Can a Travelling Electromagnetic Wave be Present in a Layered Medium?

Abstract

The problem of the presence of a travelling electromagnetic wave in an inhomogeneous medium is addressed. An argument is presented in favour of the option that the Poynting vector determines whether the wave is travelling or not. A strict harmonic solution to the Maxwell equations in a plane stratified medium is shown not to be a travelling wave. This solution can be decomposed into two travelling fields which separately do not satisfy the Maxwell equations and which are identified as the transmitted and return fields. The direction of the Poynting vector for the transmitted field satisfies the generalized Snell's law. The reflectance of a layer of such a medium is calculated and shown to be zero for some incidence angles. Phases of the two travelling fields are considered and shown to be different from those of geometric optics.