Single crystal microwave dielectrics at low temperature: losses and non-linearities

Single crystal dielectrics (SCDs) at cryogenic temperatures (<100 K) provide some of the highest Q microwave resonators which may be realised and, as a result, may have important applications across the microwave communications industry. We summarise measurement techniques used for characterising the complex permittivity of single crystal dielectrics at cryogenic temperatures. Various measurement geometries are described, including Courtney resonators, composite dielectric pucks, an indirectly heated high Q resonator perturbation technique (using both microwave and bolometric readouts) and coupled dielectric resonators. A potential technique for making spatially resolved measurements on a scale small compared with the free space wavelength is also outlined. The methods are illustrated by measurements made on a range of single crystal materials including sapphire, rutile and strontium titanate. Numerical modelling is an important element in accurate evaluation of the measurement data and this will also be considered. Until now the thermal properties of the dielectrics have been ignored in evaluating their microwave properties. We suggest that this is an issue which should not be neglected, particularly when considering the non-linear behaviour of the permittivity as a function of microwave power.