10 Q$_{ens}$ ≃ 3 1 + 3( q − 1 − 1) /N , (44) ∇ × ∇ × ˆ G − k $^{2}$ϵ ( r ) ˆ G = ˆ I , (45) GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s50>GLYPH<s48> GLYPH<s51>GLYPH<s48> GLYPH<s52>GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s51> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s49> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s50>GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s51>GLYPH<s50> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s54>GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s56>GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s100> GLYPH<s32> GLYPH<s40> GLYPH<s110>GLYPH<s109> GLYPH<s41> GLYPH<s81> GLYPH<s101>GLYPH<s110>GLYPH<s115> GLYPH<s65>GLYPH<s103> GLYPH<s82>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s50>GLYPH<s48>GLYPH<s32> GLYPH<s110>GLYPH<s109> GLYPH<s113>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s48>GLYPH<s46> GLYPH<s57>GLYPH<s53> GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s50>GLYPH<s48> GLYPH<s51>GLYPH<s48> GLYPH<s52>GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s51> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s49> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s50>GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s51>GLYPH<s50> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s54>GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s78>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s56>GLYPH<s48> GLYPH<s65>GLYPH<s103> GLYPH<s82>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s50>GLYPH<s48>GLYPH<s32> GLYPH<s110>GLYPH<s109> GLYPH<s113>GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s48>GLYPH<s46> GLYPH<s51> GLYPH<s32> GLYPH<s32> GLYPH<s100> GLYPH<s32> GLYPH<s40> GLYPH<s110>GLYPH<s109> GLYPH<s41> GLYPH<s81> GLYPH<s101>GLYPH<s110>GLYPH<s115> FIG. 9: (Color online) Fluorescence quantum efficiency vs. distance for several ensembles of high-yield emitters on spher- ical lattices around AG NP. FIG. 10: (Color online) Fluorescence quantum efficiency vs. distance for several ensembles of low-yield emitters on spher- ical lattices around AG NP. V. CONCLUSIONS a weak dependence on N . In both cases, this behavior can be easily understood from Eq. (42). Indeed, for de- generate superradiant eigenvalues we have λ$_{µ}$ = 1, and for large distances, as Γ → Γ r $_{0}$, we obtain i.e., for large ensembles, the role of molecular quantum yield is diminished. We studied here plasmon-mediated superradiance from an ensemble of dipoles near metal nanoparticle support- ing localized surface plasmon, thereby extending the Dicke effect to plasmonic systems. Our main conclu- sion is that the plasmonic Dicke effect is a robust phe- nomenon, more so than the usual photonic Dicke effect, because of a more efficient hybridization of individual dipoles via nanoparticle plasmon. We have established that hybridization takes place through two types of plas- monic coupling mechanisms – plasmon-enhanced radia- tive coupling and nonradiative plasmon coupling, the lat- ter having no analogue in the usual Dicke effect and caus- ing demise of cooperative emission at very close dipole- nanoparticle distances. While we considered a specific nanostructure – spheri- cal metal particle - the plasmon-mediated superradiance is a quite general phenomenon that should take place in any plasmonic system tuned into resonance with emit- ters, and Eq. (1) should apply provided that the usual cri- teria for cooperative emission are met. In fact, our theory remains unchanged for any nanostructure with spherical symmetry, for example metal nanoshells with dielectric core, upon simple replacement of NP polarizabilities in self-energy matrix Eq. (12) and elsewhere with appropri- ate expressions. In fact, one expects that in nanoshells the nonradiatice losses would be smaller and so the plas- monic Dicke effect would be more robust than for solid nanoparticles. This work was supported in part by the NSF under Grant Nos. DMR-0906945 and HRD-0833178, and under the EPSCOR Program. of plasmonic Dicke effect is to drastically reduce the emis- sion as compared to same number of individual dipoles. Remarkably, as the eigenvalues scale uniformly with N , the quantum efficiencies of superradiant states are nearly independent of the ensemble size, leading to the simple relation (1) that holds in the cooperative regime. This is illustrated in Figs. 9 and 10, which show en- semble quantum efficiencies Q$_{ens}$ [see Eq. (37)] for two types of dyes with quantum yields q = 0 . 95 and q = 0 . 3, respectively. Two regimes can be clearly distinguished in the distance dependence of Q$_{ens}$ : it first shows a sharp rise with its slope proportional to N (non-cooperative regime) followed by a slower d dependence (cooperative regime). The crossover between two regimes takes place at d ≃ 5 nm due to diminished high- l plasmons con- tribution to nonradiative coupling for larger distances. In the cooperative regime, the precise behavior of Q$_{ens}$ is affected by molecules’ quantum yield. For high- q molecules, all Q$_{ens}$ dependences collapse onto a single curve, Q$_{ens}$ = 3 Q , while for low- q molecules, Q$_{ens}$ shows Here we collect relevant some formulas for the elec- tric field Green dyadic in the presence of metal NP. The Green dyadic satisfies Maxwell equation where ϵ ( r ) = ϵ ( ω ) θ ( R − r ) + ϵ$_{0}$θ ( r − R ) is local dielectric function ( θ ( x ) is the step-function). The Green dyadic can be split into free space and Mie-scattered parts, Appendix