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We investigate second harmonic generation (SHG) from hexagonal periodicarrays of triangular nano-holes of aluminum using a self-consistent methodologybased on the hydrodynamics-Maxwell-Bloch approach. It is shown that angularpolarization patterns of the far-field second harmonic response abide tothree-fold symmetry constraints on tensors. When a molecular layer is added tothe system and its parameters are adjusted to achieve the strong couplingregime between a localized plasmon mode and molecular excitons, Rabi splittingis observed from occurrence of both single- and two-photon transition peakswithin the SHG power spectrum. It is argued that the splitting observed forboth transitions results from direct transitions between lower and upperpolaritonic states of the strongly coupled system. This interpretation can beaccounted by a tailored three-level quantum model, with results in agreementwith the unbiased numerical approach. Our results suggest the hybrid statesformed in strongly coupled systems directly contribute to the nonlineardynamics. This opens new directions in designing THz sources and nonlinearfrequency converters.

Second harmonic generation by strongly coupled exciton-plasmons: the role of polaritonic states in nonlinear dynamics