Theory of the Spontaneous Emission in Photonic and Plasmonic Nanoresonators

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.