Two-dimensional transition metal dichalcogenides have shown large second-order nonlinear responses due to their broken crystal inversion symmetry. However, their nonlinear interaction with light is restricted to an atomically thin layer. Placing a sheet of transition metal dichalcogenides on a resonant metasurface enhances the field interacting with the nonlinear material thus compensating for this shortcoming. But, it remains a challenge to tune resonances such, that they coincide with fundamental and second harmonic frequencies simultaneously. Here we demonstrate two independent methods to achieve that goal and numerically illustrate our findings for a MoS2 layer combined with silicon nitride photonic crystals. We numerically demonstrate 20-fold and 170-fold enhancement of second-harmonic generation compared with a design based on a single resonant structure. Although we focus on that specific configuration our approach can likewise be applied to other dielectrics combined with highly nonlinear 2D materials.
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