Quality factors of deformed dielectric cavities

An analysis is provided of the degradation that arises in the quality factor of a whispering gallery mode when a circular or spherical dielectric cavity is deformed. The large quality factors of such resonators are important to their use in applications such as sensors, wavelength filters or lasers. Yet a straightforward analysis of the effect of shape deformation on quality factors cannot given because the underlying complex ray data demanded by a standard eikonal approximation frequently does not exist. In this paper we exploit an approach that has been successfully used elsewhere to describe the strong directional emission of such systems, based on a perturbative treatment of the relevant complex ray families. Applicable when the radial perturbation is formally of the order of a wavelength, the resulting approximation successfully describes changes to the quality factor using the ray geometry in a neighbourhood of a discrete set of escaping rays guiding the directions of maximum emitted intensity.