output is 3.9 volts at 64mA.

d. Organic photovoltaics (OPV)- currently maximum is 5-6.5 %. The Konarka Power Plastic is one of the few commercially available OPV panel. The advantage of organic or plastic solar cells is that they have the potential of extremely low material and manufacturing cost and they are flexible. A disadvantage is that organic materials have a limited lifetime especially in full sun and exposed to water and oxygen.

e. Dye Sensitized Solar Cell (DSS)Demonstrate the dye sensitize solar cell. Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Lightly coat the other slide with the carbon soot from a candle slide. Pinch the slides together with the binder clips so that the slides are offset exposing the conductive ITO layer. Apply iodide solution as an electrolyte and then.

f. Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.
Research Connection: CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

Brainstorm what characteristics would be desirable for a solar cell. Some possibilities power, costs, durability, flexibility, safety, ease of producing, environmental safe and plentiful materials.

*'''Research Connection:''' CCMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The research connects includes theoretical modeling of organic systems, synthesis, prototyping and testing.

<br clear='all'>

=== Series vs Parallel circuits ===
[[Image:Pv_parallel.jpg|thumb|300px|3 solar cells wired in Parallel ]]

a. Explain the difference between voltage and current. Show that the large panel produces a higher voltage (because it has several cell areas wired in series).
Measure the voltage and current produced from each cell using the digital meter. The wood test frame provides a convenient support and visual explanation of the circuit.

[[Image:Testcellholder.jpg|thumb|300px|]]

Note that the red lead must be moved and the selector switch set to mA to get the ammeter mode. Each cell has a characteristic voltage. Silicon cells produce between .5 -.6 V oc *(volts open circuit), OPVs are usually around .4 Voc. Use the clip leads and the three small panels to demonstrate that in a series circuit the voltage is added. In a parallel circuit the voltage does not change but the current (amperage) is increased.’

b. Compare the power for a 2 x 2 cm area for the crystalline solar cell compared to the same area of amorphous silicon cell.

P= V x I
Power (watts) = Volts x Amps

Sample calculation:
Volts = .4 V
Amp = 50ma= .05 amp
Power = .02 Watts

c. The amorphous panel provided is 7.2 V and 200 ma. How many of these panels would be needed to in what configuration to generate 100 Watts?

d. Experiment with different sources of light, sunlight, or diffuse vs. direct light

*'''Research Connection:''' CMDITR Engineers and scientists are trying to develop the next generation of solar cells using organic chemicals. The advantage of these is that they can be produced cheaply, they can put printed on plastic, and materials are available.

=== Power : area relationship ===

'''The larger the cross sectional area of the light beam that is trapped, the greater the power generated.'''

a. Cover portions of the panel to show decreasing current and voltage. Solar cells measured with the meter are under no load so you get the open circuit voltage (Voc). You should notice that the current responds quickly with decreasing light while the voltage stays somewhat stable, finally the voltage drops too. To measure the power from the panel you have to measure both voltage and amperage produced.

b. Plot the power versus area for the amorphous silicon panel. Complete the table and graph from BLM 1- Power vs Area Experiment

*'''Research Connection:''' OPVs could be less expensive even if they are less efficient which means a larger area could be deployed.

=== Power : distance relationship ===

<br clear='all'>
[[Image:479px-Inverse_square_law.svg.png|thumb|300px|]]
'''Energy from a radiant light source drops off with distance.'''

a. Use the electric meter to measure the current produced by the sample silicon cell as you move away from a light source. As you move away from a diffuse light source the same amount of light is spread over a large area so the solar panel only intercepts part of the energy. This called the inverse square law. If you use a focused light source this relationship will not hold. At the distance we are from the sun it does not make any measurable difference how close (for example sea level versus on mountain top) we place solar cells to the sun.

b. Collect data and graph the experiment using BLM 2 – Power vs Distance Experiment

=== Power : Incidence Angle relationship ===

<br clear='all'>
[[Image:Seasons.too.png|thumb|300px|Effect of sun angle on insolation]]
'''The angle with respect to the sun influences the energy output.'''

a. Set up the solar panel on its inclined support with protractor. Change the angle of the solar panel and measure the current. Changing the angle has the effect of decreasing the cross section of light that is intercepted. You can see this by measuring the shadow of the panel as it is tilted. In addition low angle sun on the Earth must pass through more atmosphere so some energy is absorbed.

b. Plot the current versus the angle. Complete the data and graph on BLM 3 Power vs Angle Experiment

c. Use this information to create a bar chart showing the total power generated by a cell during the course of day if the cell were fixed on a roof with an angle of 30 degrees. The peak angle of the sun on the spring or autumn equinox is 90- your latitude. At mid summer it is 90 – latitude -23.45 degrees. At mid winter it is 90 – latitude + 23.45 degrees

[[Image:Pv angle.jpg|thumb|300px|PV panel with battery charger and protractor]]

*'''Research Connection:''' Engineers have designed tracking systems that keep PV panels facing perpendicular to sun all day long. Others have explored using concentrators to reflect light to a smaller area where the cell is.

=== Measuring Absorption Spectrum ===

'''Photovoltaics absorb light at specific wavelengths.'''

a. Use the red, green and blue filters to show that certain colors when filtered out reduce the power more than other colors.

b. Plot the current versus wavelength when different colors are placed in front of the solar cell. You can use the large filter sheets or the filter sample booklets. Be sure to pick filters with approximately the same optical density. Use the attached transmission spectra tabs to pick colors that represent an even array across the spectrum. Complete BLM 4 Power vs Wavelength Experiment

c. Compare the amorphous silicon, the polycrystalline silicon cell, and the dye densitized solar cell.

*'''Research Connection:''' When we design chemicals to use in organic photovoltaics we measure the absorption spectra of the chromophores. Ideally we want dyes that absorb across the entire visible spectrum.

=== Measuring Efficiency ===

'''Efficiency is a measure of how much of the available energy is captured by a cell.''' It is the amount of electricity produced divided by the amount shining on the solar cell. To measure efficiency we have to know how much light energy is hitting the cell and how much electricity it is producing. It’s difficult to measure the incident light. Direct sunlight is between 250 and 1,000 W/m2.

a. In full sunlight measure the power of your solar cell and calculate the efficiency. In this example the cell has an area of 2.4 x 10-3 m2 , measuring .6 Volts and .5 amps in full sun

Pi = A * Ps = 2.4 x 10<sup>-3</sup> * 1000 = 2.4 watts

Po = V x I = 0.6 x 0.5 = 0.3 W

e = Po/Pi = 0.3/2.4 = 0.12 = 12%

b. Repeat this measurement for various cells.
=== PV Cost estimation ===

'''Solar cells are still somewhat expensive.''' Several factors have to be considered in sizing a solar system. Calculate how much area is needed to power a house, how much would it cost?

a. Solar cells currently run about $5-$9 per peak watt.

b. A house might require 2kW peak power

c. If the silicon cells are 15% efficient and the

d. Incoming energy is 1000 W/m2 assume 5 hours (5 kWh/m2) per day of useful sunlight or use the “Photovoltaics Solar Resource” map from NREL to identify the available solar resource for your area.

e. If you aren’t connected to the grid you will need batteries which cost $1 amp hour

*'''Research Connection:''' Materials and manufacturing process determines the cost. Organic photovoltaics have a potential of being low cost because they can be manufactured with roll printing methods. Further research is needed to get higher efficiency, better durability (through encapusulation and decreased photobleaching) New organic solar cells may be much cheaper in the future.

<br clear='all'>
=== PV characterization ===

'''Solar cells are characterized using a voltage- current curve.'''

a. Place the test PV cell in the wood test holder. Place an ammeter and a volt meter at the two pegs labeled A and V. Gradually change the series load in the circuit by sliding the variable resistor. Adjust the load to get an even series of voltage readings such as every .1 volts and record the amps for each voltage. Plot the data. The goal is to get a curve that is closer to a right angle (with a minimum fill factor). There is a certain combination of voltage and current that delivers peak power.

b. Complete BLM 5 Current vs wavelength experiment

*'''Research Connection:''' CMDITR researcher do this same measurement with much finer accuracy.

[[Image:Opv powercurve.jpg|thumb|300px|]]

=== Dye Sensitized Solar Cell ===

'''Organic pigments can be used to capture light to power electrochemical processes.''' Demonstrate the dye sensitized solar cell.Follow the separate directions to activate a titanium dioxide coated ITO slide to form a Graetzel cell. Beginning with a coated slide, add berry juice to sensitize the TiO2. Then apply iodide solution as an electrolyte and then pinch this together with the carbon black coated slide.

*'''Research Connection:''' Dye sensitized cells have begun commercial production as research continues.
[[Nanocrystalline_-_Dye_Solar_Cell_Kit| Build the complete dye sensitized solar cell activity for high school]]

== Links ==
[http://www.nrel.gov/learning/re_photovoltaics.html NREL]

[http://www.powernaturally.org/Programs/SchoolPowerNaturally/InTheClassroom/kitlessons.asp?i=9#Lesson14 Solar Cell lessons]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://www.infinitepower.org/pdf/No19%2096-828B.pdf Photovoltaic measurements Lesson]

[http://www.nrel.gov/midc/unlv/ live insolation data for Las Vegas NREL Solar Data]

[http://en.wikipedia.org/wiki/Solar_cell Wikipedia on solar cells]

[http://depts.washington.edu/cmditr/media/PlasticPV.ppt Plastic Solar Cell Poster]

[http://www.nanosense.org/activities/cleanenergy/solarcellanimation.html Solar Cell Animations]

[http://www.iop.org/EJ/article/0031-9120/41/5/005/pe6_5_005.pdf?request-id=e7503f0f-68f9-4217-bfe8-24c174c90fa5 Other chemicals for photovoltaics demo]

[http://www.teachersdomain.org/asset/hew06_int_ohmslaw/ Ohms Law Simulation from the Teachers Domain]

[http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/watcir.html Water analogy to circuits- Hyperphysics]

== Materials in the kit ==
*Sunzoom Lite car kit
*4 AA battery PV battery charger
*4 AA recharable NiCAD or LI ion batteries
*Solar mini car
*Digital Electric meter
*Protractor
*Ruler
== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/photovoltaics.docx Cover art for Optics Kit]

http://shop.pitsco.com/store/detail.aspx?CategoryID=115&by=9&ID=2647&c=1&t=0&l=0 $8. 95 sunzoom lite car

http://store.sundancesolar.com/subusobachki6.html 4 AA battery charger $39.95

http://store.sundancesolar.com/misorokitsus.html mini solar car $9.95

http://store.sundancesolar.com/ecdimu.html Electric Meter 2 a $12.95

Light Source for indoor use- quartz desk lamp

http://scientificsonline.com/product.asp?pn=3039810 Individual silicon cells 3 @ $5.95

http://scientificsonline.com/product.asp?pn=3085037 CIS Solar Panel 3 @ $2.95

Color Filter pack for testing cells

Rechargeable Batteries

Basic Optics - Outreach Kit

2010-03-15T17:26:59Z

128.95.39.187: /* Sources for Building your own kit */

<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[K-12 Outreach Introduction|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#K-12 Outreach Kits|K-12 Outreach Kits]]</td>
<td style="text-align: right; width: 33%">[[Photovoltaics- Outreach Kit|Next Topic]]</td>
</tr>
</table>
== Overview ==
The purpose of this kit is to introduce students about the basic properties of light such as color, straight beams, reflection, refraction and polarization. Each of these phenomena can be presented in a “discovery” mode in which students related their current knowledge by guessing what will happen. At a higher level some of the phenomena can be explained with formulas and confirmed with measurements. Following each demo description are ideas of how to tie the demo into the CMDITR science.

== User Guide ==
Key Concepts and Demos

=== Diffraction Grating ===

<br clear='all'>
[[Image:Diffraction fluorescent.jpg|thumb|300px|]]
'''White light is composed of many colors.''' Pass around the diffraction grating. Have them describe what they see. Are the colors the same for any light you look at? The diffraction grating is able to split white light into colors that make it up. (The diffraction grating works because of constructive and destructive interference, but this is higher level concept.) Students may be able to notice that the colors difference between an incandescent bulb, and LED and fluorescent bulb shown below. Connect this idea to other sources of rainbows colors such as a rainbow (reflection and dispersion within a drop of water), oil sheen on water (interference between nanolayers), or prisms (transmission and dispersion).

=== Additive Color Mixing ===

<br clear='all'>
'''When red, green and blue are added together they produce white.''' Pass out the color flashlights. These produce red, green and blue light. What happens when two or more colors of light are combined?
*A RGB monitor has tiny red, green and blue dots. All colors including white can be made by mixing these three colors. CMDITR research with organic light emitting diodes has led to OLED displays which use thousands of red, green and blue lights to make all the points on the display.

[[Image:Colorflash.JPG|thumb|300px|left]]
[[Image:800px-LCD RGB.jpg|thumb|300px|right]]

=== Color filters ===

<br clear='all'>
[[Image:Filterkit.JPG|thumb|300px|]]
'''Light can be absorbed.''' Ask students what they know about color. Pass out colored filter samples and have students look at the room. Which color filter makes the light of a certain color go away? Colored filters absorb different colors and let other colors through.

Ask which color paints are mixed together to make other colors. Is it possible to make white paint by mixing colored paints? (No this is because each color absorbs another part of the spectrum. If you added enough colors together eventually to would absorb all the light making black.) Have student pick three colors from the sample pack that when combined makes black or grey.

*a. Solar panels are black because they absorb many colors. We are trying to design new materials that can capture solar energy and convert the energy to electricity. We could make a blue solar cell. It would might pretty but it might not work as well as one that appears black. Why?

=== Spectroscope ===

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'''The color of light can be described by wavelength.''' You may not notice it but every light has its own unique color. A spectroscope is an instrument that lets you measure all the colors present in a light source. Point the spectroscope at a fluorescent light. Notice the green line that appears at the 5450 mark. Fluorescent bulbs are actually a little bit green. Some street lights are blue or even orange. This color depends on the chemistry of the materials used in the bulb. Now place a color filter #89 that only transmits color in the green part of the spectrum. Notice that the red line disappears from the fluorescent spectrum.

[[Image:Nasaspec.JPG|thumb|300px|]]

*LED s have distinct colors. Scientists and engineers are working to make LEDs that have light with the full spectrum of sunlight so colors look right. Other applications require LEDs with a very specific wavelength to match the material they must pass through such as plastic screens or fiber optics.
*We use instruments like the spectroscope to measure the light absorbed by chemicals we produce and to measure the light the color produce when they stimulated with lasers and electricity.
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=== UV sensitive beads ===
[[Image:30823-63ani.gif|thumb|300px|]]
'''Some portions of the electromagnetic spectrum is invisible.''' Point out the colors on the electromagnetic spectrum chart and show that some types of radiation are not visible. Pass out some UV beads. These are photochromic beads which change color in the presence of UV light but revert to white in the dark. Ask students if all light is visible. Have them place the beads in various places around the classroom under lights, in the dark and in the sun. Explain that UV light is invisible but very powerful and is the cause of sun burns.

*UV light is damaging to the body. It is also damaging to organic chemicals that we use in our solar cells. One of the challenges is to make design chemicals that do not break down in the presence of UV light.

=== Glow Paper ===

'''Some materials absorb light and then continue to emit it over time. Some colors of light do not have enough energy to excite these substances.''' Turn off the lights in the room. Use the three colored flashlights, the white flashlight, daylight and the red laser to stimulate the glow-in-the dark paper. The red light should not be able to make it glow even though the laser pointer is very intense. This is because the chemical in the paper requires a minimum energy of light in order to excite its electrons to a higher energy level. Once the higher level is reached the energy slowly decays back to the ground state emitting light that is observed as glowing.

*In photonics research we carefully match the color of light we are using excite a test substance with the chemical properties of the sample.

=== Laser pointer ===

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'''Light goes in a straight line until it interacts with matter.''' All light sources produce beams of light. Lighting usually produces many beams going many directions. A laser produces a very bright, focused beam. Use the laser show the path of a light beam. Laser light is used to guide rockets, in surveying or carpentry to line things up, or even to guide farm machinery. Place the laser along a flat surface such as the floor or table and show that it is not affected by gravity. Fill the plastic tub with water and add some powdered milk powder to make the light beam visible.

=== Mirrors and lasers ===

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[[Image:Laser_reflection.jpg|thumb|300px|]]
'''Light can be reflected.''' First ask what kinds of objects reflect light. Test the theories about what will reflect by pointing the laser at the objects that are suggested. They should be able to describe the quality of shiny, glassy or metallic being needed for mirrors. Place a mirror on the block which is attached to a protractor. Place the cylinder lens end tip on the laser so that it produces flat line instead of a dot. Orient the line so it is vertical (with the cylindrical lens horizontal). This will make it easier to see the light ray and its reflection on the table. Use the protractor to measure the angle of light coming in (angle of incidence) and the angle of reflection. What is the rule for this? (the angle of incidence equals the angle of reflection) Challenge: what arrangement of mirrors would be needed to reflect a laser beam into a complete circle? Optical fiber has smooth surfaces and narrow diameter. Light reflects inside the tube until it emerges from the end. This is called total internal reflection.

