Understanding deviations from ray optics at curved interfaces

TL;DR

This paper investigates how boundary curvature affects wave-inspired corrections to ray optics, such as the Goos-H"anchen shift and Fresnel filtering, providing analytical and numerical insights for curved interfaces in microoptics.

Contribution

It offers a detailed analysis of deviations from planar interface behavior at curved boundaries, enhancing understanding of wave effects in microoptics devices.

Findings

Fresnel filtering increases significantly with curvature.

Goos-H"anchen shift becomes less significant at curved interfaces.

An intuitive model explains the curvature dependence of these effects.

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. These corrections are known as the Goos-H\"anchen shift, a lateral shift along the interface, and the Fresnel filtering effect, an angular shift, that violates Snell's law and the principle of ray-path reversibility. Whereas they are well established at planar interfaces, an accurate description of microlasers and other microoptics devices requires their precise knowledge at the curved boundaries characteristic for these devices. Here, we present analytical and numerical results that highlight the role of boundary curvature and show the clear deviations from the planar case. We introduce an intuitive picture that allows for a straightforward understanding why Fresnel filtering grows considerably with curvature whereas the Goos-H\"anchen shift becomes less important.