Calculation of the spectrum of whispering gallery modes in cylindrical resonators with perturbed boundary conditions

The spectrum of whispering gallery modes for resonators with a small deformation of the boundary is calculated analytically. Cylindrical resonators with two different cross sections (segment close to a circle and segment close to a semicircle) are considered. The calculation is performed for resonators with metal boundaries, but the obtained result is a good approximation for dielectric resonators as well. The applicability limits of the found expressions for the spectra are analysed. It is shown that the spectra calculated using the obtained expressions coincide well with computer-calculated spectra. The perturbation-induces changes in the field distribution are qualitatively studied using numerical simulation.