Dielectric Square Resonator Investigated with Microwave Experiments

TL;DR

This study experimentally investigates the symmetry, field distributions, and spectral properties of a dielectric square resonator using microwave measurements, comparing results with a semiclassical model to understand classical-quantum correspondence.

Contribution

It provides a detailed experimental analysis of dielectric square resonators, linking measured resonant states to classical tori and validating semiclassical models.

Findings

Resonant states are associated with specific classical tori.

The spectrum exhibits a regular structure related to classical trajectories.

The refractive index can be precisely determined from momentum space data.

Abstract

We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.