FDTD Modeling of Wave Propagation in Cole-Cole Media With Multiple Relaxation Times

A finite-difference time-domain (FDTD) method for simulating wave propagation in Cole-Cole dispersive media with multiple relaxation times is presented. The main difficulty that the proposed method circumvents is the presence of fractional derivatives in the time-domain representation of the polarization relation. The latter is approximated by a set of auxiliary differential equations using Pad approximants, where each approximant corresponds to a single relaxation time of the Cole-Cole model. The auxiliary differential equations are discretized by means of central differences and are further employed within a conventional FDTD scheme. The efficiency of the proposed method is demonstrated by simulating the propagation of a wideband Gaussian pulse that excites a one-dimensional Cole-Cole medium with two relaxation times.