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

The nonlinear optics of plasmonic nanostructures has become a hot research field. Applications range from optical bi-stability to second harmonic generation (SHG). We report on theoretical study of SHG in plasmonic lattices interacting with quantum emitters (QE) under incoherent energy pump. We generalize driven-dissipative Tavis-Cummings model by introducing anharmonic surface-plasmon mode and examine polariton modes in strong (lasing) coupling regime. Subsequent calculations of the SHG efficiency show strong enhancement due to polariton gain. We further discuss time-domain numerical simulations of SHG in 2D lattice of Ag nano-pillars coupled to QEs utilizing fully vectorial nonlinear hydrodynamic model for conduction electrons coupled to Maxwell-Bloch equations for QEs. The simulations clearly show orders of magnitude increase in the SHG efficiency as the QEs are tuned in resonance with the lattice plasmon mode and brought above the population inversion threshold by incoherent pump. By varying pump frequency and tuning QEs to a localized plasmon mode, we demonstrate further enhancement of the SHG efficiency facilitated by strong local electric fields. The incident light polarization dependance of the SHG is examined and related to the symmetries of participating plasmon modes.