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The Y2SiO5 (YSO) crystal is a dielectric material with biaxial anisotropywith known values of refractive index at optical frequencies. It is awell-known rare-earth (RE) host material for optical research and more recentlyhas shown promising performance for quantum-engineered devices. In this paper,we report the first microwave characterization of the real permittivity tensorof a bulk YSO sample, as well as an investigation of the temperature dependenceof the tensor components from 296 K down to 6 K. Estimated uncertainties werebelow 0.26%, limited by the precision of machining the cylindrical dielectric.Also, the electrical Q-factors of a few electromagnetic modes were recorded asa way to provide some information about the crystal losses over the temperaturerange. To solve the tensor components necessary for a biaxial crystal, wedeveloped the multi-mode technique, which uses simultaneous measurement of loworder Whispering Gallery Modes. Knowledge of the permittivity tensor offersimportant data, essential for the design of technologies involving YSO, such asmicrowave coupling to electron and hyperfine transitions in RE doped samples atlow temperatures.

Multi-mode technique for the determination of the biaxial Y2SiO5 permittivity tensor from 300 to 6 Kelvin