Two-dimensional equations for guided EM waves propagating in a dielectric plate surrounded by free space are employed for the study of vibrations of circular disk dielectric resonators embedded in free space. Closed-form solutions are obtained for which the continuity conditions of the tangential E and H fields at the end faces and the lateral cylindrical surfaces are accommodated. It is found that the solutions represent two types of modes: (1) the modes in which the electric field is transverse to the axis of the disk (TE modes); and (2) the modes in which the magnetic field is transverse to the axis of the resonator (TM modes). Frequency equations are solved and resonance frequencies are computed as functions of the diameter-to-thickness radio and for variations of the refractive index of the resonator. Predicted values are compared with experimental data.
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