Decay Rates of Optical Modes Unveil the Island Structures in Mixed Phase Space

TL;DR

This study investigates how optical mode decay rates in asymmetric microcavities reveal underlying island structures in mixed phase space, using extensive numerical simulations and a semiclassical model to connect classical orbits with quantum decay behavior.

Contribution

The paper introduces a large-scale numerical approach and a semiclassical model that link decay rate branches to classical periodic orbits in mixed phase space.

Findings

Decay rates form distinct branches that merge into smooth curves with increasing wavenumber.

Each decay rate branch corresponds to a specific classical periodic orbit.

The semiclassical model accurately reproduces the observed decay rate structures.

Abstract

We explore the decay rates of optical modes in asymmetric microcavities with mixed phase space across a wide range of wavelengths that extend deep into the semiclassical, i.e., short-wavelength limit. Implementing an efficient numerical method, we computed 1000000 eigenmodes and discovered that certain decay rates form sequential separate branches with increasing wavenumber that eventually merge into smooth curves. The analysis of the localization properties and Husimi distributions reveals that each branch corresponds to a periodic orbit in the closed classical system. Our findings show that these decay rates gradually resolve the structure of the islands in mixed phase space as we approach the short-wavelength limit. We present an effective semiclassical model incorporating wavenumber-dependent localization, Fresnel reflection, and the Goos-Haenchen shift and demonstrate that these effects are crucial in accounting for the observed branches of decay rate curves.