Dyadic formulation of morphology-dependent resonances. II. Perturbation theory

Abstract

A generic perturbation theory for the morphology-dependent resonances (MDR's) of dielectric spheres is developed based on the dyadic formulation of a completeness relation established previously [J. Opt. Soc. Am. B 16, 1409 (1999)]. Unlike other perturbation methods proposed previously, the formulation presented here takes full account of the vector nature of MDR's and hence does not limit its validity to perturbations that preserve spherical symmetry. However, the second-order frequency correction obtained directly from the theory, which is expressed as a sum of contributions from individual MDR's, converges slowly. An efficient scheme, based on the dyadic form of the completeness relation, is thus constructed to accelerate the rate of convergence. As an example illustrating our theory, we apply the perturbation method to study MDR's of a dielectric sphere that contains another smaller spherical inclusion and compare the results with those obtained from an exact diagonalization method. © 1999 Optical Society of America.