Double Refraction and Birefringence - Revision history

Cmditradmin at 21:28, 2 September 2009

2009-09-02T21:28:46Z

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Cmditradmin at 21:27, 2 September 2009

2009-09-02T21:27:28Z

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Cmditradmin at 21:15, 2 September 2009

2009-09-02T21:15:44Z

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			Liquid crystals can effectively shutter light by rapidly changing the index of refraction. There are several basic optical principles that are needed to explain the phenomenon.

	=== Wave Surfaces ===		=== Wave Surfaces ===

128.95.39.42: /* Double Refraction */

2009-06-29T15:47:27Z

Double Refraction

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	=== Double Refraction ===		=== Double Refraction ===
	[[Image:Calcite.jpg\|thumb\|300px\|Here is an example of a crystal of calcite.]]		[[Image:Calcite.jpg\|thumb\|300px\|Here is an example of a crystal of calcite exhibiting double refringence or double refraction.]]
	When a beam of unpolarized light enters a birefringent crystal at normal incidence (but not along the optic axis), two light beams emerge. This effect (first observed in calcite by the Vikings) is called double refraction:		When a beam of unpolarized light enters a birefringent crystal at normal incidence (but not along the optic axis), two light beams emerge. This effect (first observed in calcite by the Vikings) is called double refraction:

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	Here is an example of a crystal of calcite. The ordinary ray is able to pass straight through the crystal. The second line is produced by the extraordinary beam. The extraordinary beam does not follow Schnell’s law which holds only for isotropic materials.		Here is an example of a crystal of calcite. The ordinary ray is able to pass straight through the crystal. The second line is produced by the extraordinary beam. The extraordinary beam does not follow Schnell’s law which holds only for isotropic materials.

	If you place a cross polarizer over the crystal one or the other of the double refracted lines will disappear. They have orthogonal polarization.		If you place a cross polarizer over the crystal one or the other of the double refracted lines will disappear. They have orthogonal polarization.


	=== Birefringence ===		=== Birefringence ===

Cmditradmin: /* Anisotropic Materials */

2009-06-25T15:46:15Z

Anisotropic Materials

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	=== Anisotropic Materials ===		=== Anisotropic Materials ===
	[[Image:Anisotropic.png\|thumb\|300px\|]]		[[Image:Anisotropic.png\|thumb\|300px\|An anisotropic material has an ellipsoidal wave surface with respect to extraordinary waves which are polarized perpendicular to the optic axis. Ordinary waves polarized with the optic axis still see an isotropic material and the wave surface is spherical.]]

	In an anisotropic material the index of refraction is not the same for each direction. We ask for different polarizations of light what will the wave surface look like?		In an anisotropic material the index of refraction is not the same for each direction. We ask for different polarizations of light what will the wave surface look like?
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	We can compare two surfaces. The ordinary wave surface (Sord) has a component of polarization that is not along the unique axis (z) of the molecule, that is polarized along Nx or Ny. The extraordinary wave surface (Sext) has a polarization that is oriented along the unique axis (z). This results in a different wave surface depending on the direction. This kind of materials is called birefringent. If you have light shining along the x or y axis travels more slowly resulting in double refraction.		We can compare two surfaces. The ordinary wave surface (Sord) has a component of polarization that is not along the unique axis (z) of the molecule, that is polarized along Nx or Ny. The extraordinary wave surface (Sext) has a polarization that is oriented along the unique axis (z). This results in a different wave surface depending on the direction. This kind of materials is called birefringent. If you have light shining along the x or y axis travels more slowly resulting in double refraction.

	Other non-cubic crystals are characterized by two optical axes (i.e. there are three distinct axes) and are said to be optically biaxial.		Other non-cubic crystals are characterized by two optical axes (i.e. there are three distinct axes) and are said to be optically biaxial.

	=== Double Refraction ===		=== Double Refraction ===

Cmditradmin: /* Wave Surfaces */

2009-06-25T15:42:42Z

Wave Surfaces

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	=== Wave Surfaces ===		=== Wave Surfaces ===
	[[Image:Wavesurface.png\|thumb\|300px\|]]		[[Image:Wavesurface.png\|thumb\|300px\|An isotropic material with a larger index of refraction would have a smaller wave surface at any arbitrary time because light waves would propagate slower.]]
	There are two useful constructs when considering liquid crystals; wave surfaces and index elipsoids.		There are two useful constructs when considering liquid crystals; wave surfaces and index elipsoids.

Cmditradmin: /* Double Refraction */

2009-06-25T15:37:46Z

Double Refraction

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	=== Double Refraction ===		=== Double Refraction ===
	[[Image:Doublerefract.png\|thumb\|300px\|]]		[[Image:Doublerefract.png\|thumb\|300px\|An extraordinary ray (E-ray) is polarized perpendicular to the optic axis and experiences a different index of refraction than the ordinary ray (O-ray) ]]
	One beam follows a normal path and the other will start to diverge.		One beam follows a normal path and the other will start to diverge.

