Experimental test and application of a 2-D finite element calculation for whispering gallery sapphire resonators

This paper discusses the demonstrated accuracy and utility of a 2-D finite element methodology for whispering gallery mode sapphire resonators. The mode solutions obtained by the software compared with experimental results for a wheel-shaped sapphire resonator give an error in mode frequency of less than 0.55%. We also show parts per million agreement with analytical solutions for simple geometries such as an empty coaxial resonator. The CYRES 2D FEM software package developed at The University of Texas at El Paso has proven invaluable for the analysis and identification of modes and mode families for resonators of various geometries. The software also shows promise as a tool for optimization of new resonator designs. Current uses include design of optimum sized dielectric resonators for minimized wall losses, and new resonator geometries for temperature compensated resonators. The operational characteristics of the software and the general methodology for use of the software as a laboratory and design tool are discussed