Cooperative emission mediated by cooperative energy transfer to a plasmonic antenna

We develop a theory of cooperative emission mediated by cooperative energy transfer (CET) from an ensemble of quantum emitters (QEs) 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 sizes 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.

Figure 1

(a) Schematics of CET from QE ensemble to plasmonic antenna. (b) Schematics of plasmonic system with QEs distributed within dielectric shell surrounding metallic core.

Figure 2

Average plasmon mode volume ${\mathcal{V}}_0$ in the QE region, normalized by saturated mode volume ${\mathcal{V}}_{\mathrm{sat}}$, is plotted vs. QE region size. Inset. Schematics of core-shell nanorod in water with Au core and QE-doped ${\mathrm{SiO}}_2$ shell.

Figure 3

Cooperative Purcell factor (a) and power spectrum enhancement factor (b) are plotted vs QE region size for several nanorod lengths at fixed core aspect ratio $a/b=3.0$.

Figure 4

Cooperative acceleration of the ensemble decay rate relative to LDOS enhancement of the individual QE decay rate is plotted vs a QE distance $d$ to the metal tip. Lower inset: Schematics of a Au nanorod surrounded by QE-doped ${\mathrm{SiO}}_2$ shell in water. Upper inset: Schematics of a QE located at a distance $d$ from the Au nanorod tip in water.