Transient wave propagation in a general dispersive media using the laguerre functions in a marching-on-in-degree (MOD) methodology

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.