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We demonstrate optically tunable control of second-harmonic generation in all dielectric nano-antennas: by using a control beam which is absorbed by the nano-resonator, we thermo-optically change the refractive index of the radiating element to modulate amplitude and phase of the second-harmonic signal. For a moderate temperature increase, sizeable modulation is demonstrated; the large tunability of the single meta-atom response paves the way to exciting avenues for reconfigurable homogeneous and heterogeneous metasurfaces.

Nonlinear metasurfaces are a key-asset in nanophotonics, given their ability to scale down nonlinear optics to sub-µm thicknesses. To date, they are mainly realized using small-gap semiconductors, which hampers applications in the visible (VIS) range. High refractive-index transparent materials, such as lithium niobate (LiNbO 3 ), could be used to circumvent this limitation [1] , [2] , [3] , but efficient operation in this strategic spectral window is hindered by nanofabrication challenges. Here we show the first monolithic nonlinear metasurface based on LiNbO 3 for second-harmonic generation (SHG) in the VIS range with efficiency comparable to recent work in the near-infrared [3] . By tuning the pump polarization, we demonstrate efficient steering and polarization encoding of SHG, opening novel opportunities for nonlinear meta-optics.