Dielectric-resonator-based measuring devices: Relevance of the dielectric quality

Sapphire-based, cylindrical dielectric-loaded microwave resonators are increasingly popular to measure the electrical, magnetic and dielectric response of various substances and materials. While it is generally accepted that 'high-quality' dielectrics are necessary to obtain the best performances of a resonator as a measuring device, a quantitative assessment of the impact of the quality of the anisotropic dielectric on the performances is lacking. We study the effect of a miscut of the crystal on the properties of dielectric resonators, relevant to the performances as a measuring device. We find that mode distortion, sufficiently severe to affect the measurand, can arise with commercial-grade crystals. We give quantitative estimates on the acceptable tolerance on the crystal miscut