  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.
