DSP approach for time-domain modelling of wave-propagation in source-free frequency-dependent materials

An effective digital signal processing (DSP) approach is presented for the time-domain modeling of electromagnetic wave-propagation in source-free frequency-dependent materials. The formulations are based on incorporating the DSP algorithms developed for infinite-impulse response (IIR) digital filters into the finite difference time domain (FDTD) implementations of the dispersive Helmholtz wave-equation. The proposed formulations allow modeling different dispersive materials, such as Debye, Drude, and Lorentz models, in the same manner. The stability of the formulations was studied by means of the Routh-Hurwitz and von Neumann criterion and found to maintain the conventional FDTD stability constrains. In addition, the formulations maintain the same numerical performance of the conventional FDTD approach but with less number of computed field components. Numerical example carried out for a two-term Lorentz material is included to show the validity of the formulations.