Electromagnetic propagation and scattering in time-dependent moving media.

Abstract

A new formalism is introduced for discussing propagation of electromagnetic waves in space- and time-varying media. The approach taken here is to supplement the velocity-independent solution by a correction factor. This factor involves a four-dimensional line integral and is therefore a WKB-type solution. The formalism is relativistically exact to the first order in v/c. Special cases are discussed, demonstrating how time-harmonic velocity fields modulate the propagating electromagnetic fields. Scattering problems involving time-varying surfaces have been considered in the past. The scatterers were situated in free space (vacuum), or if material media were involved, the mechanical interaction of the moving surfaces with the medium was usually ignored. The new theory presented here facilitates the analysis of electromagnetic scattering problems in the presence of combined surface and medium motion. Consequently, mass continuity at the moving surfaces can be preserved. This makes the modeling of such problems much more realistic. Simplified canonical problems involving interaction of electromagnetic and mechanical waves are discussed to highlight the effects resulting from the new boundary considerations. Surprisingly, for bounded surfaces the time-varying medium effects vanish in the far field. This means that previous results which simply ignored the medium motion are still valid as good approximations.