We introduce a theory to analyze the behavior of light emitters in nanostructured environments rigorously. Based on spectral theory, the approach opens the possibility to quantify precisely how an emitter decays to resonant states of the structure and how it couples to a background, also in the presence of general dispersive media. Quantification on this level is essential for designing and analyzing topical nanophotonic setups, e.g., in quantum technology applications. We use a numerical implementation of the theory for computing modal and background decay rates of a single-photon emitter in a diamond nanoresonator.
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