  Open dielectric resonators of different shapes are widely used for the
manufacture of microlasers. A precise determination of their resonance
frequencies and widths is crucial for their design. Most microlasers have a
flat cylindrical geometry, and a two-dimensional approximation, the so-called
method of the effective index of refraction, is commonly employed for numerical
calculations. Our aim has been an experimental test of the precision and
applicability of a model based on this approximation. We performed very
thorough and accurate measurements of the resonance frequencies and widths of
two passive circular dielectric microwave resonators and found significant
deviations from the model predictions. From this we conclude that the model
generally fails in the quantitative description of three-dimensional dielectric
resonators.
