ABSTRACT A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The spectrum is determined through the introduction of effective “dynamic” potentials which encode the infill inhomogeneity. For angularly symmetric cavity, regardless of its radial non-uniformity, the set of modes is shown to be a superposition of TE and TM oscillations which can be described in terms of a single scalar function independently of each other. The violation of polar symmetry in the infill dielectric properties, the azimuthal symmetry being preserved, suppresses all azimuthally non-uniform modes of TM oscillations. In the absence of angular symmetry of both electric and magnetic properties of the infill, only azimuthally uniform distribution of both TM and TE fields is expected to occur in the resonator. The method is quite efficient for computational complex algorithms for solving different spectral problems, including those for studying the chaotic properties of systems' spectra.

中文翻译：

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一种计算偏心层状球腔谐振器频谱有效势的方法

摘要 开发了一种计算非均匀填充球腔谐振器本征频率的新方法。光谱是通过引入编码填充不均匀性的有效“动态”电位来确定的。对于角对称腔，无论其径向不均匀性如何，模式集显示为 TE 和 TM 振荡的叠加，可以用彼此独立的单个标量函数来描述。填充介电特性中极性对称性的破坏，保留了方位对称性，抑制了 TM 振荡的所有方位非均匀模式。在填充物的电和磁特性没有角对称性的情况下，预计在谐振器中只会出现 TM 和 TE 场的方位角均匀分布。