Fdfd Analysis of Whispering Gallery Modes

The analysis of whispering gallery modes in a cylindrical sapphire resonator is shown. The formulation involves only two components of the electric flux density. Using the FDFD method on Yee´s mesh, the electromagnetic problem is converted to a standard nonsymmetric matrix eigenvalue problem with a highly sparse and structured matrix. The resonant modes are found by means of the implicitly restarted Arnoldi method with Chebyshev acceleration. Is is shown that the application of Chebyshev preconditioning allows one to significantly reduce the computing time without increasing the memory cost.