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