Experimental test of a trace formula for two-dimensional dielectric resonators

TL;DR

This study experimentally tests a trace formula for two-dimensional dielectric resonators by analyzing resonance spectra and length spectra, revealing the impact of missing resonances and establishing a link between long-lived resonances and specific periodic orbits.

Contribution

The paper provides an experimental validation of a trace formula for dielectric resonators and addresses the effects of missing resonances on spectral analysis.

Findings

Deviations in length spectra are due to missing resonances.

Accounting for missing resonances explains the experimental spectra.

Long-lived resonances are linked to specific periodic orbits.

Abstract

Resonance spectra of two-dimensional dielectric microwave resonators of circular and square shapes have been measured. The deduced length spectra of periodic orbits were analyzed and a trace formula for dielectric resonators recently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] was tested. The observed deviations between the experimental length spectra and the predictions of the trace formula are attributed to a large number of missing resonances in the measured spectra. We show that by taking into account the systematics of observed and missing resonances the experimental length spectra are fully understood. In particular, a connection between the most long-lived resonances and certain periodic orbits is established experimentally.