Spectral Analysis of Relativistic Dyadic Green´s Function of a Moving Dielectric-Magnetic Medium

The present contribution is concerned with obtaining plane-wave spectral representations of the relativistic electric and magnetic dyadic Green´s functions of an isotropic dielectric-magnetic medium (at the frame-at-rest) that is moving in a uniform velocity. By applying a simple coordinate transformation, scalarization of the EM vectorial problem is obtained in which the EM dyads are evaluated from Helmholtz´s isotropic scalar Green´s function. The spectral plane-wave representations of the dyadic Green´s functions are obtained by applying the spatial 2D Fourier transform to the scalar Green´s function. We investigate these spectral representations in the under and over phase-speed regimes, as well as 2D and 3D formulations and discuss the associated wave phenomena.