Purcell factor of metallic nanoresonators

The spontaneous emission of a quantum emitter depends on its environment. This fundamental effect of quantum electrodynamics has become a cornerstone of nano-optics, with the objective to control light absorption and emission at the nanometer scale. At the heart of the effect lies the emitter-cavity coupling. An important figure of merit is the famous Q/V ratio introduced by Purcell in 1946 and largely used by the photonic-crystal community over the last decennia, with Q the quality factor of the cavity and V the mode volume. Here we revisit the classical problem of field coupling between quantum emitters and cavities to encompass the important case of metallic nanoresonators. We propose a generalized Purcell formula, which substantially differs from the classical one and which is capable of accurately handling cavity modes with strong radiative leakage, absorption and material dispersion. Fully-vectorial numerical calculations obtained for distinct nanocavity constructs representative of modern studies in nanophotonics provide a strong support to our theory.