Vibrations of circular disk dielectric resonators

Abstract

Two-dimensional equations for guided electromagnetic waves propagating in a dielectric plate surrounded by free space were recently derived from the three-dimensional Maxwell’s equations. These equations 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 surface 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 [transverse electric (TE) modes] and (2) the modes in which the magnetic field is transverse to the axis of the resonator [transverse magnetic (TM) modes]. Frequency equations are solved and resonance frequencies are computed as functions of the diameter-to-thickness ratio a/b for TE and TM modes. It is found that the computational results presented as Ω̂ [≡ω/(π/2b)c] vs a/b curves are independent of the refractive index n̂. Hence, these curves can be conveniently applied to the dielectric disks of any n̂. Predicted results are compared with the experimental data by Cohn [IEEE Trans. Microwave Theory Tech. MTT-16, 218 (1968)], Chow [IEEE Trans. Microwave Theory Tech. MTT-14, 439 (1966)], and Yee [IEEE Trans. Microwave Theory Tech. MTT-13, 256 (1965)], and with the computational results by Chow [IEEE Trans. Microwave Theory Tech. MTT-14, 439 (1966)] and Yee [IEEE Trans. Microwave Theory Tech. MTT-13, 256 (1965)]. It may be seen that present predictions agree overall with different sets of experimental data and for modes of various types and order.