We investigate second harmonic generation (SHG) from hexagonal periodic arrays of triangular nano-holes of aluminum using a self-consistent methodology based on the hydrodynamics-Maxwell–Bloch approach. It is shown that angular polarization patterns of the far-field second harmonic response abide to threefold symmetry constraints on tensors. When a molecular layer is added to the system and its parameters are adjusted to achieve the strong coupling regime between a localized plasmon mode and molecular excitons, Rabi splitting is observed from the occurrence of both single- and two-photon transition peaks within the SHG power spectrum. It is argued that the splitting observed for both transitions results from direct two-photon transitions between lower and upper polaritonic states of the strongly coupled system. This interpretation can be accounted by a tailored three-level quantum model, with results in agreement with the unbiased numerical approach. Our results suggest that the hybrid states formed in strongly coupled systems directly contribute to the nonlinear dynamics. This opens new directions in designing THz sources and nonlinear frequency converters.
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