Iterative perturbation scheme for morphology-dependent resonances in dielectric spheres

Abstract

The properties of morphology-dependent resonances observed in the scattering of electromagnetic waves from dielectric spheres have recently been investigated intensively, and a second-order perturbative expansion for these resonances has also been derived. Nevertheless, it is still desirable to obtain higher-order corrections to their eigenfrequencies, which will become important for strong enough perturbations. Conventional explicit expressions for higher-order corrections inevitably involve multiple sums over intermediate states, which are computationally cumbersome. In this analysis an efficient iterative scheme is developed to evaluate the higher-order perturbation results. This scheme, together with the optimal truncation rule and the Pade resummation, yields accurate numerical results for eigenfrequencies of morphology-dependent resonances even if the dielectric sphere in consideration deviates strongly from a uniform one. It is also interesting to find that a spatial discontinuity in the refractive index, say, at the edge of the dielectric sphere, is crucial to the validity of the perturbative expansion.