Computationally efficient algorithms for multi-term dielectric dispersion in FDTD

Several techniques have been described for modeling dispersive phenomena in media described by multi-pole Debye or Lorentz models. The recursive convolution approach is difficult to derive, requires complex arithmetic and assumes that the medium is linear. Another category of methods utilizes auxiliary differential equations. Since the medium does not have to be linear this method is particularly attractive for modeling nonlinear effects. In this paper the auxiliary differential equation method is reformulated so that the solution of the system of linear equations is no longer necessary. Three second order algorithms for Debye and Lorentz dispersion with are obtained. These algorithms require fewer or equal number of unknowns than the corresponding convolution schemes, but are not limited to linear media.