Transient Wave Propagation in a General Dispersive Media Using the Laguerre Functions in a Marching-on-in-Degree (Mod) Methodology

Abstract

Abstract-The objective of this paper is to illustrate how the marching-on-in-degree (MOD) method can be used for efficient and accurate solution of transient problems in a general dispersive media using the finite difference time-domain (FDTD) technique. Traditional FDTD methods when solving transient problems in a general dispersive media have disadvantages because they need to approximate the time domain derivatives by finite differences and the time domain convolutions by using finite summations. Here we provide an alternate procedure for transient wave propagation in a general dispersive medium where the two issues related to finite difference approximation in time and the time consuming convolution operations are handled analytically using the properties of the associate Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the permittivity and permeability with a series of orthogonal associate Laguerre basis functions in the time domain. In this way, the time variable can not only be decoupled analytically from the temporal variations but that the final computational form of the equations is transformed from FDTD to a FD formulation in the differential equations after a Galerkin testing. Numerical results are presented for transient wave propagation in general dispersive materials which use for example, a Debye, Drude, or Lorentz models.

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