Accurate Computation of Guided-Wave Coupling to Dielectric Resonators in 2-D Geometry

Large dielectric resonators that support whispering gallery modes are attractive for photonic applications due to high-quality factors of their resonances. The high-quality factors require the development of very accurate modeling methods for such structures. Several analytical methods reducible to matrix equations to model the excitation of large dielectric cylinders by guided waves are discussed. While it is shown that the analytical derivations produce similar matrices, the actual choice of the unknown vector and matrix scaling results in wide variations of the matrix condition numbers and, in some cases, in the failure of the numerical solution for large sizes of the matrix. A reasonable choice for the unknown vector is proposed and the smallest condition number of the resulting matrix compared to other existing choices is obtained.