EM WAVE PROPAGATION AND SCATTERING IN SPATIOTEMPORALLY VARYING MOVING MEDIAThe Exponential Model

Abstract

An approximate method for analyzing EM wave propagation and scattering in the presence of temporally and spatially varying media is investigated. The method is quasi-relativistic in the sense that for constant velocity it reduces to Einstein's Special Relativity theory to the first order in the normalized speed / v c. The present exponential model was previously used for temporally invariant velocity only. The motion must be irrotational and the characteristic wavelength and period scales of the mechanical motion must be much larger compared to those of the EM field ones. For simple periodic motion it is shown that the EM field is modulated by the motion, and a spectrum of discrete sidebands is created, with frequencies separated by the mechanical frequencies. The results suggest new approaches to the celebrated Fizeau experiment. Rather than using an interferometer setup as in the traditional experiment, the equivalent phase velocity in a periodically moving medium can be deduced from the measured. Simple examples are computed: the effect of the motion on an initially plane harmonic wave, and scattering by perfectly conducting and refractive planes and cylinders. Scattering of EM waves in the presence of moving media and scatterers is of interest for theoretical and engineering applications, see (Van Bladel, 1984) for a comprehensive introduction to the relevant literature. Einstein's SR; Minkowski, 1908; Sommerfeld, 1964; Pauli, 1958) facilitates the analysis for problems involving constant velocities. Historically this is related to the FE and the associated Fresnel drag phenomenon (Einstein, 1905; Pauli, 1958). Heuristic approximations are required for varying velocities, and it stands to reason that they will adequately apply to cases involving the normalized speed / v c to the FO only. Historically, the present exponential model seems to have originated with Collier and Tai (1965), and later considered for general temporally invariant velocities (Nathan and Censor, 1968; Censor, 1969a, 1972).