基于多项式求根的双厚度透射率模型确定透明固体光学常数

Determination of Optical Constants of Transparent Solids Based on DoubleThickness Transmittance Model of Polynomial Root

为解决光谱反演法确定透明固体光学常数的一些问题,如存在反演误差、计算耗时等。本文基于传统的双厚度透射率模型,建立了厚度满足整数比的两个光谱透射率方程。通过代数运算获得了与消光系数有关的多项式方程,求解并选择大于0小于1的实数根来计算消光系数;然后求解关于界面反射率的一元二次方程,选择大于0小于1的根来计算折射率。在确定光学常数的过程中,新方法没有反演误差、迭代计算耗时及多值问题。作为应用示例,利用已知文献中的双厚度透射率实验数据计算了CaF_(2)和Si的光学常数,并和文献的结果进行了比较。结果表明,新方法优于传统的光谱反演法,新方法为透明固体光学常数的高精度确定提供了新选择。

In determining the optical constants of transparent solids using spectral inversion methods,certain problems such as inversion errors and computational time consumption,have to be solved.This study establishes two spectral transmittance equations with the thickness satisfying the integer ratio based on the traditional double-thickness transmittance model.A polynomial equation related to the extinction coefficient is obtained through an algebraic operation,and the extinction coefficient is calculated by solving and selecting a real root greater than 0 and less than 1.Subsequently,the unitary quadratic equation is solved for interface reflectivity,thereby selecting the roots that are greater than 0 and less than 1 to calculate the refractive index.In the process of determining the optical constants,the new method does not suffer from inversion errors,timeconsuming iterative calculations,or multivalue problems.As an application example,the optical constants of CaF_(2) and Si were calculated using the experimental data of double-thickness transmittance in the literature,and the results were compared with those in the literature.The results show that the new method is superior to traditional spectral inversion methods and provides a new option for high-precision determination of optical constants of transparent solids.