Dyadic formulation of morphology-dependent resonances. III. Degenerate perturbation theory

Abstract

Based on the completeness of morphology-dependent resonances (MDRs) in a dielectric sphere and the associated MDR expansion of the transverse dyadic Green's function, a generic perturbation theory is formulated. The method is capable of handling cases with degeneracies in the MDR frequencies, which are ubiquitous in systems with a specific symmetry. One then applies the perturbation scheme to locate the MDRs of a dielectric sphere that contains several smaller spherical inclusions. To gauge the accuracy and efficiency of the perturbation scheme, we also use a transfer-matrix method to obtain an eigenvalue equation for MDRs in these systems. The results obtained from these two methods are compared, and good agreement is found. © 2002 Optical Society of America.