Perturbation theory of optical resonances of deformed dielectric spheres
Aiello A, Harris JGE, Marquardt F (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 100
Journal Issue: 2
DOI: 10.1103/PhysRevA.100.023837
Abstract
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 of 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-Schrodinger 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.
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APA:
Aiello, A., Harris, J.G.E., & Marquardt, F. (2019). Perturbation theory of optical resonances of deformed dielectric spheres. Physical Review A, 100(2). https://dx.doi.org/10.1103/PhysRevA.100.023837
MLA:
Aiello, Andrea, Jack G. E. Harris, and Florian Marquardt. "Perturbation theory of optical resonances of deformed dielectric spheres." Physical Review A 100.2 (2019).
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