Understanding energy propagation during reflection of an evanescent electromagnetic wave

Abstract

Reflection of plane electromagnetic waves at a planar surface separating two media is typically discussed at length in undergraduate texts. However, a similar analysis for the case of evanescent electromagnetic waves, although illustrative and interesting, is rarely discussed. In this paper, we present such an analysis for the reflection of an evanescent wave at a plane dielectric surface and highlight the important conceptual difference in the energy flow for this case compared to that of a plane wave. It is generally emphasized that an evanescent wave does not propagate energy away from the surface emanating these waves. We show that in the case of an evanescent wave, the pair of incident and reflected waves together propagates energy if the imaginary part of the reflectivity is non-zero. Further, the real part of the reflectivity can be greater than unity in the case of an evanescent wave without violating energy conservation. Connection of these properties to the existence of surface modes, Čerenkov radiation, and a quantum analogue are elucidated in the paper.