Optical microcavities as quantum-chaotic model systems: Openness makes the difference!

TL;DR

This paper investigates how openness affects the quantum-chaotic behavior of optical microcavities, revealing that phase-space corrections like Goos-Haenchen shift and Fresnel filtering are essential for accurate ray-wave correspondence, especially near the critical angle.

Contribution

It introduces a generalized phase-space method for dielectric interfaces, incorporating semiclassical corrections to Fresnel's law, enhancing the understanding of ray-wave correspondence in open optical microcavities.

Findings

Fresnel filtering and Goos-Haenchen shift are crucial near the critical angle.

Adjusted reflection law improves phase-space dynamics modeling.

Deviations from classical ray-wave correspondence can be explained with these corrections.

Abstract

Optical microcavities are open billiards for light in which electromagnetic waves can, however, be confined by total internal reflection at dielectric boundaries. These resonators enrich the class of model systems in the field of quantum chaos and are an ideal testing ground for the correspondence of ray and wave dynamics that, typically, is taken for granted. Using phase-space methods we show that this assumption has to be corrected towards the long-wavelength limit. Generalizing the concept of Husimi functions to dielectric interfaces, we find that curved interfaces require a semiclassical correction of Fresnel's law due to an interference effect called Goos-Haenchen shift. It is accompanied by the so-called Fresnel filtering which, in turn, corrects Snell's law. These two contributions are especially important near the critical angle. They are of similar magnitude and correspond to ray displacements in independent phase-space directions that can be incorporated in an adjusted reflection law. We show that deviations from ray-wave correspondence can be straightforwardly understood with the resulting adjusted reflection law and discuss its consequences for the phase-space dynamics in optical billiards.