Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering

TL;DR

This paper demonstrates that the spectral properties of chaotic microcavities follow a fractal Weyl law when considering multifractal extensions of the chaotic repeller, incorporating Fresnel's laws, using harmonic inversion analysis.

Contribution

It extends the fractal Weyl law to dielectric microcavities by including multifractal analysis with Fresnel's laws, validated through harmonic inversion techniques.

Findings

Fractal Weyl law holds for chaotic microcavities with multifractal repellers.

Harmonic inversion effectively analyzes spectral properties.

Fresnel's laws are crucial for the multifractal extension.

Abstract

We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic microstadium. We show that the conjectured fractal Weyl law for open chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)] is valid for dielectric microcavities only if the concept of the chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.