Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples

TL;DR

This paper extends the trace formula for dielectric cavities to various shapes, including integrable, pseudo-integrable, and chaotic, demonstrating good agreement with simulations and experiments in optical micro-lasers.

Contribution

It generalizes the trace formula to multiple cavity geometries, bridging theoretical predictions with numerical and experimental results.

Findings

Good agreement between theory, simulations, and experiments.

Trace formula applicable to diverse cavity shapes.

Enhanced understanding of resonance behaviors in optical micro-lasers.

Abstract

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE, vol. 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudo-integrable (pentagon) and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic micro-lasers.