* a. We do many experiments with lasers that pass through many lenses, filters and sensors on a special optics table. We move the laser beam around the table using mirrors and large optical fibers. Some lasers are so powerful they can burn a hole in wood if the beam is absorbed. Mirrors can reflect this light without getting hot at all.

=== Refraction with grow cubes and prisms ===

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'''Light can be refracted.''' One day before the demonstration place several of the optic grow cubes into water in a plastic bag. Each cube will expand into a 3 cm, optically clear cube. Use the single edge razor to cut the cube into various shapes used in optics. Alternatively cast a sheet of clear gelatin using three times as much gelatin as is called for on the recipe. Use the laser pointer to show how lenses and prisms work. Try making a convex lens, a concave lens, an equilateral prism, a fiber optic tube, a periscope with right angle prisms.

[[Image:Growcube.JPG|thumb|300px|left|Optic grow cubes]]
[[Image:Cubesplit.png|thumb|300px|right|Prism shape]]
[[Image:Cubeconvex.png|thumb|300px|left|Convex lens shape]]
[[Image:Cubeconcave.png|thumb|300px|right|Concave lens shape]]
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Use the acrylic prism set to demonstrate various optics phenomena. If possible use two lasers to show parallel beams.
[[Image:Lenskit.jpg|thumb|400px|left|Equilateral prism, plano convex, double concave, double convex and square prisms shapes.]]

[[Image:Lens1.jpg|thumb|400px|Use the barrel lens attachment to the laser pointer to demonstrate refraction in the acrylic lens.]]
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*We use lenses to focus light to a point for experiments, or to make a wide parallel beam.

=== Polarizing Filters ===

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[[Image:Polarizer.JPG|thumb|300px|]]
'''Light waves can be random or polarized in one direction. ''' Polarized materials only allow light with a certain orientation to pass through. Have two students hold the nylon rope and generate a wave in the crossways direction. Place two straight back chairs back to back on either side of the rope so that it’s horizontal movement is limited. The waves will be dampened. Ask the students to generate a wave in the up and down direction. This will pass through between the chairs. This how a polarized light is blocked or passed through a polarizing filter.

Use the polarizing filters to show that light from a laser or from an LCD monitor can be almost completely blocked as the filter is rotated. Two filters can be used to block non polarized light.
<br clear='all'>
[[Image:Polarizefork.JPG|thumb|300px|]]
Clear materials such as plastics can change the polarity of light when they are under stress because their molecules get aligned in a certain way by forces. If you place a clear plastic spoon between two polarizing filters or between an LCD monitor (a polarized light source) and a polarizing filter you can see rainbow colored patches where light is being blocked or refracted in response to stresses in the material.

*Liquid crystal displays have a polarized light source. The liquid crystal chemicals can be rearranged when electricity is applied to change the way they polarize light and thus let certain light pass through under the red, green and blue cells. This property can be used to control light in fiber networks and computers.

*CMDITR is creating new organic materials that can change their polarization in an electric field or when light of specific wavelength is provided.

=== Lasers and diffraction grating ===

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[[Image:Laser_diffraction.jpg|thumb|300px|]]
'''Lasers light is coherent and a precise wavelength.''' Place a diffraction grating in front of the laser pointer. There will be three dots, one for straight transmission and two diffracted dots on either side. Compare this to the pattern that appears from looking at a fluorescent bulb with a diffraction grating.
*Researchers pick lasers that have precisely the wavelength they need for their experiments. For example most optical fiber communications operate at 850nm or 1300 nm wavelength.

10) Advanced- See experiments 6, 7, 8 of the laser

== Links ==
[http://www.osa.org/educationresources/youtheducation/classroommaterials/default.aspx OSA classroom materials including the Optics Suitcase]

[http://www.opticsinfobase.org/DirectPDFAccess/B6E443C1-BDB9-137E-C94173B9BE83A7E2_184936.pdf?da=1&id=184936&seq=0 Gelatin Optics Activity]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.hands-on-optics.org/resources/ Hands On Optics from OSA, SPIE and NOAO]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.osa.org/educationresources/youtheducation/classroommaterials/LightenUpWeb2.pdf Lighten Up - OSA and Girl Scouts]

== Sources for Building your own kit ==
[http://depts.washington.edu/cmditr/media/optics.docx Cover art for Optics Kit]
*Color filters
*Nasa Spectroscope
*LED Flashlights with color filters
*Laser educational kit (laserpointer with lenses, filters, mirrors, diffraction grating)
*Grow Lens Cubes
*Prism Kit
*Glow Paper
*Polarizing filters
*Nylon rope
*UV Beads

* http://www.i-fiberoptics.com/laser-kits-projects-detail.php?id=2240 $51 Laser pointer education kit class II red laser pointer
* http://www.arborsci.com/detail.aspx?ID=1428 grow lens cubes (100s) $8 (clear gel to play with lens shapes)
* http://scientificsonline.com/product.asp_Q_pn_E_3053471 Acrylic prisms set $34
* http://scientificsonline.com/product.asp?pn=3081936 Mini Blacklight 3081936
* http://www.arborsci.com/detail.aspx?ID=37 Large Color filter Product ID: 33-0190 pack $12
* http://www.arborsci.com/detail.aspx?ID=894 Individual filter paddle samples $12
* http://www.officedepot.com/catalog/vendorRouter.do?configurableItemType=NORWOOD&id=976090 White flashlights 4 x $5
* http://www.arborsci.com/detail.aspx?ID=928 Glow paper $3.95
* http://www.arborsci.com/detail.aspx?ID=395 slide mounted polarizing filters( 50) $33
* http://www.arborsci.com/detail.aspx?ID=462 UV beads $5*
* http://solar-center.stanford.edu/posters/ Nasa Spectroscopes $7

Perturbation Theory

2010-03-11T23:42:51Z

128.95.39.187: /* Perturbation techniques */

=== Hellman-Feynman Theorem ===

The Hellman-Feynman Theorem, which expresses the dipole moment as minus derivative of the energy of the system with respect to the field. This equation expresses the response of a molecule which is 2nd order in terms of the energy of the molecule and first order in terms of the dipole moment of the molecule (1st order or 2nd order with respect to the field).

:<math>\overrightarrow {\mu} = - \frac {\delta E} {\delta \overrightarrow{F}}\,\!</math>

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} + \frac {1} {2!} \beta \overrightarrow{F}\overrightarrow{F} + \frac {1} {3!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>\frac {\delta \overrightarrow{\mu}}{\delta \overrightarrow{F}} = \alpha + \beta \overrightarrow{F} + \frac {1} {2!} \gamma \overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

=== Stark Energy Expression ===
Alpha is the linear polarizability or the first order polarizability. It describes how the molecule responds in terms of the modification of its ground state energy or of its dipole moment, in the presence of the field at the limit where the field goes to 0. Thus, alpha can be cast either as the 1st order derivative of the dipole moment with respect to the field when the field tends to 0 or minus the 2nd order derivative of the ground state energy of the molecule with respect to the field when the field goes to 0.

:<math>\alpha = \left( \frac {\delta\overrightarrow{\mu}}{\delta \overrightarrow{F}}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Beta is the 2nd order derivative of the dipole moment with respect to the field when the field goes to 0. Beta will be referred to as the 2nd order polarizability of the molecule. This can also be derived from the stark energy expression which is the 3rd order derivative of the energy with respect to the field when the field tends to 0.

:<math>\beta = \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Lastly, the gamma term corresponds to the 3rd order derivative of the dipole moment or minus the 4th order derivative of the energy with respect to the field at the limit where the field goes to 0. Gamma will be referred to as the 3rd order polarizability of the molecule.

:<math>\gamma = \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>
Stark energy describes the evolution of the energy of a system of particles in the presence of an electric field F. In the Stark energy expression, gamma corresponds to a 4th order term. However the in common terminology alpha is referred to as the linear polarizability, beta the 2nd order polarizability, and gamma the 3rd order polarizability. The Hellman-Feynman Theorem is the origin of these terms. Here it is presented as a Taylor series expansion, sometimes one uses a power series expansion.

:<math>
E_g = E^\circ_g = \overrightarrow{\mu}^\circ \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}\overrightarrow{F} - \frac {1} {3!} \beta \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} - \frac {1} {4!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>= E^\circ_g - \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

=== Electric dipole approximation ===
The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as :

<math>\mu^\circ + \alpha F + \beta F^2 ... \,\!</math>

and so on, without paying any attention to where that expression comes from.

:<math>- \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

in dimensional analysis:
:<math>\mu \equiv\,\!</math> charge * distance
:<math>F \equiv\,\!</math> volt/distance
:<math>\mu F \equiv\,\!</math> charge * volt :<math>\equiv\,\!</math> energy

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as μ<sup>not</sup> plus α * f plus β * f <sup>2</sup> and so on, without paying any attention to where that expression comes from.

:<math>\overrightarrow{\mu} = e \sum(i) \overrightarrow{\pi}_i 9i\,\!</math>

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

=== Perturbation theory ===
The perturbation theory will not be discussed at the quantum- mechanics level. The energy of the ground state of the system is the energy for the unperturbed system. Perturbation can be observed at different orders. At first order, the perturbation is referred as w. If that perturbation is the impact of the electric field of the light in the electric dipole approximation, the perturbation can be expressed as minus μF.

At the first order, the perturbation is operating on the unperturbed wave function of the ground state. Perturbation theory involves modification of systems due to the perturbation of all the wave functions for the unperturbed system. At first order, the perturbation is simply acting on the ground state wave function. Then it is integrated over space and the complex conjugate is taken. At second order, the wave functions of the excited state are taken into account to describe the modification of the system. An unperturbed system has a well defined wave function for the ground state and well defined wave functions for the excited states. The perturbed system is described on the basis of the wave functions of the unperturbed system.
:<math>=\int \Psi* e \overrightarrow{\pi} \Psi dr\,\!</math>

:<math>E_g = E^\circ_g + \langle \Psi_g | w | \Psi_g \rangle + \sum_p \frac {\langle \Psi_g | W | \Psi_p \rangle \langle \Psi_p | W | \Psi_g \rangle + ...}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>E_g = E^\circ_g -\overrightarrow{\mu ^\circ} \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}^2 - ....\,\!</math>

:<math>W = - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

In terms of non-linear optics, the perturbation theory expressions will show what the excited states are in your isolated molecule that will contribute to the linear polarizability, 2nd order polarizability, or the 3rd order polarizability and allow you to pinpoint exactly what excited states do play a major role in your optical response.

The complete set of wave functions for the unperturbed state will form the basic set for the perturbation expressions. In principle this includes all excited states. The 2nd order term in terms of perturbation and will correspond to alpha, the linear polarizability. In most conjugated systems, only the first excited state needs to be examined. This will often be the case for alpha and pi conjugated systems as well as for beta. But not for gamma in which two or more excited states must be taken into account. However, the number of states that need close attention can be heavily restricted.

:<math>E_g = E_g^\circ - \underbrace{\langle | \Psi_g | W | \Psi _g \rangle} \overrightarrow{F} + \,\!</math>

::::<math>\overrightarrow{\mu^\circ}\,\!</math>

:<math>\underbrace{\sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}}\,\!</math>

:::::<math>-\frac {1} {2!}\alpha\,\!</math>

A one to one correspondence can be made between the terms in the stark energy expression and the perturbation theory expression when the perturbation is minus μF.

As a side note, as you go to higher orders, things will look a bit more complicated because there are more summations over excited states. For example in 3rd order, there will be a double summation over excited states. In 4th order, there will be a triple summation over excited states. But it will always be products of matrix elements of this kind at the numerator, and the differences in energies of the states for the unperturbed molecule will be in the denominator. The expressions look more complex but by looking at the terms individually, notice that the same kind of terms come up.
P is summation over all excited states

- μF is the electric dipole approximation. The operator expression, μ is the unit electric charge times the position, which is the dipole moment. The electric field does not do anything to the wave functions of the unperturbed state. This expression here? is the expression of the dipole moment for the ground state Φ<sub>g</sub> is the wave function of the ground state in the unperturbed state, which is simply μ<sup> &o;</sup>. At first order, the goal is to find the possible dipole moment. If there is a central symmetry, there won’t be any permanent dipole moment of the molecule. If there is a permanent dipole moment, there will be an interaction between that permanent dipole moment and the external field. At second order, the expression includes the summation over all the excited states p. Here perturbation is replaced by its expression er. Since this deals with the wave functions of the unperturbed system, the electric field is outside. This shows a transition dipole between the ground state and excited state p. and the transition dipole between excited state p and the ground state. These terms are equal. They are the exact same transition dipole. The denominator is the square of the transition dipole between the ground state and excited state p.

The numerator is the difference in energy between the ground state energy and the excited state energy.
Finally, by closely examining the stark energy expression, a connection can be made between the term that is linear in the field, μ<sup>o</sup>F minus ½ α. This shows the expression for alpha as a function of this perturbation expression.

:<math>\alpha=2 \sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>=2 \sum \frac {M_{gp} ^2} {E^\circ _{gp}}\,\!</math>

In this expression there is no longer a minus sign because the denominator is reversed; E of Pnot – E of gnot.

Now there is a compact expression where alpha is equal to 2 times the summation over all excited states of transition dipole with state p times? transition dipole with state p over the transition energy. Taking into account of the perturbation theory, alpha, the linear polarizability, can be described as a sum over all excited states of the square of the transition dipole between the ground state and the excited state, over the transition energy from the ground state.

[[Image:Perturblevels.png|thumb|300px|]]

A pictorial description shows the process of going from the ground state to excited state p and that is a transition dipole between g and p. There is also another transition dipole when coming back from p to g. That is why the expression for alpha shows transition dipole squared. As previously explained, the expressions for beta will look more complex due to the double summations over excited states. The expression for gamma will look even more complex due to the triple summations over excited states. However for all instances, the numerator will always be products of transition dipoles and the denominator will contain the transition energy. In the literature, the perturbation theory expressions are also referred to as “sum over states expressions” the expression contains the sum over all excited states.

A few important questions include “What is the impact of the perturbation on the energy of the system?” and “Would it stabilize or destabilize the system when looking at the perturbation at different orders?”.
It is crucial to understand the differences and variations in conventions. Suppose you want to calculate the dipole moment of the molecule using two programs. First, you input the geometry of the molecule exactly in the same way for both programs. Then, you run the calculation. One program gave a dipole moment of +1.3 Debye, but the other program gave you a dipole moment of -1.3 Debye. Why is there a difference? The difference occurs because the conventions are different for chemists and physicists.

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>\overrightarrow{\mu}= \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F}+ 1/2 \beta \overrightarrow{F}\overrightarrow{F} +1/6 \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} ...\,\!</math>

Before physicists discovered the nature of electrical charge and electrical current, there wasn’t a way to identify whether the charge carriers were positively or negatively charged. Therefore, they made an assumption that it was positive charge that moves . But it turned out that their guess was wrong. We now know, it is the negatively charged electrons that provide electrical conductivity in metals or materials. Thus, in many of the conventions, physicists traditionally observe how the positive charge moves. Whereas chemists look at the displacement of an electron. As a result, the dipole moment can be written as going from left to right if you have a donor-acceptor molecule.

Suppose a quasi one dimensional D-conjugated bridge -A molecule with z the long axis and then apply an external field along z.

:<math>\overrightarrow{\mu}^\circ\,\!</math>
:<math>\rightarrow\,\!</math>

D ----- conjugate -------- A

:<math>\rightarrow\,\!</math> :<math>\overrightarrow{F}_x\,\!</math>
:<math>\leftarrow\,\!</math>

It can also be written, as going from right to left. Suppose that we have a donor acceptor molecule with a conjugated bridge between the two. In linear quasi- 1-demensional type molecules, the whole optical or non-linear optical responses will occur along the axis Z of the molecule.

=== Stabilization ===

<br clear='all'>
[[Image:Stabilization.png|thumb|300px|]]

Assume you have molecule that has a positive pole and a negative pole. You can place an electric field along the main axis in two directions. At the first order you will only observe the permanent dipole moment of the molecule and its interaction of the field; thus you have a permanent dipole moment period. You have a plus and a minus. It is also important to know which situation, the one on the top or the one on the bottom, will be more stable. As a matter of fact, the one at the bottom will be the most stable situation. This is because when you have two dipole moments on top of one another, the anti-parallel? situation will be much more favorable then the parallel situation. In anti-parallel situation the positive charge is stabilized by the negative pole of the electric field and the negative charge is stabilized by the positive pole. Where as in the parallel situation there is a destabilization. Therefore, independently from the conventions in terms of the electric field and the dipole moment, it is clear which situation will lead to a net stabilization of the energy of the system and which one will lead to a destabilization.

At first order, nothing changes within the molecule.

At second order you will have a flux of electrons towards the left to counteract the external field in the lower case, and in the upper case you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself. At third order, it gets more complicated.

