Chapter 2

Semiclassical approaches for dielectric resonators

Stefan Bittner, Barbara Dietz and Achim Richter

Abstract

Different aspects of dielectric cavities investigated experimentally using dielectric microwave resonators are summarized. Measured frequency spectra and near field distributions of circular and square resonators are compared to different semiclassical approximations. These include the calculation of the resonance frequencies and widths of a flat three-dimensional disk using the so-called effective index of refraction model, the modeling of resonance states localized on periodic orbits in the dielectric square, and the investigation of a trace formula connecting the density of states of a resonator with the periodic orbits of the corresponding classical billiard. In conclusion, the comparisons between the experimental results and the theoretical predictions demonstrate the potency, but also the limitations of different semiclassical models for dielectric cavities.

Total Pages: 1-39 (39)

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