Gaussian dispersion analysis in the time domain: Efficient conversion with Pad? approximants

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 Pade 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 noncommercial solvers and commercial software for time-domain simulations of light propagation in dispersive media, which are experimentally characterized with GDA models. Program summary Program Title: MADIS CPC Library link to program files: https://doi .org /10 .17632 /x69b4krsy8 .1 Licensing provisions: GPLv3 Programming language: MATLAB Nature of problem: The problem of efficient time-domain simulation of the Gaussian absorption is essential for wideband modeling of the optical response from materials with inhomogeneous spectral broadening, such as glasses, polymers, and other natural and artificial composite materials with structural or phase disorder. Solution method: A Coupled Oscillator (CO) approximation to the Gaussian absorption in both the frequency and time domains is derived to solve this problem. The time-domain CO approximation is coupled to the finite-difference time-domain (FDTD) solver for the Maxwell equations in the MADIS (MAterial DIspersion Simulator) package. Verification of the Maxwell solvers' accuracy and stability is performed with the FDTD solver coupled to a compact universal implementation of the CO model, employing second-order schemes (either ADE or RC). Code prototypes of these efficient CO schemes can be ported to other methods and platforms for implementing the Gaussian absorption in open-source codes or commercial software. Additional comments including restrictions and unusual features: Patent pending. Restrict any commercial use, including for profit reproduction. (C) 2022 Published by Elsevier B.V.