A Basic Study on a Resonance Characteristics of a Semi-Spherical Resonator with a High Permittivity in Millimeter Wave Band

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A subject of our research is to make clear resonance characteristics of Whispering Gallery Modes can a semi-spherical resonator with a high permittivity by a Point Matching Method.In 1999, We expressed field distributions of the resonance modes by a summation of spherical waves. Tangential electromagnetic fields inside the resonator were matched to those outside the resonator at appropriate matching points on the boundary. As the result, a 4N×4N (N ; number of matching points) determinant was derived as an eigenvalue equation of the semi-spherical resonator. As N matching points, in this analysis, were located on a boundary of the resonator to make equi-angles, we failed to obtain resonance frequencies and unloaded Q factors with a good convergence. In 2000, we improved our location of the matching point to obtain eigenvalue with a good convergence. For a location of the matching points, we also introduced a new technique derived from electromagnetic field distribution of the Whispering Gallery Modes. Since an azimuthal angle dependence of the Whispering Gallery Mode with a resonance mode number m was presented by the associated Legendre function P^m_n (cos θ), we defined abscissas θ. of the matching points as solutions of P^m_<m+2Z-1> (cos θ)=0. Considering the field symmetry, we also modified the eigenvalue equation to a new eigenvalue equation which was expressed (4N-2)×(4N-2) determinant. From results of numerical analysis, we could find that the resonance frequencies and unloaded Q factor well converged for number of matching points N.A comparison of numerical results and experimental ones showed a good agreement with each other.