# Consequences of a wave-correction extended ray dynamics for integrable and chaotic optical microcavities

## TL;DR

This paper explores how wave-inspired corrections to ray optics influence the understanding of emission patterns in both chaotic and integrable optical microcavities, revealing new attractors and significant deviations from traditional models.

## Contribution

It introduces an extended ray optical model with semiclassical corrections and analyzes their effects on microcavity emission, highlighting differences between chaotic and integrable geometries.

## Key findings

- Wave-inspired corrections create attractors in phase space.
- Extended model predicts different far-field emission patterns.
- Chaotic and integrable cavities show distinct emission behaviors.

## Abstract

Ray optics has proven to be an effcient and versatile tool to describe dielectric optical microcavities and their far-field emission based on the principle of ray-wave correspondence. Whereas often the well-known ray-optics at planar interfaces yields reasonable results, semiclassically and boundary-curvature induced corrections will become more important as the cavity size is further reduced. In this paper we summarize the various ray optics descriptions of optical microresonators, paying in addition special attention to the differences that arise between chaotic vs. non-chaotic (integrable or nearly integrable) resonator geometries, respectively. Whereas the far-field pattern in the chaotic case is known to be determined by the overlap of the unstable manifold with the leaky region, it results from the emission of trajectories with the smallest nonzero decay rates in the non-chaotic situation. We present an enhanced ray optical description, extended by wave-inspired (semiclassical) corrections, and discuss their consequences for the ray dynamics. In particular we find clear indications for the presence of attractors resulting from the non-Hamiltonian character of the extended ray dynamics in phase space. We illustrate their impact on the far-field emission and show that it can considerably differ from the conventional ray description result.