Introduction

The electromagnetic waves of terahertz (THz) frequency correspond to the far-infrared wavelength, which are able to penetrate many materials due to its long wavelength and are extensively applied from security check to THz communications. After the emergence of the femtosecond lasers (titanium-sapphire lasers) in 1980s^[1], A method for spectroscopy in the THz range was first described in 1989 by Grischkowsky et al.,^[2] which is known as terahertz time-domain spectroscopy (THz-TDS). This technology is different from normal optical spectroscopy for it probes the properties of matter with short pulses of terahertz radiation and detects the electric field of a pulse instead of the intensity of the light field. 

Table of contents

General Working principles

Generation and detection of THz radiation

Photoconductive method is widely used for generation of broadband, coherent THz radiation, which can also be used for a field-resolved detection of the THz field.

Based on electromagnetic theory, the radiation signals in the terahertz frequencies range can be generated by a current transient that evolves on the time scale of a few hundred femtoseconds to a few picoseconds as a characteristic radiation signature.

As illustrated in Figure 1, the metallic electrodes apply the bias electric field to the photoconductive gap formed by using an ultrafast laser pulse from titanium-sapphire lasers or mode-locked fiber lasers^[3]to excite the electrons of the biased semiconductor^[4]surface into the conduction band between the electrodes. The bias field will accelerate the free charges (photo-induced current) that finally recombine within the characteristic recombination time lasting for about a picosecond of the semiconductor and the resulting current transients generate the THz pulses that are emitted into the substrate by a suitable THz dipole antenna structure formed by the metallized bridge between the two electrodes. It should be noted that the shape and length of the antenna play a vital role in the emission and the spectrum of the THz pulse (Low frequency antennas are very large for lower frequencies imply larger wavelengths. ). The THz radiation since the Fourier transform of a picosecond length signal will contain THz components which means after the Fourier mathematical transform the time-varying signal can convert into signal depending on temporal frequency is collected into a collimated beam by a substrate lens attached to the structure and thus ultrafast current impulses in the THz range can be generated.

The detector measures the electrical field of the THz pulses rather than the total energy which usually can be detected by bolometers. During photoconductive detection process, no voltage bias will be applied into the antenna leads and the voltage bias is generated by the electric field of the THz pulse to be detected focused onto the antenna. The induced-current     

is usually amplified with a low-bandwidth amplifier and thus can be treated as the measured parameter relative to the strength of the THz radiation, sampled in an extremely narrow slice of the entire electric field waveform due to the ultrashort lifetime of the charge carriers.

Figure 1. A photoconductive switch for generation of ultrashort THz pulses. (Figure: Nea Möttönen, inspired by reference^[5])

THz-TDS Experiment apparatus

Figure 2 demonstrates a brief THz time domain spectroscopy (THz-TDS) experiment apparatus. A typical THz-TDS system includes a femtosecond laser, beamsplitters (PBS), delay stages, steering mirrors, a terahertz generator, terahertz beam focusing and collimating optics such as parabolic mirrors and off-axis parabolic mirrors (PM), and a terahertz detector.

A beamsplitter (PBS) is used to divide the ultrafast laser pulse into two separate beams usually with equal optical power, one for the terahertz generator and one for the detector.

Delay stages is to lengthen the laser light path along a well-defined path to achieve a delay. Inducing a retroreflector into a delay stage to redirect the beam can adjust the path length and thus also vary the time at which the terahertz detector is gated corresponding to the source terahertz radiation.   

Parabolic mirrors (PM) as illustrated in Figure 3 is to collimate and focus THz radiation. The incidence of the THz radiation on an off-axis parabolic mirror (PM) will become collimated while the incidence on a parabolic mirror will focus into a point. Samples are usually put on the place of focus for the most concentrated THz radiation.

Purge box is to reduce the influence of the gaseous water molecules on the THz spectroscopy experiment for water molecules can adsorb the radiation in the THz range relative to the rotational modes, while molecules without electric dipole moment like Nitrogen will not. Therefore, filling with nitrogen in a purge box will avoid the unexpected discrete adsorptions in the THz region. (Purge box is not represented in Figure 2. It should encompass the entire light  path section. )

Figure 2. A  typical THz time domain spectroscopy system with half waveplate (HWP), polarizing beamsplitter (PBS), parabolic mirrors (PM#), steering mirrors (M#), photoconductive antenna and quarter waveplate (QWP). Figure from Wikipedia. (License: CC BY-SA 4.0)

Figure 3. Schematic diagram of a parabolic mirror. (Figure: Shukning Choi)

THz-TDS detection mode

The detector can receive the beam of THz pulses transporting from the transmissive or reflective optics generated by the emitter. In Figure 4, the general geometries for transmission and reflection mode are illustrated.

Transmission mode: Although It is easier to align transmissive optics than reflective optics, frequency-dependent absorption which usually causes the attenuation of the high frequency components of the THz radiation, leading to the information loss of high-frequency range in the spectroscopy system.

Reflection mode: Off-axis paraboloidal mirrors with metallic reflectors are used in the reflective optics. However, elliptical mirrors can also be included, depending on the required focusing and imaging of the THz beam through the optical system. Reflective optics has little loss due to the high conductivity of most metals in the THz range, despite the difficulty of aligning properly.

Figure 4. Schematic diagram of the general geometries difference between transmission and reflection mode. (Figure: Shukning, Choi)

Examples

Simple example on THz-TDS spectra

The raw experimental data of the incident THz transient generated in a low-temperature-grown gallium arsenide antenna, as illustrated in Figure 5 (Left), after Fourier transformation, obtaining the time-domain representation of the pulse or the frequency/ amplitude spectra of the pulse demonstrated in Figure 5 (Right).

Figure 5. (Left) THz-bandwidth transient recorded in the time domain (Figure from Wikipedia, License: CC BY 2.5) and (Right) its corresponding amplitude spectrum (Figure from Wikipedia, License: CC BY 2.5).

Advantages of THz spectroscopy

1. The THz region of the electromagnetic radiation interacts strongly with systems that have characteristic lifetimes in the picosecond range and energetic transitions in meV range, such as transient molecular dipoles^[6], phonons in crystalline solids^[7], weakly bond molecular crystals^[8], relaxational dynamics in aqueous liquids^[9].

2. THz-TDS detects the electric field of a THz pulse instead of counting the number of photons at each frequency.

3. THz-TDS can obtain the amplitude and phase of each frequency component of the THz pulse and thus the real and imaginary parts of an optical constant can be known at corresponding frequency without the need of frequencies beyond the measured bandwidth or Kramers-Kronig relations.

References