Whispering gallery modes in a hemispherical isotropic dielectric resonator with a perfectly conducting planar surface

The eigenmodes of a hemispherical dielectric resonator placed on a perfectly conducting planar surface are studied. The resonator is shown to support independent E-and H-type oscillations. For E and H oscillations, the sums n + m of the polar and azimuthal indices are, respectively, even and odd. Accordingly, E and H oscillations exhibit, respectively, n-and (n + 1)-fold frequency degeneracy in azimuthal index m. The distributions of the whispering gallery mode fields on the surface of the hemisphere and on the external conducting plane are obtained. The energy distribution among the eigenmodes with polar index n=36 is studied. The polar angle that corresponds to the maximum of the whispering gallery mode field and the width of the energy localization region in terms of the polar angle are calculated. The number of field variations in the spherical coordinates are correlated with the indices of the resonator’s eigenmodes. The eigenfrequencies and Q factors of the resonator are plotted versus the permittivity of the isotropic environment in the 8-mm wavelength range.