COMPLETENESS AND TIME-INDEPENDENT PERTURBATION OF MORPHOLOGY-DEPENDENT RESONANCES IN DIELECTRIC SPHERES

Morphology-dependent resonances commonly observed in both the elastic and the inelastic scattering of light waves from dielectric spheres ar e in fact direct manifestations of complex frequency poles of the scat tering matrix. Time-independent solutions to the wave equation at thes e poles are termed quasi-normal modes, which are characterized by the outgoing wave boundary condition at infinity and cannot be normalized in the usual sense. These resonances (or quasi-normal modes) are shown to form a complete set inside the dielectric sphere, provided that th ere is a spatial discontinuity in the refractive index, say, at the ed ge of the sphere. Novel definitions of norm and inner product are intr oduced. In addition, a time-independent perturbation method based on t his completeness relation is developed to evaluate shifts in resonance frequencies when the refractive index is changed. (C) 1996 Optical So ciety of America