'''First order energy term'''
:<math>E(\overrightarrow{F}) - E^\circ = - \overrightarrow{\mu^\circ} \overrightarrow{F}\,\!</math>

:<math>= - \overrightarrow{\mu}_z ^{ \circ}- \overrightarrow{F}_z\,\!</math>

There is stabilization if :<math>\overrightarrow{F}_z\,\!</math> is parallel to :<math>\overrightarrow{\mu}^\circ\,\!</math>

There is destabilization if :<math>\overrightarrow{F}_z\,\!</math> is anti-parallel to :<math>\overrightarrow{\mu}_z^{\circ}\,\!</math>

In other words, with the indicated conventions, stabilization will occur if the field is parallel to the dipole moment and destabilization will occur in the opposing case. But again, that depends on the conventions chosen for the field and dipole moment. Remember that at first order in the field ( the linear term of the energy expression) only the interaction between the permanent dipole moment, is examined. However, at higher orders, we examine how the system responds to the external field on the molecule. As a result, we look at the polarizabiliy, or in the case of alpha the linear polarizability. In perturbation theory the second order term gives the stabilization.

This can easily be seen from the previous expression. Alpha is a summation over all excited states of the squares of the transition dipole, which makes it positive. The transition energy going from the ground state will always be positive by definition of the ground state.

'''Second order energy term'''
:<math>- \frac{1}{2} \alpha_{zz} \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

Alpha is positive and we multiply by F times F, which will be positive. Therefore, the whole second order term leads to a stabilization of the system.

Think back about the simple example shown previously. At first order, nothing changes within the molecule. At second order, look at the response of the molecule to the external field. What will happen here? What will happen is that you will have a flux of electrons towards the left to counteract the external field, and here you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself.

Alpha is a tensor of rank two and there are nine tensor components for alpha. Beta is a tensor of rank three. Since each of these indices can be x y z, there will be a possible of 27 tensor components.
'''third order energy term'''
:<math>- \frac{1}{6} \beta_{zzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

There is stablilization or destablization depending on whether :<math>\overrightarrow{F}_z\,\!</math> is parallel or antiparallel to the vectorial part of β, and depends on the sign of β which depends on Δ μ <sub>eg</sub>

In a two state model expression, beta depends very much on the difference in state dipole moment between the ground state and the active excited state. Β will be positive if that active excited state has a dipole moment that is larger than the dipole moment in the ground state, and β will be negative if the dipole moment in the excited state is smaller than in the ground state. This is an easy way of understanding the variation in the sign of β.

'''Fourth order energy term'''

:<math>- \frac{1}{24} \gamma_{zzzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\overrightarrow{F}_z\,\!</math>

This is stabilizing if γ is >0 and destabilizing if γ is <0

For fourth order, in this case, the field components would lead to a positive term by necessity. Thus, we will have either stabilization if γ is positive or destabilization if γ is negative. This is consistent with the process called the self-focusing of light in the material with positive γ. If you shine a high intensity laser light into a molecule that has a very large positive γ response, the beam will self-focus. The system tends to go to higher local fields and therefore obtain a larger stabilization by focusing the light. Where as a negative γ leads to a defocusing of your light. This property can be use for protection from high intensity light.

Gamma is a tensor of rank four and there will be 81 tensor components. When looking at extended π conjugated molecules, (quasi 1-dimensional) the components along the long axis of the molecule will dominate everything. However, with molecules that become more complex in shape there are a number of components that can become important as well. Also, there are symmetry relationships among those components. In the literature on non-linear optics, there is something referred to as Climan symmetry that is based on the point groups of the different molecules that gives the relationship between the different tensor components. However, here we are mostly concerned with at the α<sub>zz</sub> component, the β<sub>zzz</sub>, or γ<sub>zzzz</sub> What will be provided is a difference between the global value and the tensor component along the main axis. It is difficult to know whether the third order term leads to stabilization or destabilization because β could be positive or negative. Also, the combination of the three field terms can be positive or negative so it really depends.

=== Dipole changes ===
We can also look at what happens to the dipole moment. In the case of the α, the permanent dipole can be zero if we have a centrosymmetric molecule or it can be any value depending on the nature of the molecule. If it is non-centrosymmetric there will be an increase or decrease depending on the direction of the field at first order.

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} = \overrightarrow{\mu^\circ_z} + \alpha \overrightarrow{F_z}\,\!</math>

First order: The dipole increases or decreases according to whether F<sub>z</sub> is parallel or antiparallel to :<math>\overrightarrow{\mu^\circ_z}\,\!</math>

Second order:

The change depends on how the field is aligned with respect to the permanent dipole moment. At the next order FF is always positive so dipole it will be decided by the value of β. The sign of β can often be related to the difference in dipole moment between the ground state and the active excited state. If there is an increase in the dipole moment going from the ground state to the excited state, β will be positive. That excited state now contributes to the description of the system because with a larger dipole moment, it is reasonable to assume that the μ of the system will increase. The opposite will occur for a negative β. All these considerations will become clearer when the perturbative expressions for beta and gamma are discussed in detail.

:<math>1/2 \Beta : \overrightarrow{F} \overrightarrow{F}\,\!</math>

In the context of the two state model, beta has a sign of :<math>\Delta \mu_{eg}\,\!</math>

:<math>\beta >0 : \mu \uparrow\,\!</math>

:<math>\beta <0 : \mu \downarrow\,\!</math>

Third order
For the impact of γ, the dipole moment depends on the sign of γ and the field alignments in the expression of the dipole moment. There will be three fields that will play a role.

=== Calculation of polarizabilities ===
Polarization of a medium due to an electric field.

In spite of the different conventions used to look at the physics of the system, it is good enough to just look at what the external field with respect to the permanent dipole moment does. Papers in the field of non-linear optics, especially for inorganic materials, often look at the macroscopic polarization that occurs when the field is applied. Since the experimentalists are not concerned with the possible derivations that are necessary when calculating α, β, γ, they often use an expression that is a power series expansion instead of a Taylor series expansion.

This expression of the polarization of the medium corresponding to the possible permanent polarization when the material is non-central symmetric. The expression contains a first order term which is the first order electrical susceptibility. Remember, the :<math>\chi^{(1)}\,\!</math> is a tensor; there will be 9 tensor components there. That is the equivalent of α for the microscopic scale.

:<math>\overrightarrow{P} = \overrightarrow{P_0} + \chi^{(1)} \overrightarrow{F} + \chi^{(2)} \overrightarrow{F}\overrightarrow{F} +\ chi^{(3)} \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} +\,\!</math>

:<math>\chi^{(1)}\,\!</math> is the first order electrical susceptibility (second rank tensor).

:<math>\chi^{(2)}\,\!</math> is the first order electrical susceptibility (third-rank tensor).

:<math>\chi^{(3)}\,\!</math> is the third order electrical susceptibility, and so on.

Only :<math>\chi^{(1)}, \chi^{(2)}, \chi^{(3)}\,\!</math> will be considered, although experimentally there are people that have shown :<math>\chi^{(5)}, \chi^{(6)}\,\!</math> processes that are very specific.

Molecular materials at the microscopic level

:<math>\overrightarrow{\mu} = \overrightarrow{\mu_0} + \alpha \overrightarrow{F} + \beta \overrightarrow{F} \overrightarrow{F} + \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

where

:<math>\alpha\,\!</math> is first order polarizability

:<math>\beta\,\!</math> is the secord order polarizability or first order hyperpolarizability

:<math>\gamma\,\!</math> is the third order polarizability or second order hyperpolarizability

This is the corresponding expression for the dipole moment of a given molecule on the microscopic level. It is expressed in the power series expression. α is referred to as the polarizability. In the context of non linear optics, when looking at the β and γ terms, α can be more rigorously referred to as the first order polarizability. β is the second order polarizability or (some people prefer to use the expression) first order hyperpolarizability. γ is the third order polarizability or the second order hyperpolarizability. The reason why μ is expressed in both a power series expression and in a Taylor series expression is that most of the programs that make calculations use Taylor series expansion. However, the β or the γ that one calculates can differ from one program to another. It can differ by a factor of 2 for β, and by a factor of 6 for γ. Therefore, it is wise to also compare your calculated data with what is reported experimentally. Usually, experimentalists use a power series expansion. Thus, if they had done the calculation taking into account the Taylor series expansion, they will have immediately a difference by a factor of 2 or a factor of 6 with the experiment.

'''Stark Energy'''

Switching back to the Taylor series expressions. This shows the stark energy expression written in a more rigorous way taking into account for all the possible components of the field and for the tensor components of the α, β, and γ tensors.

:<math>E(F) = E_0 - \sum_{i} \mu_{0i}F_i - \frac {1} {2!} \sum_{ij} \alpha_{ij} F_i F_j - \frac {1} {3!} \sum_{ijk} F_i F_jF_k - \frac {1}{4!} \sum_{ijkl} \gamma_{ijkl} F_i F_j F_k\,\!</math>

'''Dipole Moment'''

This shows a similar expression for the dipole moment. These two expressions are fully consistent with each other, given the Hellman-Feynman theory.

:<math>\mu_i(F) = \mu_{0i} + \sum_j \alpha_ij F_j + \frac {1} {2!} \sum_{jk} \beta_{ijk} F_j F_k + \frac {1} {3!} \sum_{jkl} \gamma_{ijkl} F_j F_k\,\!</math>

:<math>\mu_i = - \frac {\partial E(f)}{ \partial F_i}\,\!</math>

These expressions clearly show what was confirmed earlier regarding the tensors and its respective rank. For example, γ will be a tensor of rank 4 because you are looking at the impact on the i component of the dipole moment when applying a field along j, a field along k, or a field along L. That is the reason why the α, β, and γ contain all those tensor components.

:<math>\alpha_{ij} = -\frac{ \partial ^2E(F)} {\partial F_i \partial F_j} = \frac {\partial ^1 \mu_i} {\partial F_j}\,\!</math>

:<math>\beta_{ijk} = -\frac{ \partial ^3E(F)} {\partial F_i \partial F_j \partial F_k} = \frac {\partial ^2 \mu_i} {\partial F_j \partial F_k}\,\!</math>

:<math>\gamma_{ijkl} = -\frac{ \partial ^4E(F)} {\partial F_i \partial F_j \partial F_k \partial F_l} = \frac {\partial ^3 \mu_i} {\partial F_j \partial F_k \partial F_l}\,\!</math>

=== Derivative Techniques ===

From those derivative expressions and the perturbative expressions, two types of calculations can be derived to evaluate the molecular polarizabilities from quantum-mechanical approaches. There is one major set of calculations that involve the derivation of either the energy or the dipole moment with respect to the external field. Those derivations can be done either numerically using methods referred to as finite-field methods, or analytically using Coupled Perturbed Hartree-Fock (CPHF) methods.

In a finite-field calculation, you take the interaction with the external field and put it into your Hamiltonian for the isolated molecule without any external perturbation. It has a kinetic term, a nucleic attraction term, a coulomb term, and exchange term. Now here, a fifth term is added to those present four terms. The fifth term expresses the interaction with your field. Several calculations are then made in which several values of the external field are taken into account. Then you do a numerical derivation of the dipole moments that you will have calculated as a response to the external field.

:<math>H(\overrightarrow{F} = H_0 - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

The MO's are self-consistant with the eigenfunctions of :<math>H(\overrightarrow{F})\,\!</math>. What is interesting with those finite field methods is that since the perturbation interaction with the electric field is put into the Hamiltonian, the molecular orbitals that are derived are affected by that interaction. Then the α, β, γ tensor components are calculated by applying standard numerical procedures. Calculations are made with different values of the field. Different values of for dipole moment for the molecule are obtained. A numerical derivation is then made to get to α, β, and γ. For instance, two calculations are made for the α <sub>ii</sub> component. The calculation is made with the field in one direction, and then again with the field in the opposite direction. It is important to have a value of the field that is large enough so that the molecule can respond and give a numerically accurate variation in the dipole moment. However, it should not be too large or the equivalent of a dielectric breakdown of your molecule will be obtained and the calculation will simply not converge. Therefore, it is crucial know what values of the fields are needed to evaluate.

:<math>\alpha_ii = \frac {\partial\mu_i} {\partial F_i} = \frac {1}{2F_i} [\mu_i(F_i) - \mu_i(-F_i)]\,\!</math>
:<math>
\gamma_{iiii} = \frac {\partial^3 \mu_i} {\partial F_i \partial F_i \partial F_i} = \frac {1} {48F_i^3} [\mu_i(3F_i)-\mu_i(-3F_i)- 3\mu_i (F_i)+ 3\mu_i (-F_i)]\,\!</math>

We pick a compromise value that is able to insure accuracy but also avoid divergence.

:<math>F_i \approx 5 x 10^8 Vm^{-1}\,\!</math>

'''Coupled perturbed Hartree-Fock method'''

Another method that can be used to make those calculations is the analytical methods with analytical expressions for the variation of the energy with respect to the electric field.

:<math>\beta_{ijk} = - \frac {\partial^3 E(F)} {\partial F_i \partial F_j \partial F_k}\,\!</math>

=== Perturbation techniques ===

'''Sum over state (SOS) method'''
Besides making numerical or analytical calculations based on the derivation expressions, the perturbation theory expressions can also be used. This method is usually referred to as Sum Over States (SOS) method. This method was seen before for alpha. It is based on the perturbation expression for Stark energy terms which are related to optical nonlinearities based on their order in the field strength. α is calculated by evaluating the transition dipoles and the transition energies for all the excited states in the molecule.

You can look at the convergence of your values as a function of going over many excited states. However, it is important to understand that the higher energy you go, the larger the denominator becomes. Therefore, those terms will have smaller weight. Also, at very high excited states, the transition dipole will die down as well. For example, in the case of α the lowest excited states have the largest response.

:<math>\alpha_{ij} = \sum_m \frac {<\psi_0|\mu_i | \psi_m > <\psi_m|\mu_j | \psi_0 >} {E_m- E_0}\,\!</math>

For the β terms, we have exactly the same components. However, the expression looks more complicated because it contains a double summation over excited states. That is transition dipole going from the ground state n to excited state to m. Then it goes from excited state m back to the ground state. The denominator has the transition energies. There is also a second term that goes over a summation over excited state due to the dipole moment starting in the ground state. Then there is a transition dipole going from the ground state to excited state n and then it comes back from n to the ground state, over transition energies. To generate these expressions go through the perturbation theory and work the second order and the third order perturbation theory expression, one can do so by placing the dipole (er), the dipole operator, and the electric field.

:<math>\alpha_{ijk} = \sum_n \sum_m \frac {<\psi_0|\mu_i | \psi_n > <\psi_m|\mu_j | \psi_0 ><\psi_m|\mu_k | \psi_0 >} {(E_n- E_0)(E_m- E_0)} - \sum_n \frac {<\psi_0|\mu_i | \psi_0 > <\psi_0|\mu_j | \psi_n ><\psi_n|\mu_k | \psi_0 >}{(E_m- E_0)(E_n- E_0)}\,\!</math>

The reason why it is interesting to evaluate the non-linear optic properties with those perturbation expressions (sum over state expressions) is because it pinpoints which excited states play important roles in optical and non-linear optical response. Another reason why they are heavily exploited is because the frequency dependence can easily be introduced with the response. With the finite-field method, it gets extremely complicated to introduce the frequency dependence.

The finite-field method is usually incorporated in many quantum chemistry packages. You just press key telling “calculate the molecular polarizabilites” and then you get numbers for those polarizabilites. However that is the problem; it only gives numbers and these are the static values where ω is equal to zero.
It doesn’t provide an in depth understanding of what is occurring. There have been extensions to those methods that provide some kind of understanding regarding finite field methods of the local spatial contributions to the non-linear optical response. But it is a sophisticated approach that is not often used. Thus, in many instances, it more beneficial to use the sum-over states expression because it gives an idea of which electronic states matter. Also, frequency dependence can easily be introduced. The same thing can be done at the γ level.

:<math>\beta^{SHG}(-2\omega;\omega \omega) = 1/2 \sum_n \sum \_m \frac {<\psi_0 | \mu_i | \psi_n><\psi_n|\mu_j|\psi_m><\psi_m |\mu_k|\psi_0>} {(\hbar\omega-(E_m-E_0))(2\hbar\omega-(E_m-E_0))}\,\!</math>

where

:<math>(\hbar\omega-(E_m-E_0))\,\!</math> represents one-photon resonance

:<math>(2\hbar\omega-(E_m-E_0))\,\!</math> represents two-photon resonance

Useful simplifications can be introduced if it is found that a single excited state dominates second order polarizability.

In the case of the first term, when the excited state m is different from excited state n, it will go from the ground state to m and then to n,. Then from n back down to the ground state. This slide shows the pictorial description of the products of the transition dipoles. However, if m is equal to n, you will go from the ground state to m, but then stay on m. Then you will come back down to the ground state. Staying on m if m is equal to n simply means that the state dipole moment of excited state m is being observed. Then there is a second term here that comes with a minus contribution where you have the state dipole in the ground state, and then you go from the ground state to m and then from m back to the ground state. This is the pictorial way that can describe the 3 different types of terms is found in the sum over states expression.

