Trace formula for a dielectric microdisk with a point scatterer

TL;DR

This paper extends the trace formula for dielectric microcavities to include a small scatterer, revealing how both periodic and diffractive rays influence the resonance spectrum, with implications for microlaser design.

Contribution

It introduces a trace formula for a dielectric disk with a point scatterer, incorporating diffractive effects into the spectral analysis.

Findings

Resonance spectrum shows signatures of periodic and diffractive rays.

Diffractive rays significantly influence the resonance spectrum.

Comparison with closed cavity highlights differences in spectral features.

Abstract

Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In the present paper we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays, but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.