We analyze the optical resonances of a dielectric sphere the surface of which has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and the modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces, or arbitrary surface waves. A dielectric sphere is effectively an open system the description

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... which requires the introduction of non-Hermitian operators characterized by complex eigenvalues and non-normalizable eigenfunctions. We avoid these difficulties using the Kapur-Peierls formalism, which enables us to extend the popular Rayleigh-Schrödinger perturbation theory to the case of electromagnetic Debye potentials describing the light fields inside and outside the near-spherical dielectric object. We find analytical formulas, valid within certain limits, for the deformation-induced first-and second-order corrections to the central frequency and bandwidth of a resonance. As an application of our method, we compare our results with preexisting ones, finding full agreement.