The Application of Kamers-Kronig Relation in Time Domain Spectral Measurement of Reflection Terahertz
CAI He1，2, ZHANG Jing3, ZHENG Yan1, SUN Jin-hai1, ZHANG Xu-tao1, LI Liang-sheng1, LIU Yong-qiang1, YIN Hong-cheng1
1. Beijing Institute of Environment Features, Beijing 100854, China
2. Science and Technology on Electromagnetic Scattering Laboratory，Beijing 100854, China
3. Beijing Institute of Electonic System Engineering，Beijing 100854，China
Abstract：Terahertz timedomain spectroscopy (THzTDS) technology is extremely significant in measuring the dielectric parameters of materials in the Terahertz band, and it is also important for analyzation and identification of these materials. The THzTDS technology is based on coherent detection, which can measure the amplitude and phase of terahertz wave simultaneously. The electromagnetic parameters of materials can be retrieved from the complex transmittance or complex reflectivity which measured by transmission or reflection of the materials. In most practical application, the refractive index and extinction coefficient cannot be obtained when materials are hard to penetrated by THz wave, and the weak absorption approximation condition cannot be met in the measurement. Therefore, reflection measurement has more application value in this field. However, in the published research results, researchers still generally use the transmission measurement scheme and rarely use the reflection scheme to obtain the material parameters. The reason is that the position error of the sample in the reflection measurement is difficult to eliminate, so it is impossible to extract the reflection phase accurately. In this paper, the Kamers-Kronig relation, which is widely used in the field of optics, is applied to the reflection measurement of terahertz timedomain spectral system to solve the problem that the phase information cannot be obtained accurately and the dielectric parameters cannot be extracted correctly. In order to verify the accuracy of the Kamers-Kronig relationship, on the one hand, the complex transmittance and reflectivity of silicon materials are measured by transmission detection and reflection detection respectively, and then the material parameters are inversed. The results indicated that they have a good consistency. On the other hand, Kamers-Kronig relation and maximum entropy method(MEM) are used to inverse the material parameters of the silicon reflection measurement data, and these two methods can also agree with each other, which ensuring the reliability of the extracted data. Finally, the results obtained by the Kamers-Kronig relation and the maximum entropy method are compared and discussed in this paper, respectively. Compared with the maximum entropy method, The Kamers-Kronig relation is more applicable in the extraction of material parameters and absorption spectrum. Therefore, the Kamers-Kronig relation is not only suitable for the coherent measurement, but also for the incoherent measurement in which the phase information cannot obtain. However, the method needs the reflectivity amplitude information of the whole frequency band, the frequency which we can’t measure needs to be extrapolated, so it is more suitable for the matter whose reflectivity changes little with the frequency. This paper provides an effective method for obtaining the terahertz optical parameters of materials by using the reflection THzTDS system, which can solve the problem of extracting the reflection measurement parameters in the vast number of cases. It is of great significance to the application of Terahertz Technology.
Key words：Terahertz; Kamers-kronig relationship; Reflection; Material parameters
蔡 禾，张 景，郑 岩，孙金海，张旭涛，李粮生，刘永强，殷红成. Kamers-Kronig关系在反射太赫兹时域光谱测量中的应用[J]. 光谱学与光谱分析, 2021, 41(01): 105-110.
CAI He, ZHANG Jing, ZHENG Yan, SUN Jin-hai, ZHANG Xu-tao, LI Liang-sheng, LIU Yong-qiang, YIN Hong-cheng. The Application of Kamers-Kronig Relation in Time Domain Spectral Measurement of Reflection Terahertz. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2021, 41(01): 105-110.
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