Sapphire-rutile frequency-temperature compensated whispering gallery microwave resonators

Using the Whispering Gallery (WG) mode method we report on the measured uniaxial anisotropy of both rutile and sapphire at microwave frequencies, and determine that the loss tangent as well as the permittivity exhibit anisotropy for both materials. The loss tangent of rutile below 40 K was measured to be significantly smaller than what was measured previously using other techniques. Because rutile exhibits low loss and an opposite temperature coefficient of permittivity to sapphire, it is an ideal material for compensating the frequency-temperature dependence of a sapphire resonator. A sapphire-rutile composite resonator was constructed from a cylindrical sapphire monocrystal with two thin disks of monocrystal rutile held tightly against the ends. Most of the electromagnetic modes exhibited turning points (or compensation points) in the frequency-temperature characteristic. The temperature of compensation for WG quasi TM modes was measured to be below 90 K with Q-factors of the order of a few million depending on the mode. For WG quasi TE modes the temperature of compensation was measured to be between 100 to 160 K with Q-factors of the order of a few hundreds of thousand depending on the mode. The second derivatives of the compensation points were of the order 0.1 ppm/K², which agreed well with the predicted values