Spontaneous decay of a quantum emitter near a plasmonic nanostructure

We develop a theory for spontaneous decay of a quantum emitter (QE) situated near metal-dielectric structure supporting localized surface plasmons. If plasmon resonance is tuned close to the QE emission frequency, the emission is enhanced due to energy transfer from the QE to a localized plasmon mode followed by photon emission by plasmonic antenna. The emission rate is determined by intimate interplay between the plasmon coupling to radiation field and the Ohmic losses in metal. Here we develop plasmon Green's function approach that includes plasmon's interaction with radiation to obtain explicit expressions for radiative decay rate and optical polarizability of a localized plasmon mode in arbitrary plasmonic nanostructure. Within this approach, we provide consistent definition of plasmon mode volume by relating it to plasmon mode density, which characterizes the plasmon field confinement, and recover the standard cavity form of the Purcell factor, but now for plasmonic systems. We show that, for QE placed at a "hot spot" near a sharp tip of a small metal nanostructure, the plasmon mode volume scales with the metal volume while being very sensitive to the proximity to the tip. Finally, we derive the enhancement factor for radiated power spectrum for any nanoplasmonic system and relate it to the Purcell factor for spontaneous decay rate. We illustrate our results by numerical example of a QE situated near gold nanorod tip.