[[Image:Example.jpg|thumb|300px|]]

Perturbation Theory

2010-03-11T23:27:58Z

128.95.39.187: /* Perturbation techniques */

Perturbation Theory

2010-03-11T23:27:15Z

128.95.39.187: /* Perturbation techniques */

=== Hellman-Feynman Theorem ===

The Hellman-Feynman Theorem, which expresses the dipole moment as minus derivative of the energy of the system with respect to the field. This equation expresses the response of a molecule which is 2nd order in terms of the energy of the molecule and first order in terms of the dipole moment of the molecule (1st order or 2nd order with respect to the field).

:<math>\overrightarrow {\mu} = - \frac {\delta E} {\delta \overrightarrow{F}}\,\!</math>

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} + \frac {1} {2!} \beta \overrightarrow{F}\overrightarrow{F} + \frac {1} {3!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>\frac {\delta \overrightarrow{\mu}}{\delta \overrightarrow{F}} = \alpha + \beta \overrightarrow{F} + \frac {1} {2!} \gamma \overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

=== Stark Energy Expression ===
Alpha is the linear polarizability or the first order polarizability. It describes how the molecule responds in terms of the modification of its ground state energy or of its dipole moment, in the presence of the field at the limit where the field goes to 0. Thus, alpha can be cast either as the 1st order derivative of the dipole moment with respect to the field when the field tends to 0 or minus the 2nd order derivative of the ground state energy of the molecule with respect to the field when the field goes to 0.

:<math>\alpha = \left( \frac {\delta\overrightarrow{\mu}}{\delta \overrightarrow{F}}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Beta is the 2nd order derivative of the dipole moment with respect to the field when the field goes to 0. Beta will be referred to as the 2nd order polarizability of the molecule. This can also be derived from the stark energy expression which is the 3rd order derivative of the energy with respect to the field when the field tends to 0.

:<math>\beta = \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Lastly, the gamma term corresponds to the 3rd order derivative of the dipole moment or minus the 4th order derivative of the energy with respect to the field at the limit where the field goes to 0. Gamma will be referred to as the 3rd order polarizability of the molecule.

:<math>\gamma = \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>
Stark energy describes the evolution of the energy of a system of particles in the presence of an electric field F. In the Stark energy expression, gamma corresponds to a 4th order term. However the in common terminology alpha is referred to as the linear polarizability, beta the 2nd order polarizability, and gamma the 3rd order polarizability. The Hellman-Feynman Theorem is the origin of these terms. Here it is presented as a Taylor series expansion, sometimes one uses a power series expansion.

:<math>
E_g = E^\circ_g = \overrightarrow{\mu}^\circ \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}\overrightarrow{F} - \frac {1} {3!} \beta \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} - \frac {1} {4!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>= E^\circ_g - \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

=== Electric dipole approximation ===
The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as :

<math>\mu^\circ + \alpha F + \beta F^2 ... \,\!</math>

and so on, without paying any attention to where that expression comes from.

:<math>- \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

in dimensional analysis:
:<math>\mu \equiv\,\!</math> charge * distance
:<math>F \equiv\,\!</math> volt/distance
:<math>\mu F \equiv\,\!</math> charge * volt :<math>\equiv\,\!</math> energy

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as μ<sup>not</sup> plus α * f plus β * f <sup>2</sup> and so on, without paying any attention to where that expression comes from.

:<math>\overrightarrow{\mu} = e \sum(i) \overrightarrow{\pi}_i 9i\,\!</math>

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

=== Perturbation theory ===
The perturbation theory will not be discussed at the quantum- mechanics level. The energy of the ground state of the system is the energy for the unperturbed system. Perturbation can be observed at different orders. At first order, the perturbation is referred as w. If that perturbation is the impact of the electric field of the light in the electric dipole approximation, the perturbation can be expressed as minus μF.

At the first order, the perturbation is operating on the unperturbed wave function of the ground state. Perturbation theory involves modification of systems due to the perturbation of all the wave functions for the unperturbed system. At first order, the perturbation is simply acting on the ground state wave function. Then it is integrated over space and the complex conjugate is taken. At second order, the wave functions of the excited state are taken into account to describe the modification of the system. An unperturbed system has a well defined wave function for the ground state and well defined wave functions for the excited states. The perturbed system is described on the basis of the wave functions of the unperturbed system.
:<math>=\int \Psi* e \overrightarrow{\pi} \Psi dr\,\!</math>

:<math>E_g = E^\circ_g + \langle \Psi_g | w | \Psi_g \rangle + \sum_p \frac {\langle \Psi_g | W | \Psi_p \rangle \langle \Psi_p | W | \Psi_g \rangle + ...}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>E_g = E^\circ_g -\overrightarrow{\mu ^\circ} \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}^2 - ....\,\!</math>

:<math>W = - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

In terms of non-linear optics, the perturbation theory expressions will show what the excited states are in your isolated molecule that will contribute to the linear polarizability, 2nd order polarizability, or the 3rd order polarizability and allow you to pinpoint exactly what excited states do play a major role in your optical response.

The complete set of wave functions for the unperturbed state will form the basic set for the perturbation expressions. In principle this includes all excited states. The 2nd order term in terms of perturbation and will correspond to alpha, the linear polarizability. In most conjugated systems, only the first excited state needs to be examined. This will often be the case for alpha and pi conjugated systems as well as for beta. But not for gamma in which two or more excited states must be taken into account. However, the number of states that need close attention can be heavily restricted.

:<math>E_g = E_g^\circ - \underbrace{\langle | \Psi_g | W | \Psi _g \rangle} \overrightarrow{F} + \,\!</math>

::::<math>\overrightarrow{\mu^\circ}\,\!</math>

:<math>\underbrace{\sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}}\,\!</math>

:::::<math>-\frac {1} {2!}\alpha\,\!</math>

A one to one correspondence can be made between the terms in the stark energy expression and the perturbation theory expression when the perturbation is minus μF.

As a side note, as you go to higher orders, things will look a bit more complicated because there are more summations over excited states. For example in 3rd order, there will be a double summation over excited states. In 4th order, there will be a triple summation over excited states. But it will always be products of matrix elements of this kind at the numerator, and the differences in energies of the states for the unperturbed molecule will be in the denominator. The expressions look more complex but by looking at the terms individually, notice that the same kind of terms come up.
P is summation over all excited states

- μF is the electric dipole approximation. The operator expression, μ is the unit electric charge times the position, which is the dipole moment. The electric field does not do anything to the wave functions of the unperturbed state. This expression here? is the expression of the dipole moment for the ground state Φ<sub>g</sub> is the wave function of the ground state in the unperturbed state, which is simply μ<sup> &o;</sup>. At first order, the goal is to find the possible dipole moment. If there is a central symmetry, there won’t be any permanent dipole moment of the molecule. If there is a permanent dipole moment, there will be an interaction between that permanent dipole moment and the external field. At second order, the expression includes the summation over all the excited states p. Here perturbation is replaced by its expression er. Since this deals with the wave functions of the unperturbed system, the electric field is outside. This shows a transition dipole between the ground state and excited state p. and the transition dipole between excited state p and the ground state. These terms are equal. They are the exact same transition dipole. The denominator is the square of the transition dipole between the ground state and excited state p.

The numerator is the difference in energy between the ground state energy and the excited state energy.
Finally, by closely examining the stark energy expression, a connection can be made between the term that is linear in the field, μ<sup>o</sup>F minus ½ α. This shows the expression for alpha as a function of this perturbation expression.

:<math>\alpha=2 \sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>=2 \sum \frac {M_{gp} ^2} {E^\circ _{gp}}\,\!</math>

In this expression there is no longer a minus sign because the denominator is reversed; E of Pnot – E of gnot.

Now there is a compact expression where alpha is equal to 2 times the summation over all excited states of transition dipole with state p times? transition dipole with state p over the transition energy. Taking into account of the perturbation theory, alpha, the linear polarizability, can be described as a sum over all excited states of the square of the transition dipole between the ground state and the excited state, over the transition energy from the ground state.

[[Image:Perturblevels.png|thumb|300px|]]

A pictorial description shows the process of going from the ground state to excited state p and that is a transition dipole between g and p. There is also another transition dipole when coming back from p to g. That is why the expression for alpha shows transition dipole squared. As previously explained, the expressions for beta will look more complex due to the double summations over excited states. The expression for gamma will look even more complex due to the triple summations over excited states. However for all instances, the numerator will always be products of transition dipoles and the denominator will contain the transition energy. In the literature, the perturbation theory expressions are also referred to as “sum over states expressions” the expression contains the sum over all excited states.

A few important questions include “What is the impact of the perturbation on the energy of the system?” and “Would it stabilize or destabilize the system when looking at the perturbation at different orders?”.
It is crucial to understand the differences and variations in conventions. Suppose you want to calculate the dipole moment of the molecule using two programs. First, you input the geometry of the molecule exactly in the same way for both programs. Then, you run the calculation. One program gave a dipole moment of +1.3 Debye, but the other program gave you a dipole moment of -1.3 Debye. Why is there a difference? The difference occurs because the conventions are different for chemists and physicists.

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>\overrightarrow{\mu}= \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F}+ 1/2 \beta \overrightarrow{F}\overrightarrow{F} +1/6 \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} ...\,\!</math>

Before physicists discovered the nature of electrical charge and electrical current, there wasn’t a way to identify whether the charge carriers were positively or negatively charged. Therefore, they made an assumption that it was positive charge that moves . But it turned out that their guess was wrong. We now know, it is the negatively charged electrons that provide electrical conductivity in metals or materials. Thus, in many of the conventions, physicists traditionally observe how the positive charge moves. Whereas chemists look at the displacement of an electron. As a result, the dipole moment can be written as going from left to right if you have a donor-acceptor molecule.

Suppose a quasi one dimensional D-conjugated bridge -A molecule with z the long axis and then apply an external field along z.

:<math>\overrightarrow{\mu}^\circ\,\!</math>
:<math>\rightarrow\,\!</math>

D ----- conjugate -------- A

:<math>\rightarrow\,\!</math> :<math>\overrightarrow{F}_x\,\!</math>
:<math>\leftarrow\,\!</math>

It can also be written, as going from right to left. Suppose that we have a donor acceptor molecule with a conjugated bridge between the two. In linear quasi- 1-demensional type molecules, the whole optical or non-linear optical responses will occur along the axis Z of the molecule.

=== Stabilization ===

<br clear='all'>
[[Image:Stabilization.png|thumb|300px|]]

Assume you have molecule that has a positive pole and a negative pole. You can place an electric field along the main axis in two directions. At the first order you will only observe the permanent dipole moment of the molecule and its interaction of the field; thus you have a permanent dipole moment period. You have a plus and a minus. It is also important to know which situation, the one on the top or the one on the bottom, will be more stable. As a matter of fact, the one at the bottom will be the most stable situation. This is because when you have two dipole moments on top of one another, the anti-parallel? situation will be much more favorable then the parallel situation. In anti-parallel situation the positive charge is stabilized by the negative pole of the electric field and the negative charge is stabilized by the positive pole. Where as in the parallel situation there is a destabilization. Therefore, independently from the conventions in terms of the electric field and the dipole moment, it is clear which situation will lead to a net stabilization of the energy of the system and which one will lead to a destabilization.

At first order, nothing changes within the molecule.

At second order you will have a flux of electrons towards the left to counteract the external field in the lower case, and in the upper case you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself. At third order, it gets more complicated.

'''First order energy term'''
:<math>E(\overrightarrow{F}) - E^\circ = - \overrightarrow{\mu^\circ} \overrightarrow{F}\,\!</math>

:<math>= - \overrightarrow{\mu}_z ^{ \circ}- \overrightarrow{F}_z\,\!</math>

There is stabilization if :<math>\overrightarrow{F}_z\,\!</math> is parallel to :<math>\overrightarrow{\mu}^\circ\,\!</math>

There is destabilization if :<math>\overrightarrow{F}_z\,\!</math> is anti-parallel to :<math>\overrightarrow{\mu}_z^{\circ}\,\!</math>

In other words, with the indicated conventions, stabilization will occur if the field is parallel to the dipole moment and destabilization will occur in the opposing case. But again, that depends on the conventions chosen for the field and dipole moment. Remember that at first order in the field ( the linear term of the energy expression) only the interaction between the permanent dipole moment, is examined. However, at higher orders, we examine how the system responds to the external field on the molecule. As a result, we look at the polarizabiliy, or in the case of alpha the linear polarizability. In perturbation theory the second order term gives the stabilization.

This can easily be seen from the previous expression. Alpha is a summation over all excited states of the squares of the transition dipole, which makes it positive. The transition energy going from the ground state will always be positive by definition of the ground state.

'''Second order energy term'''
:<math>- \frac{1}{2} \alpha_{zz} \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

Alpha is positive and we multiply by F times F, which will be positive. Therefore, the whole second order term leads to a stabilization of the system.

Think back about the simple example shown previously. At first order, nothing changes within the molecule. At second order, look at the response of the molecule to the external field. What will happen here? What will happen is that you will have a flux of electrons towards the left to counteract the external field, and here you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself.

Alpha is a tensor of rank two and there are nine tensor components for alpha. Beta is a tensor of rank three. Since each of these indices can be x y z, there will be a possible of 27 tensor components.
'''third order energy term'''
:<math>- \frac{1}{6} \beta_{zzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

There is stablilization or destablization depending on whether :<math>\overrightarrow{F}_z\,\!</math> is parallel or antiparallel to the vectorial part of β, and depends on the sign of β which depends on Δ μ <sub>eg</sub>

In a two state model expression, beta depends very much on the difference in state dipole moment between the ground state and the active excited state. Β will be positive if that active excited state has a dipole moment that is larger than the dipole moment in the ground state, and β will be negative if the dipole moment in the excited state is smaller than in the ground state. This is an easy way of understanding the variation in the sign of β.

'''Fourth order energy term'''

:<math>- \frac{1}{24} \gamma_{zzzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\overrightarrow{F}_z\,\!</math>

This is stabilizing if γ is >0 and destabilizing if γ is <0

For fourth order, in this case, the field components would lead to a positive term by necessity. Thus, we will have either stabilization if γ is positive or destabilization if γ is negative. This is consistent with the process called the self-focusing of light in the material with positive γ. If you shine a high intensity laser light into a molecule that has a very large positive γ response, the beam will self-focus. The system tends to go to higher local fields and therefore obtain a larger stabilization by focusing the light. Where as a negative γ leads to a defocusing of your light. This property can be use for protection from high intensity light.

Gamma is a tensor of rank four and there will be 81 tensor components. When looking at extended π conjugated molecules, (quasi 1-dimensional) the components along the long axis of the molecule will dominate everything. However, with molecules that become more complex in shape there are a number of components that can become important as well. Also, there are symmetry relationships among those components. In the literature on non-linear optics, there is something referred to as Climan symmetry that is based on the point groups of the different molecules that gives the relationship between the different tensor components. However, here we are mostly concerned with at the α<sub>zz</sub> component, the β<sub>zzz</sub>, or γ<sub>zzzz</sub> What will be provided is a difference between the global value and the tensor component along the main axis. It is difficult to know whether the third order term leads to stabilization or destabilization because β could be positive or negative. Also, the combination of the three field terms can be positive or negative so it really depends.

=== Dipole changes ===
We can also look at what happens to the dipole moment. In the case of the α, the permanent dipole can be zero if we have a centrosymmetric molecule or it can be any value depending on the nature of the molecule. If it is non-centrosymmetric there will be an increase or decrease depending on the direction of the field at first order.

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} = \overrightarrow{\mu^\circ_z} + \alpha \overrightarrow{F_z}\,\!</math>

First order: The dipole increases or decreases according to whether F<sub>z</sub> is parallel or antiparallel to :<math>\overrightarrow{\mu^\circ_z}\,\!</math>

Second order:

The change depends on how the field is aligned with respect to the permanent dipole moment. At the next order FF is always positive so dipole it will be decided by the value of β. The sign of β can often be related to the difference in dipole moment between the ground state and the active excited state. If there is an increase in the dipole moment going from the ground state to the excited state, β will be positive. That excited state now contributes to the description of the system because with a larger dipole moment, it is reasonable to assume that the μ of the system will increase. The opposite will occur for a negative β. All these considerations will become clearer when the perturbative expressions for beta and gamma are discussed in detail.

:<math>1/2 \Beta : \overrightarrow{F} \overrightarrow{F}\,\!</math>

In the context of the two state model, beta has a sign of :<math>\Delta \mu_{eg}\,\!</math>

:<math>\beta >0 : \mu \uparrow\,\!</math>

:<math>\beta <0 : \mu \downarrow\,\!</math>

Third order
For the impact of γ, the dipole moment depends on the sign of γ and the field alignments in the expression of the dipole moment. There will be three fields that will play a role.

=== Calculation of polarizabilities ===
Polarization of a medium due to an electric field.

