EFFECT OF PERTURBATIONS ON THE WIDTHS OF NARROW MORPHOLOGY-DEPENDENT RESONANCES IN MIE SCATTERING

The extremely narrow morphology-dependent resonances of a microdroplet seen in Mie scattering are important for the nonlinear optical phenomena in these microdroplets, the large storage time being responsible for optical feedback. A formalism is developed within the scalar wave analog to calculate the change in the widths caused by a small perturbation, such as a distortion of the microdroplet shape from perfect sphericity. This formalism may be viewed as the generalization of the usual Rayleigh-Schrodinger perturbation scheme to the imaginary part of the energy. The results are checked against T-matrix calculations. In particular, it is proved that any perturbation can only increase the widths of these resonances, provided that terms of O(1/Q0) can be ignored in the first- and second-order corrections, where Q0 is the original quality factor of the resonance. The result can be interpreted in terms of a generalized golden rule and is relevant to similar problems involving quasi-normal modes in quantum mechanics. The full theory beyond the scalar wave approximation can be developed, and it is expected that all qualitative features will survive.