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投稿e-mail: jbnuns_sub@bnu.edu.cn

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标题

Kramers-Kronig关系中外延函数指数因子确定

作者

贾琼珍 孙 萍

机构

北京市应用光学重点实验室,北京师范大学物理学系

摘要

在基于Kramers-Kronig(K-K)关系求解太赫兹(THz)频段介质的折射率和吸收系数时,针对反射率高频端外延指数函数的指数因子的确定问题,提出采用时域有限差分(FDTD)算法模拟优化指数因子的方法,从而保证提取介质折射率和吸收系数的精确性。该方法根据FDTD 算法模拟与实测的样品的时域信号的最小二乘差来确定指数因子,当最小二乘差取极小值时所对应的指数因子即为最优解。葡萄糖多晶粉末压片的实验表明,采用本文所提出的利用FDTD 算法模拟优化确定的指数因子为0.495,当用K-K 关系求解折射率和吸收系数时得到的结果更加精确。

关键词

太赫兹反射时域光谱;Kramers-Kronig 关系;时域有限差分算法;折射率;吸收系数

引用

贾琼珍,孙 萍. Kramers-Kronig关系中外延函数指数因子确定[J]. 北京师范大学学报(自然科学版),2015,51(5):459-464.

基金

国家自然科学面上基金资助项目(61371055,11274282)

分类号

O433

DOI

10.16360/j.cnki.jbnuns.2015.05.005

Title

Determining the index factor of extension function for Kramers–Kronig relation

Author

JIA Qiongzhen,SUN Ping

Affiliations

Beijing Area Major Laboratory of Applied Optics, Department of Physics, Beijing Normal University

Abstract

Kramers-Kronig can be used to extract refractive index and absorption coefficient of medium in terahertz (THz) region. But it is needed for reflectance to set up an extension function at high frequency. The exponential function is a kind of empirical extension function. In general, the index factor of exponential function is 2 or 4 experientially. In this paper, the optimized method used for the algorithm of finite difference time domain (FDTD) is proposed to determinate the index factor. Accuracy of refractive index and absorption coefficient is improved by this method. Determination of index factor is based on least square difference between simulation and measured time domain signals. The index factor corresponds to the minimum of least square difference. Glucose polycrystalline pellet experiment shows that accuracy of refractive index and absorption coefficient is guaranteed when the optimized index factor is 0.495. This method provides a reference to extract refractive index and absorption coefficient of medium by Kramers-Kronig relation in the THz region.

Key words

Terahertz time domain reflection spectroscopy; Kramers-Kronig relation; Finite difference time domain; Refractive index; Absorption coefficient

cite

JIA Qiongzhen,SUN Ping. Determining the index factor of extension function for Kramers–Kronig relation[J]. Journal of Beijing Normal University(Natural Science),2015,51(5):459-464.

DOI

10.16360/j.cnki.jbnuns.2015.05.005

Copyright © 2014 Journal of Beijing Normal University (Natural Science)
Designed by Mr. Sun Chumin. Email: cmsun@mail.bnu.edu.cn