In spite of the different conventions used to look at the physics of the system, it is good enough to just look at what the external field with respect to the permanent dipole moment does. Papers in the field of non-linear optics, especially for inorganic materials, often look at the macroscopic polarization that occurs when the field is applied. Since the experimentalists are not concerned with the possible derivations that are necessary when calculating α, β, γ, they often use an expression that is a power series expansion instead of a Taylor series expansion.

This expression of the polarization of the medium corresponding to the possible permanent polarization when the material is non-central symmetric. The expression contains a first order term which is the first order electrical susceptibility. Remember, the :<math>\chi^{(1)}\,\!</math> is a tensor; there will be 9 tensor components there. That is the equivalent of α for the microscopic scale.

:<math>\overrightarrow{P} = \overrightarrow{P_0} + \chi^{(1)} \overrightarrow{F} + \chi^{(2)} \overrightarrow{F}\overrightarrow{F} +\ chi^{(3)} \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} +\,\!</math>

:<math>\chi^{(1)}\,\!</math> is the first order electrical susceptibility (second rank tensor).

:<math>\chi^{(2)}\,\!</math> is the first order electrical susceptibility (third-rank tensor).

:<math>\chi^{(3)}\,\!</math> is the third order electrical susceptibility, and so on.

Only :<math>\chi^{(1)}, \chi^{(2)}, \chi^{(3)}\,\!</math> will be considered, although experimentally there are people that have shown :<math>\chi^{(5)}, \chi^{(6)}\,\!</math> processes that are very specific.

Molecular materials at the microscopic level

:<math>\overrightarrow{\mu} = \overrightarrow{\mu_0} + \alpha \overrightarrow{F} + \beta \overrightarrow{F} \overrightarrow{F} + \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

where

:<math>\alpha\,\!</math> is first order polarizability

:<math>\beta\,\!</math> is the secord order polarizability or first order hyperpolarizability

:<math>\gamma\,\!</math> is the third order polarizability or second order hyperpolarizability

This is the corresponding expression for the dipole moment of a given molecule on the microscopic level. It is expressed in the power series expression. α is referred to as the polarizability. In the context of non linear optics, when looking at the β and γ terms, α can be more rigorously referred to as the first order polarizability. β is the second order polarizability or (some people prefer to use the expression) first order hyperpolarizability. γ is the third order polarizability or the second order hyperpolarizability. The reason why μ is expressed in both a power series expression and in a Taylor series expression is that most of the programs that make calculations use Taylor series expansion. However, the β or the γ that one calculates can differ from one program to another. It can differ by a factor of 2 for β, and by a factor of 6 for γ. Therefore, it is wise to also compare your calculated data with what is reported experimentally. Usually, experimentalists use a power series expansion. Thus, if they had done the calculation taking into account the Taylor series expansion, they will have immediately a difference by a factor of 2 or a factor of 6 with the experiment.

'''Stark Energy'''

Switching back to the Taylor series expressions. This shows the stark energy expression written in a more rigorous way taking into account for all the possible components of the field and for the tensor components of the α, β, and γ tensors.

:<math>E(F) = E_0 - \sum_{i} \mu_{0i}F_i - \frac {1} {2!} \sum_{ij} \alpha_{ij} F_i F_j - \frac {1} {3!} \sum_{ijk} F_i F_jF_k - \frac {1}{4!} \sum_{ijkl} \gamma_{ijkl} F_i F_j F_k\,\!</math>

'''Dipole Moment'''

This shows a similar expression for the dipole moment. These two expressions are fully consistent with each other, given the Hellman-Feynman theory.

:<math>\mu_i(F) = \mu_{0i} + \sum_j \alpha_ij F_j + \frac {1} {2!} \sum_{jk} \beta_{ijk} F_j F_k + \frac {1} {3!} \sum_{jkl} \gamma_{ijkl} F_j F_k\,\!</math>

:<math>\mu_i = - \frac {\partial E(f)}{ \partial F_i}\,\!</math>

These expressions clearly show what was confirmed earlier regarding the tensors and its respective rank. For example, γ will be a tensor of rank 4 because you are looking at the impact on the i component of the dipole moment when applying a field along j, a field along k, or a field along L. That is the reason why the α, β, and γ contain all those tensor components.

:<math>\alpha_{ij} = -\frac{ \partial ^2E(F)} {\partial F_i \partial F_j} = \frac {\partial ^1 \mu_i} {\partial F_j}\,\!</math>

:<math>\beta_{ijk} = -\frac{ \partial ^3E(F)} {\partial F_i \partial F_j \partial F_k} = \frac {\partial ^2 \mu_i} {\partial F_j \partial F_k}\,\!</math>

:<math>\gamma_{ijkl} = -\frac{ \partial ^4E(F)} {\partial F_i \partial F_j \partial F_k \partial F_l} = \frac {\partial ^3 \mu_i} {\partial F_j \partial F_k \partial F_l}\,\!</math>

=== Derivative Techniques ===

From those derivative expressions and the perturbative expressions, two types of calculations can be derived to evaluate the molecular polarizabilities from quantum-mechanical approaches. There is one major set of calculations that involve the derivation of either the energy or the dipole moment with respect to the external field. Those derivations can be done either numerically using methods referred to as finite-field methods, or analytically using Coupled Perturbed Hartree-Fock (CPHF) methods.

In a finite-field calculation, you take the interaction with the external field and put it into your Hamiltonian for the isolated molecule without any external perturbation. It has a kinetic term, a nucleic attraction term, a coulomb term, and exchange term. Now here, a fifth term is added to those present four terms. The fifth term expresses the interaction with your field. Several calculations are then made in which several values of the external field are taken into account. Then you do a numerical derivation of the dipole moments that you will have calculated as a response to the external field.

:<math>H(\overrightarrow{F} = H_0 - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

The MO's are self-consistant with the eigenfunctions of :<math>H(\overrightarrow{F})\,\!</math>. What is interesting with those finite field methods is that since the perturbation interaction with the electric field is put into the Hamiltonian, the molecular orbitals that are derived are affected by that interaction. Then the α, β, γ tensor components are calculated by applying standard numerical procedures. Calculations are made with different values of the field. Different values of for dipole moment for the molecule are obtained. A numerical derivation is then made to get to α, β, and γ. For instance, two calculations are made for the α <sub>ii</sub> component. The calculation is made with the field in one direction, and then again with the field in the opposite direction. It is important to have a value of the field that is large enough so that the molecule can respond and give a numerically accurate variation in the dipole moment. However, it should not be too large or the equivalent of a dielectric breakdown of your molecule will be obtained and the calculation will simply not converge. Therefore, it is crucial know what values of the fields are needed to evaluate.

:<math>\alpha_ii = \frac {\partial\mu_i} {\partial F_i} = \frac {1}{2F_i} [\mu_i(F_i) - \mu_i(-F_i)]\,\!</math>
:<math>
\gamma_{iiii} = \frac {\partial^3 \mu_i} {\partial F_i \partial F_i \partial F_i} = \frac {1} {48F_i^3} [\mu_i(3F_i)-\mu_i(-3F_i)- 3\mu_i (F_i)+ 3\mu_i (-F_i)]\,\!</math>

We pick a compromise value that is able to insure accuracy but also avoid divergence.

:<math>F_i \approx 5 x 10^8 Vm^{-1}\,\!</math>

'''Coupled perturbed Hartree-Fock method'''

Another method that can be used to make those calculations is the analytical methods with analytical expressions for the variation of the energy with respect to the electric field.

:<math>\beta_{ijk} = - \frac {\partial^3 E(F)} {\partial F_i \partial F_j \partial F_k}\,\!</math>

=== Perturbation techniques ===

'''Sum over state (SOS) method'''
Besides making numerical or analytical calculations based on the derivation expressions, the perturbation theory expressions can also be used. This method is usually referred to as Sum Over States (SOS) method. This method was seen before for alpha. It is based on the perturbation expression for Stark energy terms which are related to optical nonlinearities based on their order in the field strength. α is calculated by evaluating the transition dipoles and the transition energies for all the excited states in the molecule.

You can look at the convergence of your values as a function of going over many excited states. However, it is important to understand that the higher energy you go, the larger the denominator becomes. Therefore, those terms will have smaller weight. Also, at very high excited states, the transition dipole will die down as well. For example, in the case of α the lowest excited states have the largest response.

:<math>\alpha_{ij} = \sum_m \frac {<\psi_0|\mu_i | \psi_m > <\psi_m|\mu_j | \psi_0 >} {E_m- E_0}\,\!</math>

For the β terms, we have exactly the same components. However, the expression looks more complicated because it contains a double summation over excited states. That is transition dipole going from the ground state n to excited state to m. Then it goes from excited state m back to the ground state. The denominator has the transition energies. There is also a second term that goes over a summation over excited state due to the dipole moment starting in the ground state. Then there is a transition dipole going from the ground state to excited state n and then it comes back from n to the ground state, over transition energies. To generate these expressions go through the perturbation theory and work the second order and the third order perturbation theory expression, one can do so by placing the dipole (er), the dipole operator, and the electric field.

:<math>\alpha_{ijk} = \sum_n \sum_m \frac {<\psi_0|\mu_i | \psi_n > <\psi_m|\mu_j | \psi_0 ><\psi_m|\mu_k | \psi_0 >} {(E_n- E_0)(E_m- E_0)} - \sum_n \frac {<\psi_0|\mu_i | \psi_0 > <\psi_0|\mu_j | \psi_n ><\psi_n|\mu_k | \psi_0 >}{(E_m- E_0)(E_n- E_0)}\,\!</math>

The reason why it is interesting to evaluate the non-linear optic properties with those perturbation expressions (sum over state expressions) is because it pinpoints which excited states play important roles in optical and non-linear optical response. Another reason why they are heavily exploited is because the frequency dependence can easily be introduced with the response. With the finite-field method, it gets extremely complicated to introduce the frequency dependence.

The finite-field method is usually incorporated in many quantum chemistry packages. You just press key telling “calculate the molecular polarizabilites” and then you get numbers for those polarizabilites. However that is the problem; it only gives numbers and these are the static values where ω is equal to zero.
It doesn’t provide an in depth understanding of what is occurring. There have been extensions to those methods that provide some kind of understanding regarding finite field methods of the local spatial contributions to the non-linear optical response. But it is a sophisticated approach that is not often used. Thus, in many instances, it more beneficial to use the sum-over states expression because it gives an idea of which electronic states matter. Also, frequency dependence can easily be introduced. The same thing can be done at the γ level.

:<math>\beta^{SHG}(-2\omega;\omega \omega) = 1/2 \sum_n \sum \_m \frac {<\psi_0 | \mu_i | \psi_n><\psi_n|\mu_j|\psi_m><\psi_m |\mu_k|\psi_0>} {(\hbar\omega-(E_m-E_0))(2\hbar\omega-(e_m-e_0))}\,\!</math>

where

:<math>(\hbar\omega-(E_m-E_0))\,\!</math> represents one-photon resonance

:<math>(2\hbar\omega-(e_m-e_0))\,\!</math> represents two-photon resonance

Perturbation Theory

2010-03-11T23:25:35Z

128.95.39.187: /* Perturbation techniques */

Perturbation Theory

2010-03-11T23:25:17Z

128.95.39.187: /* Perturbation techniques */

=== Hellman-Feynman Theorem ===

The Hellman-Feynman Theorem, which expresses the dipole moment as minus derivative of the energy of the system with respect to the field. This equation expresses the response of a molecule which is 2nd order in terms of the energy of the molecule and first order in terms of the dipole moment of the molecule (1st order or 2nd order with respect to the field).

:<math>\overrightarrow {\mu} = - \frac {\delta E} {\delta \overrightarrow{F}}\,\!</math>

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} + \frac {1} {2!} \beta \overrightarrow{F}\overrightarrow{F} + \frac {1} {3!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>\frac {\delta \overrightarrow{\mu}}{\delta \overrightarrow{F}} = \alpha + \beta \overrightarrow{F} + \frac {1} {2!} \gamma \overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

=== Stark Energy Expression ===
Alpha is the linear polarizability or the first order polarizability. It describes how the molecule responds in terms of the modification of its ground state energy or of its dipole moment, in the presence of the field at the limit where the field goes to 0. Thus, alpha can be cast either as the 1st order derivative of the dipole moment with respect to the field when the field tends to 0 or minus the 2nd order derivative of the ground state energy of the molecule with respect to the field when the field goes to 0.

:<math>\alpha = \left( \frac {\delta\overrightarrow{\mu}}{\delta \overrightarrow{F}}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Beta is the 2nd order derivative of the dipole moment with respect to the field when the field goes to 0. Beta will be referred to as the 2nd order polarizability of the molecule. This can also be derived from the stark energy expression which is the 3rd order derivative of the energy with respect to the field when the field tends to 0.

:<math>\beta = \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Lastly, the gamma term corresponds to the 3rd order derivative of the dipole moment or minus the 4th order derivative of the energy with respect to the field at the limit where the field goes to 0. Gamma will be referred to as the 3rd order polarizability of the molecule.

:<math>\gamma = \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>
Stark energy describes the evolution of the energy of a system of particles in the presence of an electric field F. In the Stark energy expression, gamma corresponds to a 4th order term. However the in common terminology alpha is referred to as the linear polarizability, beta the 2nd order polarizability, and gamma the 3rd order polarizability. The Hellman-Feynman Theorem is the origin of these terms. Here it is presented as a Taylor series expansion, sometimes one uses a power series expansion.

:<math>
E_g = E^\circ_g = \overrightarrow{\mu}^\circ \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}\overrightarrow{F} - \frac {1} {3!} \beta \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} - \frac {1} {4!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>= E^\circ_g - \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

=== Electric dipole approximation ===
The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as :

<math>\mu^\circ + \alpha F + \beta F^2 ... \,\!</math>

and so on, without paying any attention to where that expression comes from.

:<math>- \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

in dimensional analysis:
:<math>\mu \equiv\,\!</math> charge * distance
:<math>F \equiv\,\!</math> volt/distance
:<math>\mu F \equiv\,\!</math> charge * volt :<math>\equiv\,\!</math> energy

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as μ<sup>not</sup> plus α * f plus β * f <sup>2</sup> and so on, without paying any attention to where that expression comes from.

:<math>\overrightarrow{\mu} = e \sum(i) \overrightarrow{\pi}_i 9i\,\!</math>

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

=== Perturbation theory ===
The perturbation theory will not be discussed at the quantum- mechanics level. The energy of the ground state of the system is the energy for the unperturbed system. Perturbation can be observed at different orders. At first order, the perturbation is referred as w. If that perturbation is the impact of the electric field of the light in the electric dipole approximation, the perturbation can be expressed as minus μF.

At the first order, the perturbation is operating on the unperturbed wave function of the ground state. Perturbation theory involves modification of systems due to the perturbation of all the wave functions for the unperturbed system. At first order, the perturbation is simply acting on the ground state wave function. Then it is integrated over space and the complex conjugate is taken. At second order, the wave functions of the excited state are taken into account to describe the modification of the system. An unperturbed system has a well defined wave function for the ground state and well defined wave functions for the excited states. The perturbed system is described on the basis of the wave functions of the unperturbed system.
:<math>=\int \Psi* e \overrightarrow{\pi} \Psi dr\,\!</math>

:<math>E_g = E^\circ_g + \langle \Psi_g | w | \Psi_g \rangle + \sum_p \frac {\langle \Psi_g | W | \Psi_p \rangle \langle \Psi_p | W | \Psi_g \rangle + ...}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>E_g = E^\circ_g -\overrightarrow{\mu ^\circ} \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}^2 - ....\,\!</math>

:<math>W = - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

In terms of non-linear optics, the perturbation theory expressions will show what the excited states are in your isolated molecule that will contribute to the linear polarizability, 2nd order polarizability, or the 3rd order polarizability and allow you to pinpoint exactly what excited states do play a major role in your optical response.

The complete set of wave functions for the unperturbed state will form the basic set for the perturbation expressions. In principle this includes all excited states. The 2nd order term in terms of perturbation and will correspond to alpha, the linear polarizability. In most conjugated systems, only the first excited state needs to be examined. This will often be the case for alpha and pi conjugated systems as well as for beta. But not for gamma in which two or more excited states must be taken into account. However, the number of states that need close attention can be heavily restricted.

:<math>E_g = E_g^\circ - \underbrace{\langle | \Psi_g | W | \Psi _g \rangle} \overrightarrow{F} + \,\!</math>

::::<math>\overrightarrow{\mu^\circ}\,\!</math>

:<math>\underbrace{\sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}}\,\!</math>

:::::<math>-\frac {1} {2!}\alpha\,\!</math>

A one to one correspondence can be made between the terms in the stark energy expression and the perturbation theory expression when the perturbation is minus μF.

