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 Padé 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.
© 1998 Optical Society of America
Original Manuscript: July 22, 1997
Manuscript Accepted: December 19, 1997
Published: May 1, 1998
K. M. Lee, P. T. Leung, and K. M. Pang, "Iterative perturbation scheme for morphology-dependent resonances in dielectric spheres," J. Opt. Soc. Am. A 15, 1383-1393 (1998)