Terahertz Radiation

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1 THz ~ 300 µm wavelength ~33 wave numbers ~ 4 meV- Courtesy of www.SURA.org

Terahertz (THz) is Far-Infrared radiation located between microwaves and infrared in the electromagnetic spectrum. It is low-energy, non-ionizing radiation which can penetrate many non-polar, non-conducting materials such as clothing, paper, masonry or plastic. Possible applications of THz include:

  • Medical imaging - THz can penetrate several millimeters into tissues with low water content, or deep into teeth, without damage. For example: THz can be used for burn depth assessment, skin cancer identification, etc.
  • Security screening- THz can penetrate clothing and reveal hidden weapons. Explosives, biological agents, and controlled substances have specific spectral signatures allowing for chemical identification.
  • Spectroscopy- THz time domain spectroscopy can measure the low-energy, far-infrared properties of substances that are opaque in the visible and near-infrared regions of the spectrum. In particular, collective vibrations, phonon resonances, and scattering rates of charge carriers are typically in the THz range.
  • Manufacturing- Circuit boards, device components, and the contents of paper packages can be easily visualized for quality control. For example, THz inspections can identify voids in space shuttle foam, like those responsible for the Columbia disaster.


History of THz Science

Far-infrared studies have occurred since the invention of the bolometer in 1881 by astronomer Samuel Langley. Much of the early far-infrared work was done by Rubens, who discovered reststrahlen sources enabling measurements crucial to Planck's blackbody radiation theory. Far-infrared transmission studies of superconductors confirmed the energy gap predicted by Bardeen,Cooper, and Schrieffer's superconductivity theory. Since the invention of frequency-division multiplexing in 1949, Fourier-transform infrared spectroscopy became a standard tool in physical chemistry. Over the years, numerous sources and detectors have been discovered e.g. Golay cell, water-vapor laser, pyroelectric detector, synchrotrons, free-electron lasers, and quantum cascade lasers.

Modern pulsed-THz sources grew out of the work of Auston, Nuss, and Grischkowsky on photoconductive switches, electrical pulses on transmission lines, and far-infrared emission from nonlinear crystals in the 1980s. Since their pioneering work, photoconductive switches have become one of two popular methods of generation and coherent detection of bright THz pulses with high sensitivity. The other popular modern method involves generation of broadband THz radiation via "optical rectification" and coherent detection of the THz waveform through free-space electro-optic sampling, both occurring in nonlinear optical media.


THz generation and detection

A bench-top optical-pump THz-probe setup

THz radiation is typically generated via optical rectification (OR) in a nonlinear optical (NLO) material or impulsively from photoconductive dipole antennae (PDA). In a PDA, THz radiation is emitted by an ultra-fast transient photo-current created in a biased semiconductor. The semiconductor is photo-excited with an ultra-short pulse to generate short-lived charges, which are accelerated with an applied electric field. Though PDAs are bright THz sources, finite carrier lifetimes limit the bandwidth available from photoconductive materials to less than that acheivable via OR in NLO materials.

OR is more properly though of as difference frequency mixing. In a NLO material, the polarization induced by an AC electric field will not reverse its sign at the same time as the driving field, leading to a nonlinear polarization and thus frequency mixing. If the field is applied with a femptosecond laser pulse, with a large spectral bandwidth, difference frequency mixing of different frequency components results in electromagnetic waves in the terahertz region. This is the optical analog of the audible beat frequency generated by two struck tuning forks. The efficiency of THz generation depends on the second order nonlinear susceptibility of the medium.


THz time-domain spectrometer experimental schematic

In a typical experimental setup a sub-100 fs "pump" laser pulse travels through a second-order NLO, i.e. electro-optic (EO), material which generates THz by optical rectification. The radiation is collected and focused with front-surface mirrors and directed towards to detector, where it is overlapped collinearly with the sampling, "probe" beam. The probe is separated into s- and p- polarization components using a wollaston polarizing beam splitter. The two component polarization beams are directed into balanced photo-diodes, which yield null current for equal s- and p- beam intensities. The THz electric field induces a change in the index of refraction of the EO sensor material via the electrooptic effect, rotating the "probe" polarization. This produces unequal s- and p- beam intensities, leading to current flow proportional to the THz electric field amplitude and direction. Delay stages are used to change the delay between the THz and "probe" beams, allowing the "probe" to sample the THz waveform. The shape of the recorded current matches the THz waveform, i.e. the electric field of the THz pulse.


See Sum and Difference Frequency Generation

EO Polymers for THz

EO poled polymers have the potential to acheive orders of magnitude higher optical nonlinearities than crystalline materials. Poled polymers have acheived electro-optic coefficients >400 pm/V, which is two orders of magnitude larger than the inorganic crystal ZnTe, which is a standard material for THz generation.


Phase matching (i.e. velocity matching) is necessary for efficient THz generation. Due to phonon lattice resonances in the THz regime, NLO crystals can be quite dispersive. Many crystals are also disperive in the visible and near infrared (NIR). Polymers have very low dispersion. Their NIR and THz indeces of refraction are nearly the same, yielding very good phase matching.

Phase (velocity) matching by comparing the THz (a) and the visible (b) indices of refraction of EO poled polymers. The Lorentz Oscillator model of the THz index of ZnTe is included in the inset of (a) for reference.

See Sinyukov, Hayden [1]

See Hayden 2003 [2]


Spectroscopy Applications

Time domain spectroscopy and Optical pump THz Probe compared

When THz radiation passes through an object its dielectric properties can be revealed.

THz Time Domain Spectroscopy

In THz Time Domain Spectroscopy, a ~1ps single-cycle THz pulse is propagated through a sample.

The electric field of the THz pulse is sampled via the electrooptic effect in a second order nonlinear material.