As a side note, as you go to higher orders, things will look a bit more complicated because there are more summations over excited states. For example in 3rd order, there will be a double summation over excited states. In 4th order, there will be a triple summation over excited states. But it will always be products of matrix elements of this kind at the numerator, and the differences in energies of the states for the unperturbed molecule will be in the denominator. The expressions look more complex but by looking at the terms individually, notice that the same kind of terms come up.
P is summation over all excited states

- μF is the electric dipole approximation. The operator expression, μ is the unit electric charge times the position, which is the dipole moment. The electric field does not do anything to the wave functions of the unperturbed state. This expression here? is the expression of the dipole moment for the ground state Φ<sub>g</sub> is the wave function of the ground state in the unperturbed state, which is simply μ<sup> &o;</sup>. At first order, the goal is to find the possible dipole moment. If there is a central symmetry, there won’t be any permanent dipole moment of the molecule. If there is a permanent dipole moment, there will be an interaction between that permanent dipole moment and the external field. At second order, the expression includes the summation over all the excited states p. Here perturbation is replaced by its expression er. Since this deals with the wave functions of the unperturbed system, the electric field is outside. This shows a transition dipole between the ground state and excited state p. and the transition dipole between excited state p and the ground state. These terms are equal. They are the exact same transition dipole. The denominator is the square of the transition dipole between the ground state and excited state p.

The numerator is the difference in energy between the ground state energy and the excited state energy.
Finally, by closely examining the stark energy expression, a connection can be made between the term that is linear in the field, μ<sup>o</sup>F minus ½ α. This shows the expression for alpha as a function of this perturbation expression.

:<math>\alpha=2 \sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>=2 \sum \frac {M_{gp} ^2} {E^\circ _{gp}}\,\!</math>

In this expression there is no longer a minus sign because the denominator is reversed; E of Pnot – E of gnot.

Now there is a compact expression where alpha is equal to 2 times the summation over all excited states of transition dipole with state p times? transition dipole with state p over the transition energy. Taking into account of the perturbation theory, alpha, the linear polarizability, can be described as a sum over all excited states of the square of the transition dipole between the ground state and the excited state, over the transition energy from the ground state.

[[Image:Perturblevels.png|thumb|300px|]]

A pictorial description shows the process of going from the ground state to excited state p and that is a transition dipole between g and p. There is also another transition dipole when coming back from p to g. That is why the expression for alpha shows transition dipole squared. As previously explained, the expressions for beta will look more complex due to the double summations over excited states. The expression for gamma will look even more complex due to the triple summations over excited states. However for all instances, the numerator will always be products of transition dipoles and the denominator will contain the transition energy. In the literature, the perturbation theory expressions are also referred to as “sum over states expressions” the expression contains the sum over all excited states.

A few important questions include “What is the impact of the perturbation on the energy of the system?” and “Would it stabilize or destabilize the system when looking at the perturbation at different orders?”.
It is crucial to understand the differences and variations in conventions. Suppose you want to calculate the dipole moment of the molecule using two programs. First, you input the geometry of the molecule exactly in the same way for both programs. Then, you run the calculation. One program gave a dipole moment of +1.3 Debye, but the other program gave you a dipole moment of -1.3 Debye. Why is there a difference? The difference occurs because the conventions are different for chemists and physicists.

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>\overrightarrow{\mu}= \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F}+ 1/2 \beta \overrightarrow{F}\overrightarrow{F} +1/6 \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} ...\,\!</math>

Before physicists discovered the nature of electrical charge and electrical current, there wasn’t a way to identify whether the charge carriers were positively or negatively charged. Therefore, they made an assumption that it was positive charge that moves . But it turned out that their guess was wrong. We now know, it is the negatively charged electrons that provide electrical conductivity in metals or materials. Thus, in many of the conventions, physicists traditionally observe how the positive charge moves. Whereas chemists look at the displacement of an electron. As a result, the dipole moment can be written as going from left to right if you have a donor-acceptor molecule.

Suppose a quasi one dimensional D-conjugated bridge -A molecule with z the long axis and then apply an external field along z.

:<math>\overrightarrow{\mu}^\circ\,\!</math>
:<math>\rightarrow\,\!</math>

D ----- conjugate -------- A

:<math>\rightarrow\,\!</math> :<math>\overrightarrow{F}_x\,\!</math>
:<math>\leftarrow\,\!</math>

It can also be written, as going from right to left. Suppose that we have a donor acceptor molecule with a conjugated bridge between the two. In linear quasi- 1-demensional type molecules, the whole optical or non-linear optical responses will occur along the axis Z of the molecule.

=== Stabilization ===

<br clear='all'>
[[Image:Stabilization.png|thumb|300px|]]

Assume you have molecule that has a positive pole and a negative pole. You can place an electric field along the main axis in two directions. At the first order you will only observe the permanent dipole moment of the molecule and its interaction of the field; thus you have a permanent dipole moment period. You have a plus and a minus. It is also important to know which situation, the one on the top or the one on the bottom, will be more stable. As a matter of fact, the one at the bottom will be the most stable situation. This is because when you have two dipole moments on top of one another, the anti-parallel? situation will be much more favorable then the parallel situation. In anti-parallel situation the positive charge is stabilized by the negative pole of the electric field and the negative charge is stabilized by the positive pole. Where as in the parallel situation there is a destabilization. Therefore, independently from the conventions in terms of the electric field and the dipole moment, it is clear which situation will lead to a net stabilization of the energy of the system and which one will lead to a destabilization.

At first order, nothing changes within the molecule.

At second order you will have a flux of electrons towards the left to counteract the external field in the lower case, and in the upper case you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself. At third order, it gets more complicated.

'''First order energy term'''
:<math>E(\overrightarrow{F}) - E^\circ = - \overrightarrow{\mu^\circ} \overrightarrow{F}\,\!</math>

:<math>= - \overrightarrow{\mu}_z ^{ \circ}- \overrightarrow{F}_z\,\!</math>

There is stabilization if :<math>\overrightarrow{F}_z\,\!</math> is parallel to :<math>\overrightarrow{\mu}^\circ\,\!</math>

There is destabilization if :<math>\overrightarrow{F}_z\,\!</math> is anti-parallel to :<math>\overrightarrow{\mu}_z^{\circ}\,\!</math>

In other words, with the indicated conventions, stabilization will occur if the field is parallel to the dipole moment and destabilization will occur in the opposing case. But again, that depends on the conventions chosen for the field and dipole moment. Remember that at first order in the field ( the linear term of the energy expression) only the interaction between the permanent dipole moment, is examined. However, at higher orders, we examine how the system responds to the external field on the molecule. As a result, we look at the polarizabiliy, or in the case of alpha the linear polarizability. In perturbation theory the second order term gives the stabilization.

This can easily be seen from the previous expression. Alpha is a summation over all excited states of the squares of the transition dipole, which makes it positive. The transition energy going from the ground state will always be positive by definition of the ground state.

'''Second order energy term'''
:<math>- \frac{1}{2} \alpha_{zz} \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

Alpha is positive and we multiply by F times F, which will be positive. Therefore, the whole second order term leads to a stabilization of the system.

Think back about the simple example shown previously. At first order, nothing changes within the molecule. At second order, look at the response of the molecule to the external field. What will happen here? What will happen is that you will have a flux of electrons towards the left to counteract the external field, and here you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself.

Alpha is a tensor of rank two and there are nine tensor components for alpha. Beta is a tensor of rank three. Since each of these indices can be x y z, there will be a possible of 27 tensor components.
'''third order energy term'''
:<math>- \frac{1}{6} \beta_{zzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

There is stablilization or destablization depending on whether :<math>\overrightarrow{F}_z\,\!</math> is parallel or antiparallel to the vectorial part of β, and depends on the sign of β which depends on Δ μ <sub>eg</sub>

In a two state model expression, beta depends very much on the difference in state dipole moment between the ground state and the active excited state. Β will be positive if that active excited state has a dipole moment that is larger than the dipole moment in the ground state, and β will be negative if the dipole moment in the excited state is smaller than in the ground state. This is an easy way of understanding the variation in the sign of β.

'''Fourth order energy term'''

:<math>- \frac{1}{24} \gamma_{zzzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\overrightarrow{F}_z\,\!</math>

This is stabilizing if γ is >0 and destabilizing if γ is <0

For fourth order, in this case, the field components would lead to a positive term by necessity. Thus, we will have either stabilization if γ is positive or destabilization if γ is negative. This is consistent with the process called the self-focusing of light in the material with positive γ. If you shine a high intensity laser light into a molecule that has a very large positive γ response, the beam will self-focus. The system tends to go to higher local fields and therefore obtain a larger stabilization by focusing the light. Where as a negative γ leads to a defocusing of your light. This property can be use for protection from high intensity light.

Gamma is a tensor of rank four and there will be 81 tensor components. When looking at extended π conjugated molecules, (quasi 1-dimensional) the components along the long axis of the molecule will dominate everything. However, with molecules that become more complex in shape there are a number of components that can become important as well. Also, there are symmetry relationships among those components. In the literature on non-linear optics, there is something referred to as Climan symmetry that is based on the point groups of the different molecules that gives the relationship between the different tensor components. However, here we are mostly concerned with at the α<sub>zz</sub> component, the β<sub>zzz</sub>, or γ<sub>zzzz</sub> What will be provided is a difference between the global value and the tensor component along the main axis. It is difficult to know whether the third order term leads to stabilization or destabilization because β could be positive or negative. Also, the combination of the three field terms can be positive or negative so it really depends.

=== Dipole changes ===
We can also look at what happens to the dipole moment. In the case of the α, the permanent dipole can be zero if we have a centrosymmetric molecule or it can be any value depending on the nature of the molecule. If it is non-centrosymmetric there will be an increase or decrease depending on the direction of the field at first order.

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} = \overrightarrow{\mu^\circ_z} + \alpha \overrightarrow{F_z}\,\!</math>

First order: The dipole increases or decreases according to whether F<sub>z</sub> is parallel or antiparallel to :<math>\overrightarrow{\mu^\circ_z}\,\!</math>

Second order:

The change depends on how the field is aligned with respect to the permanent dipole moment. At the next order FF is always positive so dipole it will be decided by the value of β. The sign of β can often be related to the difference in dipole moment between the ground state and the active excited state. If there is an increase in the dipole moment going from the ground state to the excited state, β will be positive. That excited state now contributes to the description of the system because with a larger dipole moment, it is reasonable to assume that the μ of the system will increase. The opposite will occur for a negative β. All these considerations will become clearer when the perturbative expressions for beta and gamma are discussed in detail.

:<math>1/2 \Beta : \overrightarrow{F} \overrightarrow{F}\,\!</math>

In the context of the two state model, beta has a sign of :<math>\Delta \mu_{eg}\,\!</math>

:<math>\beta >0 : \mu \uparrow\,\!</math>

:<math>\beta <0 : \mu \downarrow\,\!</math>

Third order
For the impact of γ, the dipole moment depends on the sign of γ and the field alignments in the expression of the dipole moment. There will be three fields that will play a role.

=== Calculation of polarizabilities ===
Polarization of a medium due to an electric field.

In spite of the different conventions used to look at the physics of the system, it is good enough to just look at what the external field with respect to the permanent dipole moment does. Papers in the field of non-linear optics, especially for inorganic materials, often look at the macroscopic polarization that occurs when the field is applied. Since the experimentalists are not concerned with the possible derivations that are necessary when calculating α, β, γ, they often use an expression that is a power series expansion instead of a Taylor series expansion.

This expression of the polarization of the medium corresponding to the possible permanent polarization when the material is non-central symmetric. The expression contains a first order term which is the first order electrical susceptibility. Remember, the :<math>\chi^{(1)}\,\!</math> is a tensor; there will be 9 tensor components there. That is the equivalent of α for the microscopic scale.

:<math>\overrightarrow{P} = \overrightarrow{P_0} + \chi^{(1)} \overrightarrow{F} + \chi^{(2)} \overrightarrow{F}\overrightarrow{F} +\ chi^{(3)} \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} +\,\!</math>

:<math>\chi^{(1)}\,\!</math> is the first order electrical susceptibility (second rank tensor).

:<math>\chi^{(2)}\,\!</math> is the first order electrical susceptibility (third-rank tensor).

:<math>\chi^{(3)}\,\!</math> is the third order electrical susceptibility, and so on.

Only :<math>\chi^{(1)}, \chi^{(2)}, \chi^{(3)}\,\!</math> will be considered, although experimentally there are people that have shown :<math>\chi^{(5)}, \chi^{(6)}\,\!</math> processes that are very specific.

Molecular materials at the microscopic level

:<math>\overrightarrow{\mu} = \overrightarrow{\mu_0} + \alpha \overrightarrow{F} + \beta \overrightarrow{F} \overrightarrow{F} + \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

where

:<math>\alpha\,\!</math> is first order polarizability

:<math>\beta\,\!</math> is the secord order polarizability or first order hyperpolarizability

:<math>\gamma\,\!</math> is the third order polarizability or second order hyperpolarizability

This is the corresponding expression for the dipole moment of a given molecule on the microscopic level. It is expressed in the power series expression. α is referred to as the polarizability. In the context of non linear optics, when looking at the β and γ terms, α can be more rigorously referred to as the first order polarizability. β is the second order polarizability or (some people prefer to use the expression) first order hyperpolarizability. γ is the third order polarizability or the second order hyperpolarizability. The reason why μ is expressed in both a power series expression and in a Taylor series expression is that most of the programs that make calculations use Taylor series expansion. However, the β or the γ that one calculates can differ from one program to another. It can differ by a factor of 2 for β, and by a factor of 6 for γ. Therefore, it is wise to also compare your calculated data with what is reported experimentally. Usually, experimentalists use a power series expansion. Thus, if they had done the calculation taking into account the Taylor series expansion, they will have immediately a difference by a factor of 2 or a factor of 6 with the experiment.

'''Stark Energy'''

Switching back to the Taylor series expressions. This shows the stark energy expression written in a more rigorous way taking into account for all the possible components of the field and for the tensor components of the α, β, and γ tensors.

:<math>E(F) = E_0 - \sum_{i} \mu_{0i}F_i - \frac {1} {2!} \sum_{ij} \alpha_{ij} F_i F_j - \frac {1} {3!} \sum_{ijk} F_i F_jF_k - \frac {1}{4!} \sum_{ijkl} \gamma_{ijkl} F_i F_j F_k\,\!</math>

'''Dipole Moment'''

This shows a similar expression for the dipole moment. These two expressions are fully consistent with each other, given the Hellman-Feynman theory.

:<math>\mu_i(F) = \mu_{0i} + \sum_j \alpha_ij F_j + \frac {1} {2!} \sum_{jk} \beta_{ijk} F_j F_k + \frac {1} {3!} \sum_{jkl} \gamma_{ijkl} F_j F_k\,\!</math>

:<math>\mu_i = - \frac {\partial E(f)}{ \partial F_i}\,\!</math>

These expressions clearly show what was confirmed earlier regarding the tensors and its respective rank. For example, γ will be a tensor of rank 4 because you are looking at the impact on the i component of the dipole moment when applying a field along j, a field along k, or a field along L. That is the reason why the α, β, and γ contain all those tensor components.

:<math>\alpha_{ij} = -\frac{ \partial ^2E(F)} {\partial F_i \partial F_j} = \frac {\partial ^1 \mu_i} {\partial F_j}\,\!</math>

:<math>\beta_{ijk} = -\frac{ \partial ^3E(F)} {\partial F_i \partial F_j \partial F_k} = \frac {\partial ^2 \mu_i} {\partial F_j \partial F_k}\,\!</math>

:<math>\gamma_{ijkl} = -\frac{ \partial ^4E(F)} {\partial F_i \partial F_j \partial F_k \partial F_l} = \frac {\partial ^3 \mu_i} {\partial F_j \partial F_k \partial F_l}\,\!</math>

=== Derivative Techniques ===

From those derivative expressions and the perturbative expressions, two types of calculations can be derived to evaluate the molecular polarizabilities from quantum-mechanical approaches. There is one major set of calculations that involve the derivation of either the energy or the dipole moment with respect to the external field. Those derivations can be done either numerically using methods referred to as finite-field methods, or analytically using Coupled Perturbed Hartree-Fock (CPHF) methods.

In a finite-field calculation, you take the interaction with the external field and put it into your Hamiltonian for the isolated molecule without any external perturbation. It has a kinetic term, a nucleic attraction term, a coulomb term, and exchange term. Now here, a fifth term is added to those present four terms. The fifth term expresses the interaction with your field. Several calculations are then made in which several values of the external field are taken into account. Then you do a numerical derivation of the dipole moments that you will have calculated as a response to the external field.

:<math>H(\overrightarrow{F} = H_0 - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

The MO's are self-consistant with the eigenfunctions of :<math>H(\overrightarrow{F})\,\!</math>. What is interesting with those finite field methods is that since the perturbation interaction with the electric field is put into the Hamiltonian, the molecular orbitals that are derived are affected by that interaction. Then the α, β, γ tensor components are calculated by applying standard numerical procedures. Calculations are made with different values of the field. Different values of for dipole moment for the molecule are obtained. A numerical derivation is then made to get to α, β, and γ. For instance, two calculations are made for the α <sub>ii</sub> component. The calculation is made with the field in one direction, and then again with the field in the opposite direction. It is important to have a value of the field that is large enough so that the molecule can respond and give a numerically accurate variation in the dipole moment. However, it should not be too large or the equivalent of a dielectric breakdown of your molecule will be obtained and the calculation will simply not converge. Therefore, it is crucial know what values of the fields are needed to evaluate.

