Modes of wave-chaotic dielectric resonators

TL;DR

This paper investigates the complex modes of wave-chaotic dielectric resonators, exploring their classical-quantum correspondence, introducing a numerical method for mode calculation, and analyzing emission properties using phase space techniques.

Contribution

It presents a new numerical approach for calculating resonator modes and links classical phase space structures to wave solutions in wave-chaotic dielectric resonators.

Findings

Efficient numerical method for mode calculation requiring two diagonalizations

Clear relationship established between phase space structures and resonant modes

High-efficiency computation of emission pattern observables

Abstract

Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial structure, and cannot be classified through mode indices which would require additional constants of motion in the ray dynamics. Understanding and controlling the emission properties of such resonators requires the investigation of the correspondence between classical phase space structures of the ray motion inside the resonator and resonant solutions of the wave equations. We first discuss the breakdown of the conventional eikonal approximation in the short wavelength limit, and motivate the use of phase-space ray tracing and phase space distributions. Next, we introduce an efficient numerical method to calculate the quasi-bound modes of dielectric resonators, which requires only two diagonalizations per N states, where N is approximately equal to the number of half-wavelengths along the perimeter. The relationship between classical phase space structures and modes is displayed via the Husimi projection technique. Observables related to the emission pattern of the resonator are calculated with high efficiency.