Kramers-Kronig关系中积分奇点的处理方法研究

Calculation of integral singularities in Kramers-Kronig relations

在应用Kramers-Kronig关系求解物质的吸收系数和实折射率时,积分奇点的处理方法对这2个光学参数的精确性影响很大.本文提出了一种处理积分奇点的非线性插值法,并将其与常用的平均值法和洛必达法则法进行对比分析.结果表明:平均值法和洛必达法则法在光学参数变化缓慢的情况下适用,而非线性插值法在变化缓慢和变化迅速的情况下均适用.对水汽的计算结果表明,采用平均值法和洛必达法则法计算得到的实折射率的最大误差为5%,而非线性插值法的误差小于1.5%.

When Kramers-Kronig relation is applied to solve absorption coefficient and real refractive index of materials, how to deal with integral singularity exerts great influence on the accuracy of these two optical parameters. We proposed a nonlinear interpolation method to deal with singularity of the integral, and compared it with commonly used average value method and L＇H6pital＇s rule method. It was found that the average value method and I.＇H6pital＇s rule method were suitable for slow changes in optical parameters, while non-linear interpolation method was applicable both for slow and rapid changes. Water vapor calculations showed that the maximum error in real refractive index by average and L＇H6pital＇s rule methods was 5%, while the error by nonlinear interpolation method was less than 1.5%.