Analytical Analysis Method of Whispering Gallery Mode of Sapphire Dielectric Resonators and the Optimization of the Q Value in Liquid Helium Temperature

A novel approximate analytical method is presented for calculating parameters of Whispering Gallery Mode (WGM) in a sapphire dielectric resonator (SDR). It is based on ray optics and wave theory. The frequency of WGM is computed with less computation time and the influence of sapphire's parameters on the frequency is also analyzed. The Q value of SDR in the liquid helium temperature is optimized by adjusting the coupling coefficient and the surface roughness of the sapphire. According to the computed results, a SDR employing WGM at X-Band is fabricated. The loaded QL value reaches 4.0 x 10(8) and the eigen frequency is 9.205 GHz in the liquid helium temperature.