FDTD for Nth-order dispersive media

Previously, a method for applying the finite-difference time domain (FDTD) method to dispersive media with complex permittivity described by a function with a single first-order pole was presented. This method involved the recursive evaluation of a discrete convolution, and was therefore relatively efficient. In this work, the recursive convolution approach is extended to media with dispersions described by multiple second-order poles. The significant change from the first-order implementation is that the single backstore variable for each second-order pole is complex. The approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second-order poles, and excellent agreement is obtained with the exact solution