FDTD Modeling of Havriliak-Negami Media

A finite-difference time-domain (FDTD) method for modeling wave propagation in Havriliak-Negami dispersive media is presented. In such media, the time-domain representation of the polarization relation involves time derivatives of fractional orders. Hence, the direct application of the FDTD method meets significant difficulties. In the proposed method, an auxiliary differential equation of integer order that approximates the polarization relation is derived. This approximation is based on Padé approximants of the relative complex permittivity. As a result the auxiliary differential equation can be easily discretized by means of finite differences and then included within the standard FDTD scheme. The efficiency of the proposed method is demonstrated by simulating the propagation of wideband pulses.