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We report on theoretical study of second-harmonic generation (SHG) inplasmonic nanostructures interacting with two-level quantum emitters (QE) underincoherent energy pump. We generalize driven-dissipative Tavis-Cummings modelby introducing anharmonic surface plasmon-polariton (SPP) mode coupled to QEsand examine physical properties of corresponding SPP-QE polariton states. Ourcalculations of the SHG efficiency for strong QE-SPP coupling demonstrateorders of magnitude enhancement facilitated by the polariton gain. We furtherdiscuss time-domain numerical simulations of SHG in a square lattice comprisedof Ag nanopillars coupled to QEs utilizing fully vectorial nonperturbativenonlinear hydrodynamic model for conduction electrons coupled to Maxwell-Blochequations for QEs. The simulations support the idea of gain enhanced SHG andshow orders of magnitude increase in the SHG efficiency as the QEs are tuned inresonance with the lattice plasmon mode and brought above the populationinversion threshold by incoherent pump. By varying pump frequency and tuningQEs to a localized plasmon mode, we demonstrate further enhancement of the SHGefficiency facilitated by strong local electric fields. The incident lightpolarization dependence of the SHG is examined and related to the symmetries ofparticipating plasmon modes.

Second-harmonic generation in nonlinear plasmonic lattices enhanced by quantum emitter gain medium