Perturbation approach to resonator state solution using the Fourier-Bessel numerical solver

Abstract

The Fourier-Bessel (FFB) numerical solver is a useful tool for obtaining the steady states of resonator structures that conform to a cylindrical symmetry. Recently the FFB solver has been greatly simplified by reconfiguring the matrix generating expressions using Maxwell's curl expressions rather than the standard wave equations. This presentation provides a numerical framework suitable for the application on non-degenerate perturbation theory within the theoretical structure of the reconfigured FFB computation environment. It is shown that the resonator structure's perturbation contribution can be isolated as a separate matrix which dictates the shift in resonator state properties. Two distinct application examples are provide; the first has the perturbation possess the same rotational symmetry as the original structure and preserves azimuthal mode order families; the second perturbation has a symmetry different than the original structure and promotes a mixing between azimuthal mode order families. The perturbation extension promises to amplify the potential usefulness of the FFB technique when theoretically considering photonic sensors such as whispering-gallery mode, photonic crystal hole infiltration and a host of others in which the measurand undergoes small changes in its optical properties.