Incorporación de medios dispersivos en simuladores FDTD mediante la técnica de la transformación de Möebius

Abstract

This paper introduces a technique for FDTD modeling of wave propagation in general Mth-order dispersive media. Ohm´s law in the Laplace domain with an Mth-order rational model for the complex conductivity is considered as a constitutive relation. In order to discretize this model, the complex conductivity is mapped onto the Z-transform domain by means of the Mobius transformation. This leads finally to a set of difference equations that is consistent with Yee`s scheme. The resulting formulation is explicit, it has a second-order accuracy and the need for additional storage variables is minimal.