ANALYSIS OF TRANSIENT WAVE PROPAGATION IN AN ARBITRARY FREQUENCY-DISPERSIVE MEDIA USING THE ASSOCIATED LAGUERRE FUNCTIONS IN THE FDTD-MOD METHOD

摘要

In this work, we present a marching-on-in-degree (MOD) method in a finite difference time-domain (FDTD) framework for analyzing transient electromagnetic responses in a general dispersive media. The two issues related to the finite difference approximation of the time derivatives and the time-consuming convolution operations are handled analytically using the properties of the associated Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the flux densities, the permittivity and the permeability with a finite sum of orthogonal associated Laguerre functions. Through this novel approach, not only the time variable can be decoupled analytically from the temporal variations but also the final computational form of the equations is transformed from FDTD to a FD formulation through a Galerkin testing. We also propose a second MOD formulation based on the Helmholtz wave equation. Representative numerical examples are presented for transient wave propagation in general Debye, Drude, or a Lorentz dispersive medium.