Coulomb and quenching effects in small nanoparticle-based spasers

Abstract

We study numerically the effect of mode mixing and direct dipole-dipole interactions between gain molecules on spasing in a small composite nanoparticles with a metallic core and a dye-doped dielectric shell. By combining Maxwell-Bloch equations with Greens function formalism, we calculate lasing frequency and threshold population inversion for various gain densities in the shell. We find that gain coupling to nonresonant plasmon modes has a negligible effect on spasing threshold. In contrast, the direct dipole-dipole coupling, by causing random shifts of gain molecules' excitation frequencies, hinders reaching the spasing threshold in small systems. We identify a region of parameter space in which spasing can occur considering these effects.

Mode Volume, Energy Transfer, and Spaser Threshold in Plasmonic Systems with Gain

“…Since the Green dyadic includes contributions from all electromagnetic modes, the spaser threshold in general case can only be determined numerically. However, for QEs coupled to a resonant plasmon mode, that is, for ω 21 close to the mode frequency ω pl , the contribution from off-resonance modes is relatively small [39,40] and, as we show below, the spaser condition can be obtained explicitly for any nanoplasmonic system.…”

Spaser quenching by off-resonant plasmon modes

“…The main effect of gain coupling to off-resonant modes on spaser action is the disruption of the gain-plasmon feedback, and, hence, the increase of the spasing threshold (spaser quenching). According to our numerical simulations [58], the effect of quenching on spaser action is much weaker than on single-molecule fluorescence. However, no analytical model for spaser quenching and, importantly, no spaser condition accounting for off-resonant modes has so far been suggested.…”

“…In such systems, the direct coupling between gain molecules is maximal, which leads to random Coulomb shifts of molecule excitation energies and, hence, to dephasing [59,60]. For small systems, the spasing eigenstates were found via exact numerical diagonalization [58]; however, for larger systems with realistic random dipole orientations, direct numerical determination of many-body eigenstates of interacting QEs is not feasible. At the same time, for large ensembles of randomlyoriented QEs, the ensemble-averaged dipole coupling between individual QEs vanishes, while weak fluctuations of QEs' excitation energies do not significantly affect the collective system eigenstates strongly coupled to radiation [61].…”

“…In recent work [58], we carried out a numerical study of the role of gain coupling to off-resonant modes as well as of direct dipole coupling between QEs in small NP-based spasers. Due to numerical challenges, our simulations were restricted to relatively small (5 nm radius) NPs with thin (up to 2.5 nm) dye-doped dielectric shells and relatively low (up to 1000) numbers of QEs with dipole moments oriented normally to the NP surface.…”

Theoretical study of plasmonic lasing in junctions with many molecules

“…If we turn to many quantum emitters, their mutual coupling can lead to the formation of exciton states, which may have different transition energies compared to that * yzhang@phys.au.dk † moelmer@phys.au.dk ‡ may@physik.hu-berlin.de of the isolated quantum emitters, i.e. inhomogeneous broadening [19]. As a result, the energy transfer from the quantum emitters to the MNP plasmon becomes inefficient, and the coupling to other plasmon modes may occur, which further complicates the situation [16].…”