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–Schrödinger 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.
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