Dual-harmonic generation in a hybrid graphene-lithium niobate nonlinear metasurface

The control of harmonic generation is essential for advanced nonlinear nanophotonic devices. Here, we propose a hybrid nonlinear metasurface combining graphene, lithium niobate (LiNbO₃), and silicon dioxide (SiO₂) to enable simultaneous second- and third-harmonic generation (SHG and THG) mediated by guided-mode resonances (GMRs). The structure consists of graphene-lithium niobate pillars arranged on a glass substrate and exploits both the anisotropic optical response and the second-order nonlinearity of LiNbO₃ together with the third-order nonlinear response of graphene and SiO₂. By engineering the metasurface geometry, distinct GMR branches are identified in the linear optical response and accurately captured by an analytical effective-index model combined with the grating equation. Nonlinear simulations reveal that both SHG and THG efficiencies are enhanced at the GMR conditions, with a simultaneous enhancement observed in the vicinity of the crossing point between the TE₀ and TM₁ modes. These results highlight the potential of the proposed hybrid metasurface for compact, multi-resonant nonlinear optical devices enabled by geometrical tailoring of guided-mode resonances.