Terahertz time-domain spectroscopy

Ti:Sapphire Laser

In constructing a THz-TDS experiment using low temperature grown GaAs (LT-GaAs) antennas, a laser that can output photons greater than the band gap in this material is required. Ti:Sapphire accomplishes this task and puts out a pulse with duration shorter than the THz pulse it helps generate. Ti:Sapphire lasers are commonly used in TDTS for many reasons:

• They are tunable to have a central frequency of the energy gap in LT-GaAs, a common antenna for TDTS
• They are readily available as commercial, turnkey systems
• The broad available gain bandwidth allows for short (~10 fs) pulses
• The host crystal (sapphire) is transparent from the ultraviolet to the infrared
• High absorption efficiency for pumping transition (>50%)
• Ti:Sapphire crystals have a hardness of 9 out of 10 on the Mohs scale (diamond is 10/10); this has the practical implication that crystals are robust and not easily damaged by scratches
• The crystal is non-hygroscopic (doesn’t absorb water)
• Compared to previously used dye lasers, Ti:Sapphire lasers do not carry such toxicity risks

Steering Mirrors

Silver mirrors are commonly used as steering mirrors for infrared pulses as they have a nearly constant index of refraction over the bandwidth of an infrared pulse and high reflectivity (above 97.5% is typical). Silver mirrors tend to have 1-2% higher reflectivity than gold over the frequency range of an infrared pulse with central frequency (wavelength) of 800 nm.

Beamsplitters

A beamsplitter is typically used to break a single ultrashort pulse into two pulses that travel in different directions. For the purposes of THz-TDS, a 50/50 beamsplitter (divides one pulse into two equal pulses) is typically sufficient since both the emitter and detector require the same amount of power when using LT-GaAs antennas.

Delay Stage & Retroreflector

A delay stage is utilized to lengthen one of the two beam paths. A delay stage is typically equipped with a retroreflector. A retroreflector is a mirror set that sends an outgoing beam parallel to the incoming beam. Two standard, adjustable mirrors can be used, as can special retroreflectors made for this purpose (for example, a corner cube reflector). A step of the delay stage in space corresponds to a step in time, since we sweep through our pulse in time by coinciding new parts of it with the gating pulse at the detector.

Purge Box

A purge box is typically used so that absorption of THz radiation by gaseous water molecules does not occur. Water is known to have many discrete absorptions in the THz region, which are rotational modes of the water molecules. Nitrogen, as a diatomic molecule, has no electric dipole moment, and does not (for the purposes of typical THz-TDS) absorb THz radiation. Thus, a purge box can be filled with nitrogen so that unintended discrete absorptions in the THz frequency range do not occur.

Parabolic Mirrors

Off-axis parabolic mirrors are commonly used to collimate and focus THz light. Light emitting from an effective point source, such as from an LT-GaAs antenna (active region ~5 um) incident on an off-axis parabolic mirror becomes collimated, and collimated light incident on a parabolic mirror becomes focused. The sequential use of parabolic mirrors can focus light emitted from a point source. Samples for spectroscopy are commonly placed at such a focal point, where the spatial frequency distribution is nearly uniform.

A parabolic mirror is shown with important focal lengths and several exemplary rays.

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

When generating THz radiation via a photoconductive emitter, an ultrafast pulse (typically 100 femtoseconds or shorter) creates charge carriers (electron-hole pairs) in a semiconductor material. This incident laser pulse abruptly changes the antenna from an insulating state into a conducting state. Due to an electric bias applied across the antenna, a sudden electric current transmits across the antenna. This changing current lasts for about a picosecond, and thus emits terahertz radiation since the Fourier transform of a picosecond length signal will contain THz components.

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 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 photon energies of 1.55 eV and 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 ^[2] or indium gallium arsenide/indium aluminum arsenide heterostructures .^[3]

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.^[3] 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.^[4]

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.

Downmixing

The original problem responsible for the “THz gap” (the colloquial term for the lack of techniques in the THz frequency range) was that electronics routinely have limited operation at frequencies at and above 10^12 Hz. Two experimental parameters make such measurement possible in THz-TDS with LT-GaAs antennas: the femtosecond “gating” pulses and the < 1 ps lifetimes of the charge carriers in the antenna (effectively determining the antenna’s “on” time). When all optical path lengths have fixed length, an effective dc current results at the detection electronics due to their low time resolution. Picosecond time resolution does not come from fast electronic or optical techniques, but from the ability to adjust optical path lengths on the micron scale. To measure a particular segment of a THz pulse, the optical path lengths are fixed and the (effective dc) current at the detector due to the a particular segment of electric field of the THz pulse.

THz-TDS measurements are typically not single-shot measurements.

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.

No Necessity of Kramers-Kronig Analysis

THz-TDS measures the electric field of a pulse and not just the power. Thus, THz-TDS measures both the amplitude and phase information of the frequency components it contains. In contrast, measuring only the power at each frequency is essentially a photon counting technique; information regarding the phase of the light is not obtained. Thus, the waveform is not uniquely determined by such a power measurement.

Even when measuring only the power reflected from a sample, the complex optical response constant of the material can be obtained. This is so because the complex nature of an optical constant is not arbitrary; the real and imaginary parts of an optical constant are related by relations known as the Kramers-Kronig relations; knowing one determines the other. There is a difficulty in applying the Kramers-Kronig relations as written, because information about the sample (reflected power, for example) must be obtained at all frequencies. In practice, far separated frequency regions do not have significant influence on each other, and reasonable limiting conditions can be applied at high and low frequency, outside of the measured range.

THz-TDS, in contrast, does not require the use of Kramers-Kronig relations. By measuring the electric field of a THz pulse in the time-domain, the amplitude and phase of each frequency component of the THz pulse are known (in contrast to the single piece of information known by a power measurement). Thus the real and imaginary parts of an optical constant can be known at every frequency within the usable bandwidth of a THz pulse, without need to frequencies outside the usable bandwidth or Kramers-Kronig relations.