:<math>\alpha_ii = \frac {\partial\mu_i} {\partial F_i} = \frac {1}{2F_i} [\mu_i(F_i) - \mu_i(-F_i)]\,\!</math>
:<math>
\gamma_{iiii} = \frac {\partial^3 \mu_i} {\partial F_i \partial F_i \partial F_i} = \frac {1} {48F_i^3} [\mu_i(3F_i)-\mu_i(-3F_i)- 3\mu_i (F_i)+ 3\mu_i (-F_i)]\,\!</math>

We pick a compromise value that is able to insure accuracy but also avoid divergence.

:<math>F_i \approx 5 x 10^8 Vm^{-1}\,\!</math>

'''Coupled perturbed Hartree-Fock method'''

Another method that can be used to make those calculations is the analytical methods with analytical expressions for the variation of the energy with respect to the electric field.

:<math>\beta_{ijk} = - \frac {\partial^3 E(F)} {\partial F_i \partial F_j \partial F_k}\,\!</math>

=== Perturbation techniques ===

'''Sum over state (SOS) method'''
Besides making numerical or analytical calculations based on the derivation expressions, the perturbation theory expressions can also be used. This method is usually referred to as Sum Over States (SOS) method. This method was seen before for alpha. It is based on the perturbation expression for Stark energy terms which are related to optical nonlinearities based on their order in the field strength. α is calculated by evaluating the transition dipoles and the transition energies for all the excited states in the molecule.

You can look at the convergence of your values as a function of going over many excited states. However, it is important to understand that the higher energy you go, the larger the denominator becomes. Therefore, those terms will have smaller weight. Also, at very high excited states, the transition dipole will die down as well. For example, in the case of α the lowest excited states have the largest response.

:<math>\alpha_{ij} = \sum_m \frac {<\psi_0|\mu_i | \psi_m > <\psi_m|\mu_j | \psi_0 >} {E_m- E_0}\,\!</math>

For the β terms, we have exactly the same components. However, the expression looks more complicated because it contains a double summation over excited states. That is transition dipole going from the ground state n to excited state to m. Then it goes from excited state m back to the ground state. The denominator has the transition energies. There is also a second term that goes over a summation over excited state due to the dipole moment starting in the ground state. Then there is a transition dipole going from the ground state to excited state n and then it comes back from n to the ground state, over transition energies. To generate these expressions go through the perturbation theory and work the second order and the third order perturbation theory expression, one can do so by placing the dipole (er), the dipole operator, and the electric field.

:<math>\alpha_{ijk} = \sum_n \sum_m \frac {<\psi_0|\mu_i | \psi_n > <\psi_m|\mu_j | \psi_0 ><\psi_m|\mu_k | \psi_0 >} {(E_n- E_0)(E_m- E_0)} - \sum_n \frac {<\psi_0|\mu_i | \psi_0 > <\psi_0|\mu_j | \psi_n ><\psi_n|\mu_k | \psi_0 >}{(E_m- E_0)(E_n- E_0)}\,\!</math>

The reason why it is interesting to evaluate the non-linear optic properties with those perturbation expressions (sum over state expressions) is because it pinpoints which excited states play important roles in optical and non-linear optical response. Another reason why they are heavily exploited is because the frequency dependence can easily be introduced with the response. With the finite-field method, it gets extremely complicated to introduce the frequency dependence.

The finite-field method is usually incorporated in many quantum chemistry packages. You just press key telling “calculate the molecular polarizabilites” and then you get numbers for those polarizabilites. However that is the problem; it only gives numbers and these are the static values where ω is equal to zero.
It doesn’t provide an in depth understanding of what is occurring. There have been extensions to those methods that provide some kind of understanding regarding finite field methods of the local spatial contributions to the non-linear optical response. But it is a sophisticated approach that is not often used. Thus, in many instances, it more beneficial to use the sum-over states expression because it gives an idea of which electronic states matter. Also, frequency dependence can easily be introduced. The same thing can be done at the γ level.

:<math>\beta^{SHG}(-2\omega;\omega \omega) = 1/2 \sum_n \sum \_m \frac {<\psi_0 | \mu_i | \psi_n><\psi_n|\muj|\psi_m><\psi_m |\mu_k|\psi_0>} {(\hbar\omega-(E_m-E_0))(2\hbar\omega-(e_m-e_0))}\,\!</math>

Perturbation Theory

2010-03-11T23:23:17Z

128.95.39.187: /* Perturbation techniques */

=== Hellman-Feynman Theorem ===

The Hellman-Feynman Theorem, which expresses the dipole moment as minus derivative of the energy of the system with respect to the field. This equation expresses the response of a molecule which is 2nd order in terms of the energy of the molecule and first order in terms of the dipole moment of the molecule (1st order or 2nd order with respect to the field).

:<math>\overrightarrow {\mu} = - \frac {\delta E} {\delta \overrightarrow{F}}\,\!</math>

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} + \frac {1} {2!} \beta \overrightarrow{F}\overrightarrow{F} + \frac {1} {3!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>\frac {\delta \overrightarrow{\mu}}{\delta \overrightarrow{F}} = \alpha + \beta \overrightarrow{F} + \frac {1} {2!} \gamma \overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

=== Stark Energy Expression ===
Alpha is the linear polarizability or the first order polarizability. It describes how the molecule responds in terms of the modification of its ground state energy or of its dipole moment, in the presence of the field at the limit where the field goes to 0. Thus, alpha can be cast either as the 1st order derivative of the dipole moment with respect to the field when the field tends to 0 or minus the 2nd order derivative of the ground state energy of the molecule with respect to the field when the field goes to 0.

:<math>\alpha = \left( \frac {\delta\overrightarrow{\mu}}{\delta \overrightarrow{F}}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Beta is the 2nd order derivative of the dipole moment with respect to the field when the field goes to 0. Beta will be referred to as the 2nd order polarizability of the molecule. This can also be derived from the stark energy expression which is the 3rd order derivative of the energy with respect to the field when the field tends to 0.

:<math>\beta = \left( \frac {\delta^2 \overrightarrow{\mu}}{\delta \overrightarrow{F}^2}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

Lastly, the gamma term corresponds to the 3rd order derivative of the dipole moment or minus the 4th order derivative of the energy with respect to the field at the limit where the field goes to 0. Gamma will be referred to as the 3rd order polarizability of the molecule.

:<math>\gamma = \left( \frac {\delta^3 \overrightarrow{\mu}}{\delta \overrightarrow{F}^3}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>
Stark energy describes the evolution of the energy of a system of particles in the presence of an electric field F. In the Stark energy expression, gamma corresponds to a 4th order term. However the in common terminology alpha is referred to as the linear polarizability, beta the 2nd order polarizability, and gamma the 3rd order polarizability. The Hellman-Feynman Theorem is the origin of these terms. Here it is presented as a Taylor series expansion, sometimes one uses a power series expansion.

:<math>
E_g = E^\circ_g = \overrightarrow{\mu}^\circ \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}\overrightarrow{F} - \frac {1} {3!} \beta \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} - \frac {1} {4!} \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\overrightarrow{F}\,\!</math>

:<math>= E^\circ_g - \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

=== Electric dipole approximation ===
The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as :

<math>\mu^\circ + \alpha F + \beta F^2 ... \,\!</math>

and so on, without paying any attention to where that expression comes from.

:<math>- \overrightarrow{\mu}\overrightarrow{F}\,\!</math>

in dimensional analysis:
:<math>\mu \equiv\,\!</math> charge * distance
:<math>F \equiv\,\!</math> volt/distance
:<math>\mu F \equiv\,\!</math> charge * volt :<math>\equiv\,\!</math> energy

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

The stark energy expression states that the ground state energy of the molecule in the presence of the field is the ground state energy in the absence of the field minus μF. Thus, μF is considered the interaction between the field and the molecule. The electric dipole approximation is that only the electric field component of light influences dipole moment. The magnetic component is ignored. In most instances in the literature, this approximation is assumed but not stated. The expression for the dipole moment is expressed as μ<sup>not</sup> plus α * f plus β * f <sup>2</sup> and so on, without paying any attention to where that expression comes from.

:<math>\overrightarrow{\mu} = e \sum(i) \overrightarrow{\pi}_i 9i\,\!</math>

After the electric dipole, the next two terms are the electric quadrupole and the magnetic dipole. 99% of the time only the electric dipole is considered. This represents the difference in energy between the perturbed state and the unperturbed state of the molecules. Thus, this must have an energy dimension. μ is the dipole moment which is the charge times the distance, and the electric field is volt over distance. When you multiply these terms, the expression has the dimension charge times volt or ev, and ev is an energy unit. This will be used in perturbation theory.

=== Perturbation theory ===
The perturbation theory will not be discussed at the quantum- mechanics level. The energy of the ground state of the system is the energy for the unperturbed system. Perturbation can be observed at different orders. At first order, the perturbation is referred as w. If that perturbation is the impact of the electric field of the light in the electric dipole approximation, the perturbation can be expressed as minus μF.

At the first order, the perturbation is operating on the unperturbed wave function of the ground state. Perturbation theory involves modification of systems due to the perturbation of all the wave functions for the unperturbed system. At first order, the perturbation is simply acting on the ground state wave function. Then it is integrated over space and the complex conjugate is taken. At second order, the wave functions of the excited state are taken into account to describe the modification of the system. An unperturbed system has a well defined wave function for the ground state and well defined wave functions for the excited states. The perturbed system is described on the basis of the wave functions of the unperturbed system.
:<math>=\int \Psi* e \overrightarrow{\pi} \Psi dr\,\!</math>

:<math>E_g = E^\circ_g + \langle \Psi_g | w | \Psi_g \rangle + \sum_p \frac {\langle \Psi_g | W | \Psi_p \rangle \langle \Psi_p | W | \Psi_g \rangle + ...}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>E_g = E^\circ_g -\overrightarrow{\mu ^\circ} \overrightarrow{F} - \frac {1} {2!} \alpha \overrightarrow{F}^2 - ....\,\!</math>

:<math>W = - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

In terms of non-linear optics, the perturbation theory expressions will show what the excited states are in your isolated molecule that will contribute to the linear polarizability, 2nd order polarizability, or the 3rd order polarizability and allow you to pinpoint exactly what excited states do play a major role in your optical response.

The complete set of wave functions for the unperturbed state will form the basic set for the perturbation expressions. In principle this includes all excited states. The 2nd order term in terms of perturbation and will correspond to alpha, the linear polarizability. In most conjugated systems, only the first excited state needs to be examined. This will often be the case for alpha and pi conjugated systems as well as for beta. But not for gamma in which two or more excited states must be taken into account. However, the number of states that need close attention can be heavily restricted.

:<math>E_g = E_g^\circ - \underbrace{\langle | \Psi_g | W | \Psi _g \rangle} \overrightarrow{F} + \,\!</math>

::::<math>\overrightarrow{\mu^\circ}\,\!</math>

:<math>\underbrace{\sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}}\,\!</math>

:::::<math>-\frac {1} {2!}\alpha\,\!</math>

A one to one correspondence can be made between the terms in the stark energy expression and the perturbation theory expression when the perturbation is minus μF.

As a side note, as you go to higher orders, things will look a bit more complicated because there are more summations over excited states. For example in 3rd order, there will be a double summation over excited states. In 4th order, there will be a triple summation over excited states. But it will always be products of matrix elements of this kind at the numerator, and the differences in energies of the states for the unperturbed molecule will be in the denominator. The expressions look more complex but by looking at the terms individually, notice that the same kind of terms come up.
P is summation over all excited states

- μF is the electric dipole approximation. The operator expression, μ is the unit electric charge times the position, which is the dipole moment. The electric field does not do anything to the wave functions of the unperturbed state. This expression here? is the expression of the dipole moment for the ground state Φ<sub>g</sub> is the wave function of the ground state in the unperturbed state, which is simply μ<sup> &o;</sup>. At first order, the goal is to find the possible dipole moment. If there is a central symmetry, there won’t be any permanent dipole moment of the molecule. If there is a permanent dipole moment, there will be an interaction between that permanent dipole moment and the external field. At second order, the expression includes the summation over all the excited states p. Here perturbation is replaced by its expression er. Since this deals with the wave functions of the unperturbed system, the electric field is outside. This shows a transition dipole between the ground state and excited state p. and the transition dipole between excited state p and the ground state. These terms are equal. They are the exact same transition dipole. The denominator is the square of the transition dipole between the ground state and excited state p.

The numerator is the difference in energy between the ground state energy and the excited state energy.
Finally, by closely examining the stark energy expression, a connection can be made between the term that is linear in the field, μ<sup>o</sup>F minus ½ α. This shows the expression for alpha as a function of this perturbation expression.

:<math>\alpha=2 \sum_p \frac {\langle \Psi_g | e \overrightarrow{r} | \Psi_p \rangle \langle \Psi_p | e \overrightarrow{r} | \Psi_g \rangle \overrightarrow{F}\overrightarrow{F}}{ E^\circ_p - E^\circ _g}\,\!</math>

:<math>=2 \sum \frac {M_{gp} ^2} {E^\circ _{gp}}\,\!</math>

In this expression there is no longer a minus sign because the denominator is reversed; E of Pnot – E of gnot.

Now there is a compact expression where alpha is equal to 2 times the summation over all excited states of transition dipole with state p times? transition dipole with state p over the transition energy. Taking into account of the perturbation theory, alpha, the linear polarizability, can be described as a sum over all excited states of the square of the transition dipole between the ground state and the excited state, over the transition energy from the ground state.

[[Image:Perturblevels.png|thumb|300px|]]

A pictorial description shows the process of going from the ground state to excited state p and that is a transition dipole between g and p. There is also another transition dipole when coming back from p to g. That is why the expression for alpha shows transition dipole squared. As previously explained, the expressions for beta will look more complex due to the double summations over excited states. The expression for gamma will look even more complex due to the triple summations over excited states. However for all instances, the numerator will always be products of transition dipoles and the denominator will contain the transition energy. In the literature, the perturbation theory expressions are also referred to as “sum over states expressions” the expression contains the sum over all excited states.

A few important questions include “What is the impact of the perturbation on the energy of the system?” and “Would it stabilize or destabilize the system when looking at the perturbation at different orders?”.
It is crucial to understand the differences and variations in conventions. Suppose you want to calculate the dipole moment of the molecule using two programs. First, you input the geometry of the molecule exactly in the same way for both programs. Then, you run the calculation. One program gave a dipole moment of +1.3 Debye, but the other program gave you a dipole moment of -1.3 Debye. Why is there a difference? The difference occurs because the conventions are different for chemists and physicists.

:<math>= - \left( \frac {\delta^4 \overrightarrow{\mu}}{\delta \overrightarrow{F}^4}\right) \overrightarrow{F} \rightarrow 0 \,\!</math>

:<math>\overrightarrow{\mu}= \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F}+ 1/2 \beta \overrightarrow{F}\overrightarrow{F} +1/6 \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} ...\,\!</math>

Before physicists discovered the nature of electrical charge and electrical current, there wasn’t a way to identify whether the charge carriers were positively or negatively charged. Therefore, they made an assumption that it was positive charge that moves . But it turned out that their guess was wrong. We now know, it is the negatively charged electrons that provide electrical conductivity in metals or materials. Thus, in many of the conventions, physicists traditionally observe how the positive charge moves. Whereas chemists look at the displacement of an electron. As a result, the dipole moment can be written as going from left to right if you have a donor-acceptor molecule.

Suppose a quasi one dimensional D-conjugated bridge -A molecule with z the long axis and then apply an external field along z.

:<math>\overrightarrow{\mu}^\circ\,\!</math>
:<math>\rightarrow\,\!</math>

D ----- conjugate -------- A

:<math>\rightarrow\,\!</math> :<math>\overrightarrow{F}_x\,\!</math>
:<math>\leftarrow\,\!</math>

It can also be written, as going from right to left. Suppose that we have a donor acceptor molecule with a conjugated bridge between the two. In linear quasi- 1-demensional type molecules, the whole optical or non-linear optical responses will occur along the axis Z of the molecule.

=== Stabilization ===

<br clear='all'>
[[Image:Stabilization.png|thumb|300px|]]

Assume you have molecule that has a positive pole and a negative pole. You can place an electric field along the main axis in two directions. At the first order you will only observe the permanent dipole moment of the molecule and its interaction of the field; thus you have a permanent dipole moment period. You have a plus and a minus. It is also important to know which situation, the one on the top or the one on the bottom, will be more stable. As a matter of fact, the one at the bottom will be the most stable situation. This is because when you have two dipole moments on top of one another, the anti-parallel? situation will be much more favorable then the parallel situation. In anti-parallel situation the positive charge is stabilized by the negative pole of the electric field and the negative charge is stabilized by the positive pole. Where as in the parallel situation there is a destabilization. Therefore, independently from the conventions in terms of the electric field and the dipole moment, it is clear which situation will lead to a net stabilization of the energy of the system and which one will lead to a destabilization.

