Curvature dependence of semiclassical corrections to ray optics: How Goos-Hänchen shift and Fresnel filtering deviate from the planar case result

Abstract

Ray optics is a useful tool even in the regime where, actually, full wave calculations would be appropriate. However, wave-inspired adjustments are needed to ensure the accuracy of ray-based predictions. Here, we investigate these semiclassical corrections to the ray picture —the Goos-Hänchen shift and the Fresnel filtering effect— for the reflection of light beams at curved, rather than planar, interfaces. We present analytical and numerical results that highlight the role of boundary curvature and show clear deviations from the planar case. The Goos-Hänchen shift is decreased at convexely curved interfaces present in optical microcavities and microlasers compared to the planar case, and increased for concave curvature. In contrast, the Fresnel filtering effect is increased by both kinds of curvature. For a straightforward explanation of these findings we introduce an intuitive picture that explicitly takes curvature into account and that allows for a qualitative understanding of the beam shift behaviour.