Time-dependent plane wave spectral analysis of the dyadic Green’s function of a fast moving dielectric-magnetic medium

Abstract

We investigate the plane wave spectral representations of the time-dependent relativistic electric and magnetic dyadic Green’s functions (GFs) of an isotropic dielectric-magnetic medium that is moving in a constant velocity. We distinguish two speed regimes in which the medium is moving slower or faster than its wave speed. Using a scalarization process for the EM vectorial problem, the EM dyads are evaluated from scalar GF. The spectral plane wave representations of the dyadic GFss are obtained using the those of the scalar ones according to the appropriate speed regime. We investigate the resulting spectral representations and the associated wave phenomena. Such spectral representations are essentials for solving different canonical scattering problems in which the sources are decomposed into time-dependent (transient) plane waves as part of the boundary problem solutions.