Analysis of transient plasmonic interactions using an MOT-PMCHWT integral equation solver

In this work, a marching on-in-time (MOT) scheme is proposed to solve the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) (L. N. MedgyesiMitschang et al., J. Opt. Soc. Am. A, 11(4), 1383-1398, 1994) IE for analyzing transient plasmonic interactions. The MOT-PMCHWT solver calls for convolutions of the spatio-temporal basis functions with the time domain Green function of the dispersive medium. These convolutions are carried out using a semi-numerical procedure. It is shown that Green function consists of a Dirac delta term and a temporal tail. The convolution with the delta term is analytically evaluated. Samples of the temporal tail are computed from frequency domain samples using the Fast Relaxed Vector Fitting (FRVF) algorithm (B. Gustavsen, IEEE Trans. Power Delivery, 21(3), 1587-1592, 2006). FRVF generates a rational function fit to frequency domain samples, which is used in time domain to represent the tail of the Green function in terms of shifted exponentials. Applying this procedure to every source-observer pair during the computation of MOT matrix entries is computationally costly. Therefore, a look-up table consisting of Green function samples at discrete distances and times is generated. Then, an interpolation scheme is used to fill the MOT matrix elements.