Riesz-projection-based theory of light-matter interaction in dispersive nanoresonators

A theory based on Riesz projections is introduced to analyze the coupling of light sources to resonant states of nanostructures. The concept applies to general dispersive media without the explicit use of a mode orthogonality relation and allows for the precise quantification of the interaction with the nonresonant background. Exemplarily, a numerical implementation of the theory is used for the computation of modal Purcell factors of an emitter embedded into a dielectric nanoresonator supporting several weakly localized modes.

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