Optical Microcavities as Quantum-Chaotic Model Systems: Openness Makes the Difference!

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.We first Generalizing the concept of Husimi functions to dielectric interfaces, where both the wave function and its derivative are non-zero. We then we find that curved interfaces require a semiclassical correction of Fresnel’s law due to an interference effect called Goos-Hänchen 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. Implementing both effects into the ray model improves the agreement with wave optics by about one order of magnitude. 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.