  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.
