Eelectromagnetic field distribution of whispering gallery mode in a sapphire resonator

When the electromagnetic field in sapphire resonator corresponds to whispering gallery mode, it exhibits an extremely low dielectric loss. As result, oscillator has characteristics of ultra-low phase noise and high short-term frequency stability. The distribution is very important for realizing high-level oscillator. In this work, radial-axial mode matching method used theoretically analyze resonator, resonant WGH<sub><i>m</i>,0,0</sub> calculated. simulated by finite element analysis method. number studied intensity WGH<sub>15,0,0</sub> azimuthal, axial radial direction are obtained. Finally, a home-made analyzer measure microwave on surface which composed three-dimensional rotating stage , magnetic ring/probe coupling vector network analyzer. With above theoretical analysis, experimental measurement, working determined. works 9.891 GHz, parameters obtained, unloaded <i>Q</i> value 94000. temperature 292 K, frequency-temperature sensitivity about <inline-formula><tex-math id="Z-20221128040038-1">\begin{document}$71.64 \times 10^{-6}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221156_Z-20221128040038-1.jpg"/><graphic xlink:href="23-20221156_Z-20221128040038-1.png"/></alternatives></inline-formula>. consisting can be make with