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Eigenfrequencies and Modal Analysis of Uniaxial, Biaxial, and Gyroelectric Spherical Cavities

The normalized eigenfrequencies in spherical cavities filled with uniaxial, biaxial, and gyroelectric medium are calculated, and the corresponding modal analysis is performed. A discrete eigenfunction approach is employed that permits the direct calculation of the normalized eigenfrequencies. First, a discrete basis that depends on the tensorial permittivity elements is constructed for expansion of the unknown electric field inside the cavity. Then, the boundary condition is applied on the perfect electric conductor at the cavity’s surface, which leads to two infinite sets of homogeneous equations. It is found that the uniaxial/biaxial cavities maintain quasi-TMr, quasi-TEr, as well as hybrid modes, but when the medium becomes gyroelectric, the modes are purely hybrid. The proposed approach is validated against other eigenmode solvers, up to the biaxial anisotropy. The normalized eigenfrequencies of uniaxial, biaxial, and gyroelectric filled cavities are presented and the corresponding eigenmodes are discussed.