Two-dimensional relativistic longitudinal Green's function in the presence of a moving planar dielectric-magnetic discontinuity

The current contribution is concerned with obtaining the relativistic two-dimensional (three-dimensional in relativity jargon) Green's function of a time-harmonic line current that is embedded in a moving dielectric-magnetic medium with a planar discontinuity. By applying a plane-wave (PW) spectral representation for the relativistic electromagnetic Green's function of a dielectric-magnetic medium that is moving in a uniform velocity, the exact reflected and transmitted (refracted) fields are obtained in the form of a spectral integral over PWs in the so-called laboratory and comoving frames. We investigate these spectral representations, as well as their asymptotic evaluations, and discuss the associated relativistic wave phenomena of direct reflected/transmitted rays and relativistic head waves (lateral waves).