Refractive Index Measurement Using Continuous Wave Terahertz
Frequency-Domain Spectroscopy
ZHANG Tian-yao1, 2, LI Bo-yang1, LI Xing-yue1, LI Ying1, WU Xian-hao1, ZHAO Xiao-yan1, ZHANG Zhao-hui1*
1. Beijing Engineering Research Center of Industrial Spectrum Imaging, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2. Department of Materials Physics, School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China
Abstract：In the past two decades, terahertz spectroscopy has been proven to be a powerful tool potentially applied in biomedical research, industrial quality inspection, national defence, and public security. However, the dependence of traditional Terahertz time-domain spectroscopy (THz-TDS) on femtosecond lasers seriously limits the application of THz technology in practical industrial fields. Recently, terahertz frequency-domain spectroscopy (THz-FDS) based on the photo-mixing mechanism of two commercially available mid-infrared lasers has been widely studied as an alternative due to its better compactivity, lower cost, and outperformed frequency resolution. However, the data processing algorithm for THz-FDS is not comparable to the traditional THz-TDS. Previous spectroscopic studies using THz-FDS generally focus on the absorption spectra of target material extracted from the signal amplitude. Nevertheless, the phase information of the THz wave provided by the coherent detection mechanism has not been well explored. Hence, various valuable parameters such as refractive index, dielectric constant, and polarizability closely related to the phase information cannot be accurately obtained. In this paper, the relationship between the phase information of the THz wave and the periodic oscillation of the FDS original photocurrent data is well explained, accompanied by presenting actual measurement data. A theoretical model is then constructed to calculate the refractive index spectra from the original photocurrent data oscillation period. The primary reason the previous DC-basepoint algorithm could not output the correct refractive index over the low-frequency band is then pointed out. We propose an improved dual-basepoints index algorithm capable of extracting accurate refractive index spectra over the whole spectrum. In order to verify the reliability of our proposed method, polytetra fluoroethylene, a polymer widely used in the THz band, was selected as the characterization object. Multiple samples with different thicknesses were prepared. The refractive index of all those samples was 1.456±0.006. The measurement uncertainty of the refractive index between different samples is only 0.5%, and the average value is consistent with the previously reported value, which thoroughly verifies the reproducibility of this method. In addition, one sample was selected to investigate the influence of the experimental parameter setting on the refractive index measurement results. The original photocurrent data were collected on the same sample with THZ-FDS using various integration times and frequency step-size combinations. The results show that the experimental parameter setting does not significantly affect the refractive index measurement results, which verifies the algorithm’s robustness. The refractive index measurement method proposed in this paper explored the characterization parameters of the terahertz frequency domain spectral system. Therefore, this method is of great significance to the practical application and development of terahertz spectral technology.
[1] Sun F, Fan M, Cao B, et al. IEEE Transactions on Industrial Informatics, 2022, 18(4): 2508.
[2] Bo Y, Fang J, Zhang Z, et al. Pharmaceutics, 2021, 13(8): 1303.
[3] Zhang J, Mu N, Liu L, et al. Biosensors and Bioelectronics, 2021, 185: 113241.
[4] Zhang T, Zhang Z, Arnold M A. Applied Spectroscopy, 2021, 75(6): 647.
[5] Zhang T, Zhang Z, Zhao X, et al. Applied Optics, 2020, 59(16): 4775.
[6] Bennett J W, Raglione M E, Oburn S M, et al. Molecules, 2019, 24(5): 959.
[7] Smith R M, Arnold M A. Applied Spectroscopy Reviews, 2011, 46(8): 636.
[8] Safian R, Ghazi G, Mohammadian N. Optical Engineering, 2019, 58(11): 110901.
[9] Naftaly M, Vieweg N, Deninger A. Sensors, 2019, 19(19): 4203.
[10] ZHANG Tian-yao, ZHANG Zhao-hui, et al（张天尧，张朝晖，等）. Spectroscopy and Spectral Analysis（光谱学与光谱分析）, 2021, 41(6): 1688.
[11] Zhang T, Zhang Z, Arnold M A. Applied Spectroscopy, 2019, 73(3): 253.
[12] LI Ying, ZHANG Zhao-hui, et al(李 迎，张朝晖，等). Chinese Journal of Scientific Instrument(仪器仪表学报)，2020, 41(11): 129.
[13] Peng Y, Shi C, Zhu Y, et al. Photonix, 2020, 1(1): 12.
[14] Guo S, Ruan C, Kong D, et al. JOSA B, 2020, 37(7): 1942.
[15] Wilk R, Breitfeld F, Mikulics M, et al. Applied Optics, 2008, 47(16): 3023.
[16] Kong D, Wu X, Wang B, et al. Optic Express, 2018, 26(14): 17964.
[17] Vogt D W, Erkintalo M, Leonhardt R. Journal of Infrared, Millimeter, and Terahertz Waves, 2019, 40(5): 524.
[18] Roggenbuck A, Schmitz H, Deninger A, et al. New Journal of Physics, 2010, 12(4): 043017.
[19] Raglione M E, Zhang T, Arnold M A. Int. J. Exp. Spectrosc. Tech., 2018, 3: 18.
[20] Ruan C, Kong D, Dai J, et al. Chinese Optics Letters, 2019, 17(7): 073001.
