Plasmon-enhanced luminescence near noble-metal nanospheres: Comparison of exact theory and an improved Gersten and Nitzan model

We present a theoretical study of the modifications of the radiative and nonradiative decay rates of an optical emitter in close proximity to a noble-metal nanosphere, based on exact electrodynamical theory. We show that the optimal nanosphere diameter for luminescence quantum efficiency enhancement associated with resonant coupling to plasmon modes is in the range of 30-110 nm, depending on the material properties. The optimal diameter is found to be a trade-off between (1) emitter-plasmon coupling, which is most effective for small spheres, and (2) the outcoupling of plasmons into radiation, which is most efficient for large spheres. In addition, we show that the well-known Gersten and Nitzan model does not describe the existence of a finite optimal diameter unless the model is extended with the correction factor for radiation damping. With this correction and a correction for dynamic depolarization, the mathematically simpler Gersten and Nitzan model provides a reasonably accurate approximation of the decay rate modifications associated with coupling to the dipole plasmon mode. We anticipate that the Gersten and Nitzan model in the form that we validate in this paper for spheres will allow the analytical investigation of the influence of shape anisotropy on plasmon-enhanced luminescence.