Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics

TL;DR

This paper links the emission patterns of dielectric cavities to the invariant chaotic saddle's unstable manifold, explaining how energy distribution and decay modes influence far-field emission directions, with validation through simulations.

Contribution

It introduces a novel approach connecting chaotic saddle properties to emission patterns in dielectric cavities, including the effects of mixed phase space.

Findings

Far field emission directions are related to the saddle's unstable manifold patterns.

Energy decay in cavities exhibits intermediate exponential and asymptotic power-law regimes.

Far field emission remains relatively unchanged despite internal energy distribution shifts.

Abstract

In this paper, the chaotic ray dynamics inside dielectric cavities is described by the properties of an invariant chaotic saddle. I show that the localization of the far field emission in specific directions is related to the filamentary pattern of the saddle's unstable manifold, along which the energy inside the cavity is distributed. For cavities with mixed phase space, the chaotic saddle is divided in hyperbolic and non-hyperbolic components, related, respectively, to the intermediate exponential (t<t_c) and the asymptotic power-law (t>t_c) decay of the energy inside the cavity. The alignment of the manifolds of the two components of the saddle explains why even if the energy concentration inside the cavity dramatically changes from t<t_c to t>t_c, the far field emission changes only slightly. Simulations in the annular billiard confirm and illustrate the predictions.