Hemispherical isotropic dielectric resonator with idealy conductive flat surface

The eigen oscillations of a hemispherical isotropic dielectric resonator placed on an ideally conductive flat surface are studied. It is shown that for independent E and H modes of resonator the sums of polar and azimuthal indexes have odd and even values, accordingly. The distribution of the H₃₆₃₆₁ "whispering gallery" mode fields is shown on the hemispherical surface and conductive plane outside of the hemisphere. Quantities of field variations over spherical coordinates are compared to the mode indexes of the eigen oscillations of resonator. The dependences of eigen frequencies and Q-factors of the resonator buried into isotropic medium of different substances are shown in the millimeter wave band