The field transmitted through the sample is compared to that transmitted through its substrate (or through free space for free standing samples) and through fourier analysis the frequency dependent index of refraction and absorption coefficients are extracted.

The index of refraction of amorphous polycarbonate from 0-7THz.


Optical Pump THz Probe Spectroscopy

In Optical-Pump THz-Probe Spectroscopy, a THz pulse is propagated through a photo-excited sample.

In Optical Pump THz Probe Spectroscopy (OPTP) the THz waveform transmitted through the excited sample is compared to that transmitted through the unexcited sample and through fourier analysis the full frequency dependent complex conductivity can be obtained. Modeling on this photo-induced conductivity yields the mobility and carrier density, also giving the photon-to-carrier yield. Control of the delay between the excitation (the "pump") and the THz pulse (the "probe") provides the time evolution of the photoexcited state.

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(left) Photoconductivity dynamics described by pump delay dependent changes in THz transmission through the photoexcited sample. (Right) The change in the transmitted THz waveform is recorded at various delays to allow for the extraction of the evolving frequency-dependent dielectric properties.


To extract the complex conductivity we use the following approximate analytic relationship following the work of Sundstrum

<math>\tilde{\sigma} (\omega) \approx - \frac {(n_{THz} +1 )}{Z_0d}\frac {\Delta \tilde{E}(\omega)}{\tilde{E}_0(\omega)}\,\!</math>

where

<math>d\,\!</math> is the absorption depth at λexc


Advantages

  • Non-contact low energy (meV) non-perturbing optical probe with sub-ps resolution
  • Coherent detection provides magnitude and phase of THz waveform, i.e. direct access to the complex dielectric properties of materials under study
  • THz radiation is sensitive to charge carriers as carrier scattering times are fs-ps placing the scattering (damping) rate in the THz regime


Special Studies

Time-resolved broadband THz studies have the capability to reveal new physics concerning the nature of charge transport in polymers. Many models of conductivity are similar over narrow bandwidths, particularly 0-2 THz (Figure 1.26, left). Broadband (0-15 THz) OPTP will access frequency ranges where the models diverge from each other allowing a more complete understanding of the fundamental charge carrier dynamics and mechanisms.


Carrier Dynamics

Excitation at 800nm vs 400nm. (Left) A band diagram of GaAs shows that the excess 1.49eV provided by the 400nm excitation allows carriers to scatter to higher valleys. (Right) The longer rise time of the 400nm photo-induced conductivity signal corresponds to the time required for carriers to return to the high mobility gamma valley.

OPTP spectroscopy has be used to examine carrier dynamics, Drude-like and deviations from the Drude model in popular semiconductors such as semi-insulating (SI-) GaAs


File:GaAs 800sigma.png
The frequency-dependent photoconductivity of GaAs shows deviations from the simple Drude model.


Carrier trapping

comparison of the photo- conductivity of low-temperature grown (LT-) GaAs with SI-GaAs

It can also be used to identify carrier trapping. The rapid decrease in THz absorption (below) in photoexcited LT-GaAs is due to carrier trapping by As clusters.

We have applied this technique to study carrier dynamics in RR-P3HT and ultrafast charge transfer in the bulk heterojunction P3HT/PCBM 1:1 excited with either 400 nm (3.1 eV) and 800 nm (1.44 eV) light, the results of which are published in J Phys Chem C.

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Inclusion of a liquid He cryostat allowed for temperature dependent studies
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Low temperature photoconductivity increase


At low temperature there is an increase in the photoconductivity (mobility) of P3HT due to decreased torsoinal disorder which increases the effective conjugation length. The faster recombination dynamics are associated with inhibited interchain hopping at low temperature.

There is only very weak absorption at 800 nm.
File:P3HT pump.png
Both energy excitations yield similar dynamics on subpicosecond time scales.
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Ultrafast electron transfer from P3HT to PCBM is marked by an increase in the long lived photoconductive state in the bulk heterojunction compared to neat films of P3HT.
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Bulk heterojunction compared to P3HT



The extracted complex frequency-dependent conductivty of P3HT exibits characteristics of strong (Anderson) carrier localization and inhibited long range trasport due to disorder (below). Fitting of the conductivity to the Drude-Smith model provides photon-to-carrier yields of < 1.5% and a hole mobility of ~35 cm^2/Vs. The THz regime mobility agrees well with published DFT calculations of the predicted intrinsic hole mobility in well ordered P3HT.

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The complex conductivity of P3HT measured from 200 GHz - 2.1 THz extracted at 1, 1.5 and 6.2 ps after photoexcitation. The solid lines are fits to the Drude-Smith model.
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The mobility in perfectly ordered P3HT far exceeds that typically measured in devices due to the effect of disorder and defects.


The high frequency THz radiation probes carriers over short (nanoscale) distances, which corresponds to highly ordered domains in this system. Through this experiment we are able to experimentally determine the upper limit of the carrier mobility that would be seen in a device with perfect ordering, instead of the disorder limited mobility typically seen in devices.

External Links

See Wikipedia Terahertz Radiation

See Wikipedia Terahertz time-domain spectroscopy

See Wapedia Terahertz

See THz Group Wiki- password required THz Polymers Wiki


References

  1. 2003 Efficient Electrooptic Polymers for THz Applications J. Phys. Chem. B 2004, 108, 8515-8522
  2. L.M. Hayden, A. Sinyukov, M. Leahy, P. Lindahl, J. French, W. Herman, M. He, R. Twieg, "New Materials for Optical Rectification and Electro-optic Sampling of Ultra-short Pulses in the THz Regime," J. Polymer Sci. B. Polymer Phys., Vol 41, 2492 -2500 (2003)
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