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