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It is found that, when the shape of a dielectric sphere (hemisphere) operating under the whispering gallery mode conditions is perturbed by a surface curvature gradient (ellipticity), the unloaded Q factor of the sphere degrades and its resonance frequencies change. It is shown theoretically and experimentally that an elliptic irregularity removes frequency degeneracy of whispering gallery modes at millimeter waves.

Quasi-TE and quasi-TM oscillations of an anisotropic spherical body immersed in an isotropic medium are studied. An investigation of the set of Maxwell’s equations within the spherical body shows that it reduces to two coupled differential equations, which are analyzed theoretically for small values of the anisotropy parameter. An approximate solution to these differential equations is obtained. A dispersion relation determining the frequencies of the resonant oscillations is derived for the boundary conditions imposed on the surface of the spherical body. The effect of anisotropy on the spectral characteristics of the resonant oscillations is examined.

The anisotropy of parameters is an intrinsic characteristic feature of dielectrics employed in production of high-Q resonators. A theory of azimuthal-homogeneous resonant oscillations in a single-crystal sphere is developed. It is demonstrated that the anisotropy gives rise to TM oscillations of two orders at different frequencies. Oscillations with large polar indices are numerically investigated.

A rigorous theory of the propagation of electromagnetic waves in round anisotropic and semiconductor rods in the presence of an arbitrarily directed anisotropy axis or external magnetic field is developed. New types of independent waves are discovered. Exact dispersion equations are obtained for them, which define the dependence of their spectral characteristics on the parameters of the semiconductor or anisotropic crystal and on the magnitude and direction of the constant external magnetic field. The results of numerical investigations for rods made from a semiconductor or a uniaxial crystal are presented.

Forced oscillations excited by a radial magnetic dipole in a dielectric hemisphere (resonator) placed on a perfectly conducting plane are studied. It is shown that the dipole excites H modes. When the dipole radiation frequency equals the eigenfrequency of the resonator, an amplitude resonance is observed in the spectrum. The excitation efficiency is high when the magnetic dipole is placed at the maximum of the radial field component of the resonator’s eigenmode.