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Nonlinear light sources are central to a myriad of applications, driving aquest for their miniaturisation down to the nanoscale. In this quest, nonlinearmetasurfaces hold a great promise, as they enhance nonlinear effects throughtheir resonant photonic environment and high refractive index, such as inhigh-index dielectric metasurfaces. However, despite the sub-diffractiveoperation of dielectric metasurfaces at the fundamental wave, this condition isnot fulfilled for the nonlinearly generated harmonic waves, thereby allnonlinear metasurfaces to date emit multiple diffractive beams. Here, wedemonstrate the enhanced single-beam second- and third-harmonic generation in ametasurface of crystalline transition-metal-dichalcogenide material, offeringthe highest refractive index. We show that the interplay between the resonancesof the metasurface allows for tuning of the unidirectional second-harmonicradiation in forward or backward direction, not possible in any bulk nonlinearcrystal. Our results open new opportunities for metasurface-based nonlinearlight-sources, including nonlinear mirrors and entangled-photon generation.

Tunable Unidirectional Nonlinear Emission from Transition-Metal-Dichalcogenide Metasurfaces