Fd2td analysis of electromagnetic field propagation in multipole debye media with and without convolution

This paper deals with the time-domain numerical calculation of electromagnetic (EM) fields in linearly dispersive media described by multipole Debye model. The frequency-dependent finite-difference time-domain (FD2- TD) method is applied to solve Debye equations using convolution integrals or by direct integration. Original formulations of FD2-TD methods are proposed using different approaches. In the first approach based on the solution of convolution equations, the exponential analytical behavior of the convolution integrand permits an efficient recursive FD2-TD solution. In the second approach, derived by circuit theory, the transient equations are directly solved in time domain by the FD2-TD method. A comparative analysis of several FD2-TD methods in terms of stability, dispersion, computational time and memory is carried out.