Wavefront Control and Intensity Modulation of Third Harmonic Generation in Nonlocal Metasurfaces

Metasurfaces have emerged as a promising platform for integrated nonlinear optics. Nonlocal metasurfaces enable high nonlinear conversion efficiency, while the local ones can offer versatile wavefront control, yet achieving both within a single metasurface remains challenging. Here, using a nonlocal phase gradient metasurface, we firstly demonstrate efficient third harmonic generation (THG) with polarization-dependent wavefront control. Leveraging nonlocal nonlinear geometric phase existing at resonance, the third harmonic light with distinct polarizations is deflected into $\pm$ 2nd and $\pm$ 4th diffraction orders, simultaneously achieving a conversion efficiency up to $1.45\times 10^{-4}$ under a pump intensity of $1 GW/cm^{2}$. Then, by introducing a secondary fundamental beam, whose generated third harmonic light overlaps with that of the first beam, the intensity modulation of THG is obtained. The THG efficiency can be tuned from $3.9 \times 10^{-9}$ to $5.5 \times 10^{-3}$ by varying the relative phase, polarization and intensity of two fundamental beams. Through utilizing the advantages of both local and nonlocal metasurfaces, our results effectively pave the way to on-chip nonlinear photonic devices and signal processing.