Rigorous electrodynamical simulations based on the nonlinear Drude model are performed to investigate the influence of strong coupling on high harmonic generation by periodic metal gratings. It is shown that a thin dispersive material with a third order nonlinearity strongly coupled to surface plasmon-polaritons significantly affects even harmonics generated solely by the metal. The physical nature of this effect is explained using a simple analytical model and further supported by numerical simulations. Furthermore, the behavior of the second and third harmonics is investigated as a function of various physical parameters of the model material system, revealing highly complex dynamics. The nonlinear optical response of 2D few-layer WS2 with both second and third order susceptibilities coupled to a periodic plasmonic grating is shown to have a significant effect on the second harmonic generation of the metal.
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