Resonances in a circular dielectric cavity

TL;DR

This paper investigates the resonance behavior in circular dielectric cavities, revealing how decay rates and resonance positions depend on cavity parameters and polarization, with implications for optical cavity design.

Contribution

It provides a detailed analysis of resonance distributions and their asymptotic behavior in circular dielectric cavities, linking classical and quantum descriptions.

Findings

Decay-rate distribution peaks align with classical survival probabilities.

Resonance positions approach Dirichlet problem solutions at large n.

Imaginary parts of resonances scale as n^{-2m} for TM and TE modes.

Abstract

We study resonance distributions in a circular dielectric cavity. It is shown that the decay-rate distribution has a peak structure and the details of the peak are consistent with the classical survival probability time distribution. We also investigate the behavior of the complex resonance positions at the small opening limit. At the large $n$ limit, the real part of complex resonance positions approaches the solutions with different $m$ of Dirichlet problem with a scale $n^{-2}$ and the imaginary part goes zero as $n^{-2m}$ for TM and $n^{-2(m+1)}$ for TE polarization, where $m$ is the order of the resonance.