We develop a theory of cooperative emission mediated by cooperative energy transfer (CET) from an ensemble of quantum emitters (QE) to plasmonic antenna at a rate equal to the sum of individual QE-plasmon energy transfer rates. If the antenna radiation efficiency is sufficiently high, the transferred energy is radiated away at approximately the same cooperative rate that scales with the ensemble size. We derive explicit expressions, in terms of local fields, for cooperative Purcell factor and enhancement factor for power spectrum valid for plasmonic structures of any shape with characteristic size smaller than the radiation wavelength. The radiated power spectrum retains the plasmon resonance lineshape with overall amplitude scaling with the ensemble size. If QEs are located in a region with nearly constant plasmon local density of states (LDOS), e.g., inside a plasmonic nanocavity, we demonstrate that the CET rate scales linearly with the number of excited QEs, consistent with the experiment, and can be tuned in a wide range by varying the excitation power. For QEs distributed in an extended region saturating the plasmon mode volume, we show that the cooperative Purcell factor has universal form independent of the system size. The CET mechanism incorporates the plasmon LDOS enhancement as well, giving rise to possibilities of controlling the emission rate beyond field enhancement limits.
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 QE to 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 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 ”hot spot” near 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.