The nonlinear optical response of materials to exciting light is enhanced by resonances between the incident laser frequencies and the energy levels of the excited material. Traditionally, in molecular nonlinear spectroscopy one tunes the input laser frequencies to the molecular energy levels for highly enhanced doubly or triply resonant interactions. With metasurfaces the situation is different, and by proper design of the nanostructures, one may tune the material energy levels to match the incoming laser frequencies. Here we use multi-parameter genetic algorithm methodologies to optimize the nonlinear Four Wave Mixing response, and show that the intuitive conventional approach of trying to match the transmission spectrum to the relevant laser frequencies indeed leads to strong enhancement, but not necessarily to the optimal design. We demonstrate, experimentally and by direct nonlinear field calculations, that the near field mode distribution and spatial modes overlap are the dominant factor for optimized design.

We shrdy strong coupling (SC) in a system of plasmonic nanohole arrays and transition- metal dichalcogenide material (WS2). Using FDTD simulations and a genetic algorithm, we design several array geometries to obtain large Rabi splitting at room-temperature.

Hybrid photonic structures of plasmonic metasurfaces coupled to atomically thin semiconductors have emerged as a versatile platform for strong light-matter interaction, supporting both strong coupling and parametric nonlinearities. However, designing optimized nonlinear hybrid metasurfaces is a complex task, as the multiple parameters' contribution to the nonlinear response is elusive. Here we present a simple yet powerful strategy for maximizing the nonlinear response of the hybrid structures based on evolutionary inverse design of the metasurface’s near-field enhancement around the excitonic frequency. We show that the strong coupling greatly enhances the nonlinear signal, and that its magnitude is mainly determined by the Rabi splitting, making it robust to geometrical variations of the metasurface. Furthermore, the large Rabi splitting attained by these hybrid structures enables broadband operation over the frequencies of the hybridized modes. Our results constitute a significant step towards achieving flexible nonlinear control, which can benefit applications in nonlinear frequency conversion, all-optical switching, and phase-controlled nonlinear metasurfaces.

We theoretically demonstrate a tight connection between the linear response of hybrid plasmonic-excitonic metasurface modes in the strong-coupling regime and their nonlinear Four-Wave-Mixing spectral behavior, mediated by the Rabi splitting in the system.

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