Perturbation theory of nearly spherical dielectric optical resonators

Abstract

Dielectric spheres of various sizes may sustain electromagnetic whispering-gallery modes resonating at optical frequencies with very narrow linewidths. Arbitrary small deviations from the spherical shape typically shift and broaden such resonances. Our goal is to determine these shifted and broadened resonances. A boundary-condition perturbation theory for the acoustic vibrations of nearly circular membranes was developed by Rayleigh more than a century ago. We extend this theory to describe the electromagnetic excitations of nearly spherical dielectric cavities. This approach permits us to avoid dealing with decaying quasinormal modes. We explicitly find the frequencies and the linewidths of the optical resonances for arbitrarily deformed nearly spherical dielectric cavities, as power series expansions by a small parameter, up to and including second-order terms. We thoroughly discuss the physical conditions for the applicability of perturbation theory.

31 pages, 6 figures; published version

References in corpus (5)

• Brillouin-Wigner perturbation theory in open electromagnetic systems
• Resonant state expansion applied to three-dimensional open optical systems
• Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods
• Cavity Optomechanics in a Levitated Helium Drop
• Perturbation Theory of Optical Resonances of Deformed Dielectric Spheres

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