We demonstrate a novel scheme to dramatically enhance both the second- and third-harmonic generation in a graphene-insulator-graphene metasurface. The key underlying feature of our approach is the existence of a double-resonance phenomenon, namely the metasurface is designed to possess fundamental plasmon resonances at both the fundamental frequency and the higher harmonic. In particular, this dual resonant field enhancement at the two optical frequencies, combined with a favorable spatial overlap of the optical near-fields, lead to the increase of the generated higher harmonic by several orders of magnitude. Remarkably, we demonstrate that by tuning the Fermi energy of the graphene gratings the dual-resonance property can be locked-in over a broad spectral range of ~20 THz, and equally important, the enhanced nonlinear frequency generation process can be readily switched in the same device between the second and third harmonic. This new type of graphene metasurface could open up new avenues towards the development of novel ultra-compact and multi-frequency active photonic nanodevices.
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