Investigations Into The Electromagnetic Model For A Complex Frequency-doubling Cavity

With the advantages of low unit volume power consumption, strong circumstance adaptability and high stability of frequency, atomic clocks have been widely used in military and civil applications, such as communication, navigation and frequency standard. These days, however, various applications have put forward new challenges to the atomic clocks: small volume, light weight and low power consumption. Therefore a miniature, low-noise and stable frequency-doubling cavity is absolutely necessary to meet these demands. Accordingly, it is crucial to formulate the electromagnetic model of this cavity, so as to improve the performances of the atomic clock.The cavity, working as a kernel part in an atomic clock, has axial and angular discontinuity. Making use of its geometry characteristic, the fields in the cavity can be analyzed separately in three different regions. Firstly, the Gm method introduced by Tai. C. Tai is adopted, and then combining the scatter superposition theorem, the analytic formulation for the electric dyadic green function of the second kind is derived, which is necessary for the analysis, to construct the magnetic field integral equations (MFIE). Based on the principle of equivalence, the matching equations of the fields on the discontinuous axial surfaces can be obtained by the mode matching technology (MMT). The equation which extends Marek Jaworski's method, once being solved, can give out the eigen-frequency without knowing the source distribution in the aperture. Finally, the application of Generalized Fourier Series on solving the matching equation greatly improves the operation precision and gives analytic solution of electromagnetic fields in the cavity. This work presents a rigorous and analytical formulation, which can be applied to analyze other homogenous cavities as well.In order to. solve many general functions by moment method (MM), the definition domain of the original operator must be extended, which is very important when it comes to multivariate problems (fields in multidimensional space). This paper also studies a method to choose base functions without considering the boundary conditions-extended operator.