Wave four-vectors for the electromagnetic waves in relatively moving dielectric media

Abstract

The wave four-vectors are deduced for the general case where the reflection and transmission of a plane electromagnetic wave are at the interface between a stationary dielectric medium and a dielectric medium moving with an arbitrary velocity. It is demonstrated that the frequency shift in the reflected wave not only depends on the velocity v of the moving medium but also markedly depends on the refractive index n ₁ of the incident medium; the frequency shift in the transmitted wave varies with n ₁ and the refractive index n ₂ of the moving medium, as well as on v Total reflection not only occurs when n ₁ > n ₂ but also may occur when n ₁ ≤ n ₂ if 0 < v/c < 1. The law of reflection, the Snell law and the equivalent refractive index of the moving medium are discussed according to the wave four-vectors as well.