Terahertz time-domain spectroscopy

Typical pulse as measured with THz-TDS.

Fourier transform of the above pulse.

In physics, terahertz time-domain spectroscopy (THz-TDS) is a spectroscopic technique in which the properties of a material are probed with short pulses of terahertz radiation. The generation and detection scheme is sensitive to the sample material's effect on both the amplitude and the phase of the terahertz radiation. In this respect, the technique can provide more information than conventional Fourier-transform spectroscopy, which is only sensitive to the amplitude.

Explanation

Typically, the terahertz pulses are generated by an ultrashort pulsed laser and last only a few picoseconds. A single pulse can contain frequency components covering much of the terahertz range, often from 0.05 to 4 THz. For detection, the electric field of the terahertz pulse is sampled and digitized, conceptually similar to the way an audio card transforms the electrical voltage levels of an audio signal into numbers describing the audio waveform. In THz-TDS, the electric field of the THz pulse interacts in the detector with a much shorter laser pulse (e.g. 0.1 picoseconds) in a way that produces an electrical signal proportional to the electric field of the THz pulse at the time the laser pulse gates the detector on. By repeating this procedure and varying the timing of the gating laser pulse, it is possible to scan the THz pulse and reconstruct its electric field as a function of time. Subsequently, a Fourier transform is performed to extract the frequency spectrum from the time-domain data.

Advantages of THz radiation

THz radiation has several distinct advantages over other wavelengths of light used in spectroscopy: many materials are transparent to THz, THz radiation is safe for biological tissues because it is non-ionizing (unlike for example X-rays), and images formed with terahertz radiation can have relatively good resolution (less than 1 mm). Also, many interesting materials have unique spectral fingerprints in the terahertz range, which means that terahertz radiation can be used to identify them. Examples which have been demonstrated include several different types of explosives, polymorphic forms of many compounds used as Active Pharmaceutical Ingredients (API) in commercial medications as well as several illegal narcotic substances . Since many materials are transparent to THz radiation, these items of interest can be observed through visually opaque intervening layers, such as packaging and clothing. Though not strictly a spectroscopic technique, the ultrashort width of the THz radiation pulses allows for measurements (e.g., thickness, density, defect location) on difficult to probe materials (e.g., foam). The measurement capability shares many similarities to that observed with pulsed ultrasonic systems. Reflections from buried interfaces and defects can be found and precisely imaged. THz measurements are non-contact however.

Generation

There are three widely used techniques for generating terahertz pulses, all based on ultrashort pulses from titanium-sapphire lasers or mode-locked fiber lasers.

Surface emitters

When an ultra-short (100 femtoseconds or shorter) optical pulse illuminates a semiconductor and its wavelength (energy) is above the energy band-gap of the material, it photogenerates mobile carriers. Given that absorption of the pulse is an exponential process, most of the carriers are generated near the surface (typically within 1 micrometre). This has two main effects. Firstly, it generates a band bending, which has the effect of accelerating carriers of different signs in opposite directions (normal to the surface), creating a dipole; this effect is known as surface field emission. Secondly, the presence of the surface itself creates a break of symmetry, which results in carriers being able to move (in average) only into the bulk of the semiconductor. This phenomenon, combined with the difference of mobilities of electrons and holes, also produces a dipole; this is known as the photo-Dember effect, and it is particularly strong in high-mobility semiconductors such as indium arsenide.

Photoconductive emitters

In a photoconductive emitter, the optical laser pulse (100 femtoseconds or shorter) creates carriers (electron-hole pairs) in a semiconductor material. Effectively, the semiconductor changes abruptly from being an insulator into being a conductor. This conduction leads to a sudden electric current across a biased antenna patterned on the semiconductor. This changing current emits terahertz radiation, similar to what happens in the antenna of a radio transmitter. Typically the two antenna electrodes are patterned on a low temperature gallium arsenide (LT-GaAs), semi-insulating gallium arsenide (SI-GaAs), or other semiconductor (such as InP) substrate. In a commonly used scheme, the electrodes are formed into the shape of a simple dipole antenna with a gap of a few micrometers and have a bias voltage up to 40 V between them. The ultrafast (100 fs) laser pulse must have a wavelength that is short enough to excite electrons across the bandgap of the semiconductor substrate. This scheme is suitable for illumination with a Ti:sapphire oscillator laser with pulse energies of about 10 nJ. For use with amplified Ti:sapphire lasers with pulse energies of about 1 mJ, the electrode gap can be increased to several centimeters with a bias voltage of up to 200 kV.

