Theory of the Spontaneous Emission in Photonic and Plasmonic Nanoresonators

TL;DR

This paper develops a self-consistent electromagnetic theory for dipole emitters coupled to dissipative nanoresonators, providing accurate formulas for local density of states and revisiting Purcell's factor with new insights.

Contribution

It introduces a quasi-normal mode-based formalism for analyzing electromagnetic responses of photonic and plasmonic nanoresonators with dissipation and leakage.

Findings

New formula for Purcell's factor that accounts for dissipation.

Spectral detuning does not always produce Lorentzian response.

High accuracy of the semi-analytical model confirmed by numerical comparisons.

Abstract

We provide a self-consistent electromagnetic theory of the coupling between dipole emitters and dissipative nanoresonators. The theory that relies on the concept of quasi-normal modes with complex frequencies provides an accurate closed-form expression for the electromagnetic local density of states (LDOS) of any photonic or plasmonic resonator with strong radiation leakage, absorption and material dispersion. It represents a powerful tool to calculate and conceptualize the electromagnetic response of systems that are governed by a small number of resonance modes. We use the formalism to revisit Purcell's factor. The new formula substantially differs from the usual one; in particular, it predicts that a spectral detuning between the emitter and the resonance does not necessarily result in a Lorentzian response in the presence of dissipation. Comparisons with fully-vectorial numerical calculations for plasmonic nanoresonators made of gold nanorods evidence the high accuracy of the predictions achieved by our semi-analytical treatment.