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

TL;DR

This paper presents a rigorous spectral theory based on Riesz projections to analyze light-matter interactions in dispersive nanoresonators, enabling precise quantification of emitter decay and coupling in complex nanophotonic environments.

Contribution

It introduces a novel theoretical framework using spectral theory and Riesz projections for analyzing light emitters in dispersive nanostructures, with a numerical implementation demonstrated.

Findings

Quantifies emitter decay into resonant and background states.

Provides a numerical method for modal decay rate computation.

Applicable to designing nanophotonic quantum devices.

Abstract

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.