More recent advances towards cost-efficient and compact THz-TDS systems are based on mode-locked fiber lasers sources emitting at a center wavelength of 1550 nm. Therefore, the photoconductive emitters have to be based on semiconductor materials with smaller band gaps of approximately 0.74 eV such as Fe-doped indium gallium arsenide ^[1] or indium gallium arsenide/indium aluminum arsenide heterostructures .^[2]

The short duration of THz pulses generated (typically ~2 ps) are primarily due to the rapid rise of the photo-induced current in the semiconductor and the short carrier lifetime semiconductor materials (e.g., LT-GaAs). This current may persist for only a few hundred femtoseconds, up to several nanoseconds, depending on the material of which the substrate is composed. This is not the only means of generation, but is currently (as of 2008) the most common.

Pulses produced by this method have average power levels on the order of several tens of microwatts.^[2] The peak power during the pulses can be many orders of magnitude higher due to the low duty cycle of mostly >1%, which is dependent on the repetition rate of the laser source. The maximum bandwidth of the resulting THz pulse is primarily limited by the duration of the laser pulse, while the frequency position of the maximum of the Fourier spectrum is determined by the carrier lifetime of the semiconductor.^[3]

Optical rectification

In optical rectification, a high-intensity ultrashort laser pulse passes through a transparent crystal material that emits a terahertz pulse without any applied voltages. It is a nonlinear-optical process, where an appropriate crystal material is quickly electrically polarized at high optical intensities. This changing electrical polarization emits terahertz radiation.

Because of the high laser intensities that are necessary, this technique is mostly used with amplified Ti:sapphire lasers. Typical crystal materials are zinc telluride, gallium phosphide, and gallium selenide.

The bandwidth of pulses generated by optical rectification is limited by the laser pulse duration, terahertz absorption in the crystal material, the thickness of the crystal, and a mismatch between the propagation speed of the laser pulse and the terahertz pulse inside the crystal. Typically, a thicker crystal will generate higher intensities, but lower THz frequencies. With this technique, it is possible to boost the generated frequencies to 40 THz (7.5 µm) or higher, although 2 THz (150 µm) is more commonly used since it requires less complex optical setups.

Detection

The electrical field of the terahertz pulses is measured in a detector that is simultaneously illuminated with an ultrashort laser pulse. Two common detection schemes are used in THz-TDS: photoconductive sampling and electro-optical sampling. THz pulses can also be detected by bolometers, heat detectors cooled to liquid-helium temperatures. Since bolometers can only measure the total energy of a terahertz pulse, rather than its electric field over time, they are unsuitable for THz-TDS.

In both THz-TDS detection methods, a part (called the detection pulse) of the same ultrashort laser pulse used to generate the terahertz pulse is sent to the detector, where it arrives simultaneously with the terahertz pulse. The detector will produce a different electrical signal depending on whether the detection pulse arrives when the electric field of the THz pulse is low or high. An optical delay line is used to vary the timing of the detection pulse.

Because the measurement technique is coherent, it naturally rejects incoherent radiation. Additionally, because the time slice of the measurement is extremely narrow, the noise contribution to the measurement is extremely low.

The signal-to-noise ratio (S/N) of the resulting time-domain waveform obviously depends on experimental conditions (e.g., averaging time), however due to the coherent sampling techniques described, high S/N values (>70 dB) are routinely seen with 1 minute averaging times.

Photoconductive Detection

Photoconductive detection is similar to photoconductive generation. Here, the voltage bias across the antenna leads is generated by the electric field of the THz pulse focused onto the antenna, rather than some external generation. The THz electric field drives current across the antenna leads, which is usually amplified with a low-bandwidth amplifier. This amplified current is the measured parameter which corresponds to the THz field strength. Again, the carriers in the semiconductor substrate have an extremely short lifetime. Thus, the THz electric field strength is only sampled for an extremely narrow slice (femtoseconds) of the entire electric field waveform.

Electro-optical sampling

The materials used for generation of terahertz radiation by optical rectification can also be used for its detection by using the Pockels effect, where particular crystalline materials become birefringent in the presence of an electric field. The birefringence caused by the electric field of a terahertz pulse leads to a change in the optical polarization of the detection pulse, proportional to the terahertz electric-field strength. With the help of polarizers and photodiodes, this polarization change is measured.

As with the generation, the bandwidth of the detection is dependent on the laser pulse duration, material properties, and crystal thickness.

References and notes

Further reading

• C. A. Schmuttenmaer (2004). "Exploring dynamics in the far-infrared with terahertz spectroscopy" (PDF). Chemical Reviews. 104 (4): 1759–1779. doi:10.1021/cr020685g. PMID 15080711. Archived from the original (PDF) on July 8, 2007.