in relation to cavity size, refractive-index contrast to the surrounding medium, and the degree of shape deformation. A novel feature that distinguishes folded from regular whispering gallery modes is that a given shape will support high-Q folded chaotic whispering gallery modes only in certain wavelength windows.'
author:
- 'Kahli Burke and Jens U. N[ö]{}ckel'
title: 'Folded chaotic whispering-gallery modes in non-convex, waveguide-coupled planar optical microresonators'
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Introduction
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Wave-chaotic optical cavities are of interest in applications because of the degrees of design freedom that are opened up when the geometric constraints of separability and symmetry are removed [@CaoWiersigReview]: spectral density, lifetimes and emission directionality can all be tailored in sometimes dramatic ways that go far beyond perturbative effects around separable special cases. Among the first examples are planar dielectric ovals that support *chaotic whispering-gallery modes* (WGMs) [@Nockel:1997lr], where the anisotropic shape gives rise to highly universal directional emission patterns that can be explained based on the classical phase-space structure of the ray dynamics. From a theoretical point of view, this connection to classical ray physics is intriguing because the transition to chaos that occurs in generic nonseparable systems must then be studied in the presence of openness. The wave equation 