Lifetime statistics in chaotic dielectric microresonators

TL;DR

This paper investigates the statistical distribution of electromagnetic mode lifetimes in chaotic dielectric microresonators, demonstrating that a random-matrix model accurately predicts lifetime statistics after parameter adjustments, revealing mechanisms like short-lived resonances.

Contribution

It introduces a renormalized random-matrix model for lifetime statistics in chaotic microresonators, connecting short-lived resonances with fractal Weyl law and resonance trapping phenomena.

Findings

Random-matrix model accurately describes long-lived resonance lifetimes.

Renormalization of parameters accounts for short-lived resonances.

Mechanisms similar to fractal Weyl law and resonance trapping are identified.

Abstract

We discuss the statistical properties of lifetimes of electromagnetic eigenmodes in dielectric microresonators with fully chaotic ray dynamics. Using the example of a resonator of stadium geometry, we find that a recently proposed random-matrix model very well describes the lifetime statistics of long-lived resonances, provided that two effective parameters are appropriately renormalized. This renormalization is linked to the formation of anomalously short-lived resonances, a mechanism also known from the fractal Weyl law and the resonance trapping phenomenon.