Implementation of the Perfectly Matched Layer to Determine the Quality Factor of Axisymmetric Resonators in COMSOL

M.I. Cheema, and A.G. Kirk
McGill University, Montreal, QC, Canada

Due to the inseparability of the wave equation, numerical methods are needed to develop an accurate electromagnetic model for various axisymmetric resonators such as micro-discs and micro-toroids. Our purpose is the implementation of a perfectly matched layer to determine the quality factor of axisymmetric resonators with high accuracy in COMSOL. We treated the perfectly matched layer as an anisotropic absorber and implemented it in the cylindrical coordinates system. Due to the availability of analytical expressions for spherical resonators, we tested our model by determining the quality factors of a silica micro-sphere in air. We plotted the quality factor due to the TE/TM fundamental whispering gallery mode radiation for various sphere diameters at 850nm. Our simulation results are in excellent agreement with the analytical results.