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.
