  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.
