时域中的高斯色散分析：使用Padé近似的有效转换
Gaussian dispersion analysis in the time domain: efficient conversion with Padé approximants
摘要：
我们提出了一种适应高斯色散分析（GDA）的光学材料的时域模拟的方法。在GDA模型中，测量的介电函数的虚部被表示为高斯吸收项的总和。这样一个简单的模型是有效的材料，其中非均匀加宽是远远大于均匀线宽。GDA模型是许多玻璃、聚合物以及其他具有无序的天然和人造材料的介电函数的基本宽带近似。然而，在时域全波电磁解算器中有效地实现该模型从未完全实现。我们从具有高斯型吸收的孤立振荡器的因果形式-因果道森-高斯振荡器开始。然后，我们推导出明确的分析公式，以实现高斯振荡器在时域有限差分（FDTD）求解器与最小的使用内存和浮点运算。推导和FDTD实现采用我们的广义色散材料（GDM）模型-一个通用的，模块化的方法来描述与Padé近似的光色散。我们分享的FDTD原型代码，包括自动生成的近似和一个通用的FDTD色散实施，采用各种二阶精确的数值方案。这些代码可以与非商业求解器和商业软件一起使用，用于色散介质中光传播的时域模拟，实验上用GDA模型表征。
英文摘要：
We present an approach for adapting the Gaussian dispersion analysis (GDA) of optical materials to time-domain simulations. Within a GDA model, the imaginary part of a measured dielectric function is presented as a sum of Gaussian absorption terms. Such a simple model is valid for materials where inhomogeneous broadening is substantially larger than the homogeneous linewidth. The GDA model is the essential broadband approximation for the dielectric function of many glasses, polymers, and other natural and artificial materials with disorder. However, efficient implementation of this model in time-domain full-wave electromagnetic solvers has never been fully achieved. We start with a causal form of an isolated oscillator with Gaussian-type absorption - Causal Dawson-Gauss oscillator. Then, we derive explicit analytical formulas to implement the Gaussian oscillator in a finite-difference time-domain (FDTD) solver with minimal use of memory and floating point operations. The derivation and FDTD implementation employ our generalized dispersive material (GDM) model - a universal, modular approach to describing optical dispersion with Padé approximants. We share the FDTD prototype codes that include automated generation of the approximants and a universal FDTD dispersion implementation that employs various second-order accurate numerical schemes. The codes can be used with non-commercial solvers and commercial software for time-domain simulations of light propagation in dispersive media, which are experimentally characterized with GDA models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