At first order, nothing changes within the molecule.

At second order you will have a flux of electrons towards the left to counteract the external field in the lower case, and in the upper case you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself. At third order, it gets more complicated.

'''First order energy term'''
:<math>E(\overrightarrow{F}) - E^\circ = - \overrightarrow{\mu^\circ} \overrightarrow{F}\,\!</math>

:<math>= - \overrightarrow{\mu}_z ^{ \circ}- \overrightarrow{F}_z\,\!</math>

There is stabilization if :<math>\overrightarrow{F}_z\,\!</math> is parallel to :<math>\overrightarrow{\mu}^\circ\,\!</math>

There is destabilization if :<math>\overrightarrow{F}_z\,\!</math> is anti-parallel to :<math>\overrightarrow{\mu}_z^{\circ}\,\!</math>

In other words, with the indicated conventions, stabilization will occur if the field is parallel to the dipole moment and destabilization will occur in the opposing case. But again, that depends on the conventions chosen for the field and dipole moment. Remember that at first order in the field ( the linear term of the energy expression) only the interaction between the permanent dipole moment, is examined. However, at higher orders, we examine how the system responds to the external field on the molecule. As a result, we look at the polarizabiliy, or in the case of alpha the linear polarizability. In perturbation theory the second order term gives the stabilization.

This can easily be seen from the previous expression. Alpha is a summation over all excited states of the squares of the transition dipole, which makes it positive. The transition energy going from the ground state will always be positive by definition of the ground state.

'''Second order energy term'''
:<math>- \frac{1}{2} \alpha_{zz} \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

Alpha is positive and we multiply by F times F, which will be positive. Therefore, the whole second order term leads to a stabilization of the system.

Think back about the simple example shown previously. At first order, nothing changes within the molecule. At second order, look at the response of the molecule to the external field. What will happen here? What will happen is that you will have a flux of electrons towards the left to counteract the external field, and here you will have a flux of electrons toward the right. Thus, the system will always respond in a way to stabilize itself.

Alpha is a tensor of rank two and there are nine tensor components for alpha. Beta is a tensor of rank three. Since each of these indices can be x y z, there will be a possible of 27 tensor components.
'''third order energy term'''
:<math>- \frac{1}{6} \beta_{zzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\,\!</math>

There is stablilization or destablization depending on whether :<math>\overrightarrow{F}_z\,\!</math> is parallel or antiparallel to the vectorial part of β, and depends on the sign of β which depends on Δ μ <sub>eg</sub>

In a two state model expression, beta depends very much on the difference in state dipole moment between the ground state and the active excited state. Β will be positive if that active excited state has a dipole moment that is larger than the dipole moment in the ground state, and β will be negative if the dipole moment in the excited state is smaller than in the ground state. This is an easy way of understanding the variation in the sign of β.

'''Fourth order energy term'''

:<math>- \frac{1}{24} \gamma_{zzzz} \overrightarrow{F}_z \overrightarrow{F}_z \overrightarrow{F}_z\overrightarrow{F}_z\,\!</math>

This is stabilizing if γ is >0 and destabilizing if γ is <0

For fourth order, in this case, the field components would lead to a positive term by necessity. Thus, we will have either stabilization if γ is positive or destabilization if γ is negative. This is consistent with the process called the self-focusing of light in the material with positive γ. If you shine a high intensity laser light into a molecule that has a very large positive γ response, the beam will self-focus. The system tends to go to higher local fields and therefore obtain a larger stabilization by focusing the light. Where as a negative γ leads to a defocusing of your light. This property can be use for protection from high intensity light.

Gamma is a tensor of rank four and there will be 81 tensor components. When looking at extended π conjugated molecules, (quasi 1-dimensional) the components along the long axis of the molecule will dominate everything. However, with molecules that become more complex in shape there are a number of components that can become important as well. Also, there are symmetry relationships among those components. In the literature on non-linear optics, there is something referred to as Climan symmetry that is based on the point groups of the different molecules that gives the relationship between the different tensor components. However, here we are mostly concerned with at the α<sub>zz</sub> component, the β<sub>zzz</sub>, or γ<sub>zzzz</sub> What will be provided is a difference between the global value and the tensor component along the main axis. It is difficult to know whether the third order term leads to stabilization or destabilization because β could be positive or negative. Also, the combination of the three field terms can be positive or negative so it really depends.

=== Dipole changes ===
We can also look at what happens to the dipole moment. In the case of the α, the permanent dipole can be zero if we have a centrosymmetric molecule or it can be any value depending on the nature of the molecule. If it is non-centrosymmetric there will be an increase or decrease depending on the direction of the field at first order.

:<math>\overrightarrow{\mu} = \overrightarrow{\mu^\circ} + \alpha \overrightarrow{F} = \overrightarrow{\mu^\circ_z} + \alpha \overrightarrow{F_z}\,\!</math>

First order: The dipole increases or decreases according to whether F<sub>z</sub> is parallel or antiparallel to :<math>\overrightarrow{\mu^\circ_z}\,\!</math>

Second order:

The change depends on how the field is aligned with respect to the permanent dipole moment. At the next order FF is always positive so dipole it will be decided by the value of β. The sign of β can often be related to the difference in dipole moment between the ground state and the active excited state. If there is an increase in the dipole moment going from the ground state to the excited state, β will be positive. That excited state now contributes to the description of the system because with a larger dipole moment, it is reasonable to assume that the μ of the system will increase. The opposite will occur for a negative β. All these considerations will become clearer when the perturbative expressions for beta and gamma are discussed in detail.

:<math>1/2 \Beta : \overrightarrow{F} \overrightarrow{F}\,\!</math>

In the context of the two state model, beta has a sign of :<math>\Delta \mu_{eg}\,\!</math>

:<math>\beta >0 : \mu \uparrow\,\!</math>

:<math>\beta <0 : \mu \downarrow\,\!</math>

Third order
For the impact of γ, the dipole moment depends on the sign of γ and the field alignments in the expression of the dipole moment. There will be three fields that will play a role.

=== Calculation of polarizabilities ===
Polarization of a medium due to an electric field.

In spite of the different conventions used to look at the physics of the system, it is good enough to just look at what the external field with respect to the permanent dipole moment does. Papers in the field of non-linear optics, especially for inorganic materials, often look at the macroscopic polarization that occurs when the field is applied. Since the experimentalists are not concerned with the possible derivations that are necessary when calculating α, β, γ, they often use an expression that is a power series expansion instead of a Taylor series expansion.

This expression of the polarization of the medium corresponding to the possible permanent polarization when the material is non-central symmetric. The expression contains a first order term which is the first order electrical susceptibility. Remember, the :<math>\chi^{(1)}\,\!</math> is a tensor; there will be 9 tensor components there. That is the equivalent of α for the microscopic scale.

:<math>\overrightarrow{P} = \overrightarrow{P_0} + \chi^{(1)} \overrightarrow{F} + \chi^{(2)} \overrightarrow{F}\overrightarrow{F} +\ chi^{(3)} \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} +\,\!</math>

:<math>\chi^{(1)}\,\!</math> is the first order electrical susceptibility (second rank tensor).

:<math>\chi^{(2)}\,\!</math> is the first order electrical susceptibility (third-rank tensor).

:<math>\chi^{(3)}\,\!</math> is the third order electrical susceptibility, and so on.

Only :<math>\chi^{(1)}, \chi^{(2)}, \chi^{(3)}\,\!</math> will be considered, although experimentally there are people that have shown :<math>\chi^{(5)}, \chi^{(6)}\,\!</math> processes that are very specific.

Molecular materials at the microscopic level

:<math>\overrightarrow{\mu} = \overrightarrow{\mu_0} + \alpha \overrightarrow{F} + \beta \overrightarrow{F} \overrightarrow{F} + \gamma \overrightarrow{F}\overrightarrow{F}\overrightarrow{F} + ...\,\!</math>

where

:<math>\alpha\,\!</math> is first order polarizability

:<math>\beta\,\!</math> is the secord order polarizability or first order hyperpolarizability

:<math>\gamma\,\!</math> is the third order polarizability or second order hyperpolarizability

This is the corresponding expression for the dipole moment of a given molecule on the microscopic level. It is expressed in the power series expression. α is referred to as the polarizability. In the context of non linear optics, when looking at the β and γ terms, α can be more rigorously referred to as the first order polarizability. β is the second order polarizability or (some people prefer to use the expression) first order hyperpolarizability. γ is the third order polarizability or the second order hyperpolarizability. The reason why μ is expressed in both a power series expression and in a Taylor series expression is that most of the programs that make calculations use Taylor series expansion. However, the β or the γ that one calculates can differ from one program to another. It can differ by a factor of 2 for β, and by a factor of 6 for γ. Therefore, it is wise to also compare your calculated data with what is reported experimentally. Usually, experimentalists use a power series expansion. Thus, if they had done the calculation taking into account the Taylor series expansion, they will have immediately a difference by a factor of 2 or a factor of 6 with the experiment.

'''Stark Energy'''

Switching back to the Taylor series expressions. This shows the stark energy expression written in a more rigorous way taking into account for all the possible components of the field and for the tensor components of the α, β, and γ tensors.

:<math>E(F) = E_0 - \sum_{i} \mu_{0i}F_i - \frac {1} {2!} \sum_{ij} \alpha_{ij} F_i F_j - \frac {1} {3!} \sum_{ijk} F_i F_jF_k - \frac {1}{4!} \sum_{ijkl} \gamma_{ijkl} F_i F_j F_k\,\!</math>

'''Dipole Moment'''

This shows a similar expression for the dipole moment. These two expressions are fully consistent with each other, given the Hellman-Feynman theory.

:<math>\mu_i(F) = \mu_{0i} + \sum_j \alpha_ij F_j + \frac {1} {2!} \sum_{jk} \beta_{ijk} F_j F_k + \frac {1} {3!} \sum_{jkl} \gamma_{ijkl} F_j F_k\,\!</math>

:<math>\mu_i = - \frac {\partial E(f)}{ \partial F_i}\,\!</math>

These expressions clearly show what was confirmed earlier regarding the tensors and its respective rank. For example, γ will be a tensor of rank 4 because you are looking at the impact on the i component of the dipole moment when applying a field along j, a field along k, or a field along L. That is the reason why the α, β, and γ contain all those tensor components.

:<math>\alpha_{ij} = -\frac{ \partial ^2E(F)} {\partial F_i \partial F_j} = \frac {\partial ^1 \mu_i} {\partial F_j}\,\!</math>

:<math>\beta_{ijk} = -\frac{ \partial ^3E(F)} {\partial F_i \partial F_j \partial F_k} = \frac {\partial ^2 \mu_i} {\partial F_j \partial F_k}\,\!</math>

:<math>\gamma_{ijkl} = -\frac{ \partial ^4E(F)} {\partial F_i \partial F_j \partial F_k \partial F_l} = \frac {\partial ^3 \mu_i} {\partial F_j \partial F_k \partial F_l}\,\!</math>

=== Derivative Techniques ===

From those derivative expressions and the perturbative expressions, two types of calculations can be derived to evaluate the molecular polarizabilities from quantum-mechanical approaches. There is one major set of calculations that involve the derivation of either the energy or the dipole moment with respect to the external field. Those derivations can be done either numerically using methods referred to as finite-field methods, or analytically using Coupled Perturbed Hartree-Fock (CPHF) methods.

In a finite-field calculation, you take the interaction with the external field and put it into your Hamiltonian for the isolated molecule without any external perturbation. It has a kinetic term, a nucleic attraction term, a coulomb term, and exchange term. Now here, a fifth term is added to those present four terms. The fifth term expresses the interaction with your field. Several calculations are then made in which several values of the external field are taken into account. Then you do a numerical derivation of the dipole moments that you will have calculated as a response to the external field.

:<math>H(\overrightarrow{F} = H_0 - \overrightarrow{\mu} \overrightarrow{F}\,\!</math>

The MO's are self-consistant with the eigenfunctions of :<math>H(\overrightarrow{F})\,\!</math>. What is interesting with those finite field methods is that since the perturbation interaction with the electric field is put into the Hamiltonian, the molecular orbitals that are derived are affected by that interaction. Then the α, β, γ tensor components are calculated by applying standard numerical procedures. Calculations are made with different values of the field. Different values of for dipole moment for the molecule are obtained. A numerical derivation is then made to get to α, β, and γ. For instance, two calculations are made for the α <sub>ii</sub> component. The calculation is made with the field in one direction, and then again with the field in the opposite direction. It is important to have a value of the field that is large enough so that the molecule can respond and give a numerically accurate variation in the dipole moment. However, it should not be too large or the equivalent of a dielectric breakdown of your molecule will be obtained and the calculation will simply not converge. Therefore, it is crucial know what values of the fields are needed to evaluate.

:<math>\alpha_ii = \frac {\partial\mu_i} {\partial F_i} = \frac {1}{2F_i} [\mu_i(F_i) - \mu_i(-F_i)]\,\!</math>
:<math>
\gamma_{iiii} = \frac {\partial^3 \mu_i} {\partial F_i \partial F_i \partial F_i} = \frac {1} {48F_i^3} [\mu_i(3F_i)-\mu_i(-3F_i)- 3\mu_i (F_i)+ 3\mu_i (-F_i)]\,\!</math>

We pick a compromise value that is able to insure accuracy but also avoid divergence.

:<math>F_i \approx 5 x 10^8 Vm^{-1}\,\!</math>

'''Coupled perturbed Hartree-Fock method'''

Another method that can be used to make those calculations is the analytical methods with analytical expressions for the variation of the energy with respect to the electric field.

:<math>\beta_{ijk} = - \frac {\partial^3 E(F)} {\partial F_i \partial F_j \partial F_k}\,\!</math>

=== Perturbation techniques ===

'''Sum over state (SOS) method'''
Besides making numerical or analytical calculations based on the derivation expressions, the perturbation theory expressions can also be used. This method is usually referred to as Sum Over States (SOS) method. This method was seen before for alpha. It is based on the perturbation expression for Stark energy terms which are related to optical nonlinearities based on their order in the field strength. α is calculated by evaluating the transition dipoles and the transition energies for all the excited states in the molecule.

You can look at the convergence of your values as a function of going over many excited states. However, it is important to understand that the higher energy you go, the larger the denominator becomes. Therefore, those terms will have smaller weight. Also, at very high excited states, the transition dipole will die down as well. For example, in the case of α the lowest excited states have the largest response.

:<math>\alpha_{ij} = \sum_m \frac {<\psi_0|\mu_i | \psi_m > <\psi_m|\mu_j | \psi_0 >} {E_m- E_0}\,\!</math>

For the β terms, we have exactly the same components. However, the expression looks more complicated because it contains a double summation over excited states. That is transition dipole going from the ground state n to excited state to m. Then it goes from excited state m back to the ground state. The denominator has the transition energies. There is also a second term that goes over a summation over excited state due to the dipole moment starting in the ground state. Then there is a transition dipole going from the ground state to excited state n and then it comes back from n to the ground state, over transition energies. To generate these expressions go through the perturbation theory and work the second order and the third order perturbation theory expression, one can do so by placing the dipole (er), the dipole operator, and the electric field.

:<math>\alpha_{ijk} = \sum_n \sum_m \frac {<\psi_0|\mu_i | \psi_n > <\psi_m|\mu_j | \psi_0 ><\psi_m|\mu_k | \psi_0 >} {(E_n- E_0)(E_m- E_0)} - \sum_n \frac {<\psi_0|\mu_i | \psi_0 > <\psi_0|\mu_j | \psi_n ><\psi_n|\mu_k | \psi_0 >}{(E_m- E_0)(E_n- E_0)}\,\!</math>

The reason why it is interesting to evaluate the non-linear optic properties with those perturbation expressions (sum over state expressions) is because it pinpoints which excited states play important roles in optical and non-linear optical response. Another reason why they are heavily exploited is because the frequency dependence can easily be introduced with the response. With the finite-field method, it gets extremely complicated to introduce the frequency dependence.

The finite-field method is usually incorporated in many quantum chemistry packages. You just press key telling “calculate the molecular polarizabilites” and then you get numbers for those polarizabilites. However that is the problem; it only gives numbers and these are the static values where ω is equal to zero.
It doesn’t provide an in depth understanding of what is occurring. There have been extensions to those methods that provide some kind of understanding regarding finite field methods of the local spatial contributions to the non-linear optical response. But it is a sophisticated approach that is not often used. Thus, in many instances, it more beneficial to use the sum-over states expression because it gives an idea of which electronic states matter. Also, frequency dependence can easily be introduced. The same thing can be done at the γ level.

:<math>\beta^{SHG}(-2\omega;\omega \omega) = 1/2 \sum_n \sum \_m \frac {<\psi_0 | \mu_i | \psi_n><\psin|\muj|\psi_m><\psi_m |\mu_k|\psi_0>} {(\hbar\omega-(E_m-E_0))(2\hbar\omega-(e_m-e_0))}\,\!</math>

Perturbation Theory

2010-03-11T23:01:39Z

128.95.39.187: /* Perturbation techniques */