An efficient higher order numerical convolution for modelling Nth-order Lorentz dispersion

Results of using a higher order numerical convolution technique to model Nth-order, Lorentz type, dispersive media are presented. The convolution integral arising in the electromagnetic constitutive relation is approximated by the trapezoidal rule of numerical integration and implemented using a newly derived one time step recursion relation. This new method is compared to previously published techniques on the problem of a transient electromagnetic plane wave propagating in a dispersive media. All the methods considered solve the first order wave equations using the standard finite difference time domain technique. The results presented show that the new method performs the same or better than the other methods in terms of accuracy, robustness, and memory requirements.