Wave-dynamical properties of dielectric resonators investigated with microwaves

The aim of the experiments described in this thesis was the investigation of different aspects of dielectric resonators with microwave experiments. Dielectric cavities have received much attention in the last years due to applications of microlasers and -cavities in telecommunications, integrated optics or as sensors. A key issue in current research is the correspondence between the ray– and the wave–dynamics in these systems, that is their semiclassical description. Therefore, different semiclassical approaches to dielectric resonators have been tested experimentally with macroscopic flat dielectric microwave resonators. The results can be directly applied to microcavities working in the infrared up to optical frequency regime via scaling as long as the ratio between wavelength and resonator dimensions is similar. Both quasi two–dimensional setups consisting of a dielectric plate squeezed between two metal plates and three-dimensional setups with “levitating” dielectric plates surrounded by air have been investigated. Both the frequency spectra and near field distributions were measured. In the first part of the thesis, a two-dimensional approximation for three-dimensional flat dielectric resonators has been tested quantitatively with two different circular Teflon disks. The approximation is based on the projection of the three–dimensional ray-dynamics onto two dimensions and the introduction of a so-called effective index of refraction. Comparison of the model calculations with the measured resonance frequencies and widths reveal that they predict the correct order of magnitude, but significant deviations remain. It was thus shown that the model of an effective index of refraction is too imprecise for the detailed understanding of measured frequency spectra, and that furthermore the systematic error of the model calculations is not under control. In the second part of the thesis, the localization of resonance states on certain periodic orbits was investigated. The existence of such so-called superscars in polygonal metal cavities is well known and was recently predicted also for dielectric polygonal resonators. Therefore, the field distributions of a square ceramic resonator were measured experimentally. The measurements confirmed the existence of superscarred states, but also showed localized states with unexpected character. The physical origin of these states is unclear so far, motivating further investigations. In the third part of the thesis, a trace formula connecting the resonance density of two-dimensional dielectric resonators with the periodic orbits of the corresponding classical billiards was investigated with quasi two-dimensional resonators of circular and square shape. The length spectra deduced from the measured frequency spectra reveal contributions of the periodic orbits to the resonance density, but also show significant deviations from the trace formula since only a part of the expected resonances could be observed experimentally. The results demonstrate that the systematics of the observed states must be taken into account for an understanding of the experimental length spectra. A connection between the most long-lived resonances of the cavities and the most strongly confined periodic orbits of the corresponding classical billiards was established. In the fourth part of the thesis, the applicability of the trace formula for twodimensional dielectric resonators to flat three-dimensional resonators was investigated. An approach combining the trace formula with the effective index of refraction model investigated in the first part was tested for two flat circular Teflon disks. Preliminary results show good qualitative agreement between the model and the experimental data, but also that additional effects due to the dispersion of the effective index of refraction and due to the systematic error of the model must be taken into account