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	If light is not polarized perpendicular to the optic axis, the index of refraction varies as a function of the direction of propagation. The anglar sensitive index becomes the extraordinary index of refraction n<sub>e</sub>		If light is not polarized perpendicular to the optic axis, the index of refraction varies as a function of the direction of propagation. The anglar sensitive index becomes the extraordinary index of refraction n<sub>e</sub>


	=== Explanation of double refraction ===		=== Explanation of double refraction ===

Cmditradmin: /* Explanation of double refraction */

2009-06-25T15:32:42Z

Explanation of double refraction

← Older revision		Revision as of 08:32, 25 June 2009
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	=== Explanation of double refraction ===		=== Explanation of double refraction ===
	[[Image:Doublerefract_eye.png\|thumb\|300px\|]]		[[Image:Doublerefract_eye.png\|thumb\|300px\|An ellipsoidal extraordinary wave surface on the left and a spherical ordinary wave surface on the right]]

	For light traveling through a birefringent material except along the optic axis, the two orthogonally polarized rays "see" different polarizabilities and thus, different refractive indices.You can think of it as wave surfaces. Light will leave the material in a direction that is perpendicular to the tangent of the wavesurface at the exit point.		For light traveling through a birefringent material except along the optic axis, the two orthogonally polarized rays "see" different polarizabilities and thus, different refractive indices.You can think of it as wave surfaces. Light will leave the material in a direction that is perpendicular to the tangent of the wavesurface at the exit point.

Cmditradmin: /* Wave Surfaces */

2009-06-24T22:13:48Z

Wave Surfaces

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	The electric field of light is perpendicular to its direction of propagation. A point source emitting light from the center of an isotropic crystal emanates light outward uniformly in all directions. The position of the wave front defines a sphere (wave surface) whose radius is increasing with time		The electric field of light is perpendicular to its direction of propagation. A point source emitting light from the center of an isotropic crystal emanates light outward uniformly in all directions. The position of the wave front defines a sphere (wave surface) whose radius is increasing with time

	Think about a point source in the center of the material emitting light that forms a wave surface. The wave surface is the tangent to the surface of the wavefront of a wave of light coming from that point. In a isotropic material the wave surface forms a sphere. In a material with a higher index of refraction the wave surface has a smaller radius.		Think about a point source in the center of the material emitting light that forms a wave surface. The wave surface is the tangent to the surface of the wavefront of a wave of light coming from that point. In a isotropic material the wave surface forms a sphere. In a material with a higher index of refraction the wave surface has a smaller radius.

	We can also draw another construct with a surface defined by a vector whose magnitude is the refractive index of light travelling in a given direction. In isotropic material this surface would also form a sphere, however since the magnitude of each vector is greater with a higher index of refraction this surface would have a large radius for when there is a higher index of refraction. In the example the first low index material has a larger wave surface than the second material which has a high index.		We can also draw another construct with a surface defined by a vector whose magnitude is the refractive index of light travelling in a given direction. In isotropic material this surface would also form a sphere, however since the magnitude of each vector is greater with a higher index of refraction this surface would have a large radius for when there is a higher index of refraction. In the example the first low index material has a larger wave surface than the second material which has a high index.

	If we chose another material with a larger susceptibility (more polarizable), its wave surface would expand more slowly because the susceptibility relates to the square of the refractive index. At an arbitrary time (t), the wave surface shows a radius inversely proportional to the index of refraction.		If we chose another material with a larger susceptibility (more polarizable), its wave surface would expand more slowly because the susceptibility relates to the square of the refractive index. At an arbitrary time (t), the wave surface shows a radius inversely proportional to the index of refraction.

	=== Anisotropic Materials ===		=== Anisotropic Materials ===

Cmditradmin: /* Double Refraction */

2009-06-24T22:13:35Z

Double Refraction

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	=== Double Refraction ===		=== Double Refraction ===
			[[Image:Doublerefract.png\|thumb\|300px\|]]
	One beam follows a normal path and the other will start to diverge.		One beam follows a normal path and the other will start to diverge.

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	For light polarized perpendicular to the optic axis, the material appears isotropic and the index of refraction is independent of the direction of propagation. We call this angularly independent index the ordinary index of refraction n<sub>o</sub>.		For light polarized perpendicular to the optic axis, the material appears isotropic and the index of refraction is independent of the direction of propagation. We call this angularly independent index the ordinary index of refraction n<sub>o</sub>.

	If light is not polarized perpendicular to the optic axis, the index of refraction varies as a function of the direction of propagation. The ~~angularly~~ sensitive index becomes the extraordinary index of refraction n<sub>e</sub>		If light is not polarized perpendicular to the optic axis, the index of refraction varies as a function of the direction of propagation. The anglar sensitive index becomes the extraordinary index of refraction n<sub>e</sub>


			=== Explanation of double refraction ===
			[[Image:Doublerefract_eye.png\|thumb\|300px\|]]

			For light traveling through a birefringent material except along the optic axis, the two orthogonally polarized rays "see" different polarizabilities and thus, different refractive indices.You can think of it as wave surfaces. Light will leave the material in a direction that is perpendicular to the tangent of the wavesurface at the exit point.

			One ray becomes retarded relative to the other (introducing a phase shift) and diverges.
			A uniaxial material will therefore have two wave surfaces, a spherical ordinary wave surface and an ellipsoidal extraordinary wave surface. (Note that the magnitudes of the principal axes of the wave surface are inversely proportional to the refractive indices normal to the direction of propagation).

			Light rays propagate at normal incidence for a wave surface, and your eye traces that rays perceived origin within the wave surface.
			The origin of the extraordinary ray (unless the ray is traveling along or perpendicular to the optic axis) will appear displaced.
			However for the ordinary wave surface ray will be traced back to its real origin (if eminent from within the materials or strikes the material at a normal incidence) and pass through the center of the wave surface.

			=== References ===

			<references/>

	[[category:liquid crystals]]		[[category:liquid crystals]]