  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 Pad\'e 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.
