A model for chaotic dielectric microresonators

TL;DR

This paper introduces a random-matrix model for two-dimensional dielectric resonators that combines wave chaos with Fresnel laws, analyzing laser thresholds and resonance line widths with implications for open resonator statistics.

Contribution

It presents a novel combined model of wave chaos and Fresnel laws for dielectric resonators, analyzing laser thresholds and resonance statistics with new insights into their dependence on refractive index and polarization.

Findings

Laser threshold decreases with increasing refractive index.

Petermann factor scales as √N for long-living resonances.

Resonance statistics become non-universal for small refractive index.

Abstract

We develop a random-matrix model of two-dimensional dielectric resonators which combines internal wave chaos with the deterministic Fresnel laws for reflection and refraction at the interfaces. The model is used to investigate the statistics of the laser threshold and line width (lifetime and Petermann factor of the resonances) when the resonator is filled with an active medium. The laser threshold decreases for increasing refractive index $n$ and is smaller for TM polarization than for TE polarization, but is almost independent of the number of out-coupling modes $N$. The Petermann factor in the line width of the longest-living resonance also decreases for increasing $n$ and scales as $\sqrt{N}$, but is less sensitive to polarization. For resonances of intermediate lifetime, the Petermann factor scales linearly with $N$. These qualitative parametric dependencies are consistent with the random-matrix theory of resonators with small openings. However, for a small refractive index where the resonators are very open, the details of the statistics become non-universal. This is demonstrated by comparison with a particular dynamical model.