Terahertz spectroscopy, which mainly includes terahertz time-domain spectroscopy (THz-TDS) and terahertz frequency-domain spectroscopy (THz-FDS), is an important research field of terahertz science and technology. THz-TDS based on the excitation and detection of femtosecond ultrashort laser pulses has been widely used in the study of spectroscopic properties of substances owing to its wide range of operating frequency (0.2-6.0 THz) and high signal-to-noise ratio. However, the resolution of THz-TDS is affected by its detection time window. The oscillatory disturbances generated in the system limit its frequency resolution to GHz, and the mechanical scanning speed is slow. In addition, THz-TDS obtains time-domain signals, and the spectrum of the entire frequency band of the substance must be achieved through a Fourier transform; moreover, it cannot arbitrarily select a certain range of frequencies for measurement. These factors have limited the spectral analysis performance and application of THz-TDS to some extent. Continuous-wave THz-FDS based on coherent detection is another developing terahertz spectroscopy technology with the advantages of high frequency resolution, simple structure, and tunability of the output frequency. Therefore, THz-FDS has gradually become a powerful tool for research on high-Q terahertz devices. With respect to system structure, the THz-FDS system can be divided into reflection type (measuring the reflection spectrum) and transmission type (measuring the transmission spectrum) schemes. In this paper, we mainly solve the construction and performance optimization of transmission and reflection THz-FDS systems and systematically study the data processing methods to extract material electromagnetic parameters.
There are different data processing methods for both transmission and reflection THz-FDS structures. For different sample states, such as gas, liquid, and solid, we designed appropriate bearing structures and data processing methods. For the transmission THz-FDS, we compared the three methods of fitting, finding extrema, and the Hilbert transform to extract the electromagnetic parameters of samples. Finally, we selected the Hilbert transform method combined with time-domain zeroing to eliminate the Fabry-Pérot (FP) effect, and the frequency-domain resolution was approximately 14 MHz. In addition, solid samples should be sufficiently thin to avoid FP effect, and gas samples should be sealed in a container to prevent leakage. The measurement of liquid samples was more complicated because the multiple reflections and transmissions between the container cell and the liquid caused the FP effect; we used the transmission matrix method to eliminate this effect. For the reflection THz-FDS, we designed a liquid container using high-resistivity silicon and measured liquids using a self-referenced calibration method to avoid beam offset. Furthermore, we used the singly subtractive Kramers-Kronig (SSKK) method to correct for phase errors that arose during solid sample replacement.
In the study of transmission THz-FDS, we measure the transmission spectrum of the atmospheric environment in the frequency range of 0.05-2.00 THz under the condition of relative humidity of 7.5% and temperature of 24.8 ℃. Approximately 16 water vapor absorption peaks can be clearly observed (Fig. 5). In addition, we demonstrate the relationship between different water vapor concentrations and terahertz absorption intensity at three frequency points of 0.558 THz, 0.753 THz, and 0.989 THz. The results show that with an increase in the water vapor concentration, the terahertz transmittance of each frequency point presents an apparent downward trend, that is, the absorption of water vapor to the terahertz wave gradually increases (Fig. 6). We then determine the refractive index and permittivity of lactose monohydrate via the Hilbert transform, finding extrema, and fitting methods. The average refractive index is approximately 1.7, and the average real part of the permittivity is approximately 3.2. All three methods accurately exhibit the absorption peaks of lactose monohydrate at three respective frequencies of approximately 0.53 THz, 1.20 THz, and 1.37 THz, which are in good agreement with previously reported results (Fig. 7). In the process of liquid measurement, we design a sample cell using high-density polyethylene (HDPE) and utilize the transfer matrix method to eliminate the FP oscillations generated by multiple reflections and transmissions between the liquid sample and the sample cell wall. We measure the refractive indices of non-polar liquid cyclohexane and n-hexane, which are consistent with previous test results (Fig. 9). In the study of reflection THz-FDS, we use the self-referenced method to extract the accurate permittivities of methanol and ethanol, which are consistent with the fitting results of the triple Debye model (Fig. 12). Finally, we use the SSKK method to eliminate the phase error and obtain the refractive index and absorption constant of the solid-doped silicon. The measurement and computational analysis data are essentially consistent with previous research results (Fig. 14).
As a key research direction of terahertz science and technology, terahertz spectroscopy has mainly developed two spectral systems, namely THz-TDS and THz-FDS. Between them, THz-FDS has technical advantages such as high frequency resolution, simple structure, and frequency tunability, which compensate for some defects in THz-TDS research. In this study, the system structure and data processing principle of transmission and reflection THz-FDS are discussed in detail. The transmission THz-FDS built by our research group is used to study the high-resolution terahertz spectral data of water vapor samples in the atmosphere. The transmission coefficient and refractive index of lactose monohydrate obtained by the extrema method and the Hilbert transform method are compared in detail. In addition, the transfer matrix is used to eliminate the FP resonance in the process of measuring liquid samples by the transmission method, and the accurate refractive indices of non-polar liquids n-hexane and cyclohexane are thus obtained. Furthermore, in research on continuous-wave reflection THz-FDS, the permittivities of methanol and ethanol in the terahertz frequency band are accurately obtained using the self-reference method. The SSKK method is utilized to extract the refractive index and absorption coefficient of solid-doped silicon. The above research results comprehensively verify the effectiveness of our continuous-wave THz-FDS system and corresponding data processing methods, thereby laying a good foundation for the development and application of terahertz frequency-domain spectroscopy.
