Theoretical analysis of Fresnel reflection and transmission in the presence of gain media

When a monochromatic electromagnetic plane-wave arrives at the flat interface between its transparent host (i.e., incidence medium) and an amplifying (or gainy) second medium, incident beam splits into reflected wave transmitted wave. In general, there is sign ambiguity in connection with k-vector of beam, which requires outset that one decide whether should grow or decay as it recedes from interface. The question has been posed addressed most prominently context large angles dielectric medium high refractive index onto gain lower index. Here, relevant determines evanescent-like waves within exponentially away We examine this related problems more general setting, where taken to be finite-duration wavepacket whose footprint interfacial plane finite width. Cases reflection transmission through gainy slab finite-thickness well those associated semi-infinite will considered. broadness spatiotemporal spectrum our demands we develop strategy for deciding signs all k-vectors enter medium. Such emerges consideration causality constraint naturally imposed on both wavepackets.