Resonant radiative and non-radiative coupling between a molecule and a metallic tip

We study numerically the radiative and non-radiative decay rates of a molecule close to the apex of a metallic tip. We show that both rates present a resonance at different frequencies which, in general, do not coincide. This behavior is explained by a general model describing the resonant behavior of the electromagnetic response of the tip. We also investigate the influence of a small defect located close to the tip apex. We show that it may substantially modify the ratio between the radiative and non-radiative contributions, and induces a frequency shift of the resonances. This may explain why experiments on single-molecule fluorescence dramatically depend on the tip quality.