A numerical solution of the layered media Green´s function for the MPIE in the time domain

Layered media Green´s functions in the frequency domain have been extensively studied previously. Interest has increased in the evaluation of the layered media Green´s functions in the time domain, to be subsequently used for time domain integral equations (TDIEs). This is because of critical time-domain applications including the analysis of transients in high speed digital interconnects and for analyzing wideband microstrip antennas. In using time domain layered Green´s functions in conjuction with TDIEs, it is necessary to compute the layered medium Green´s function for many source-to-field distances ρ and time intervals t. In this paper, a numerical solution of the layered media Green´s function in the time domain for the mixed potential integral equation (MPIE) is reported. The particular case where the source and field points are on the top layer is presented. The method is applicable to multi-layered structures and to both lossless and lossy media. The technique also computes the Green´s function for many ρ and t values simultaneously.