An efficient and accurate algorithm based on the combination of the Green's function method and an analytical regularization technique is applied to study the complex natural frequencies and Q factors of two-dimensional (2-D) dielectric resonators (DRs) in a layered environment. Frequency shift and degeneracy splitting of the whispering-gallery modes (WGMs) of circular-cylindrical and tubular DRs immersed into layered dielectric media are computed and analyzed.
Boriskina, S. V., Benson, T. M., Sewell, P., & Nosich, A. I. (2002). Effect of a layered environment on the complex natural frequencies of two-dimensional WGM dielectric-ring resonators. Journal of Lightwave Technology, 20(8), 1563–1572. https://doi.org/10.1109/JLT.2002.800297