Nonlinear nonlocal metasurfaces

Nonlinear metasurfaces have been enabling unprecedented control over light generation and wave mixing, demonstrating enhanced wavefront control, beam shaping and steering of nonlinear light waves. However, the design and operation of nonlinear metasurfaces have been for the most part limited to localized modes, fundamentally limiting the overall nonlinearity enhancement of such devices. Periodic structures supporting extended lattice resonances can realize much larger quality-factor resonances, and hence stronger nonlinearity enhancement, but they are fundamentally limited in their wavefront shaping capabilities, due to their high symmetry. Nonlocal metasurfaces have been recently introduced in linear settings to support highly delocalized resonant modes that can promote very large quality factors, yet without requiring periodicity, hence providing also local control over the wavefront. Here, we extend the powerful features of nonlocal metasurfaces to nonlinear phenomena, experimentally demonstrating nonlinear nonlocal metasurfaces that simultaneously support high quality factor modes, and hence strong nonlinearity enhancement, as well as a spatially varying geometric phase tailored over a subwavelength scale. We show how nonlinear nonlocal metasurfaces can at the same time enhance light-matter interactions, boosting nonlinear conversion efficiency, and enable precise subwavelength control over the wavefront of the generated light. Using this platform, we demonstrate a silicon metasurface for beam steering of third-harmonic generation in the visible. Our results show control over the polarization and steering angle of the third-harmonic signal, extending the framework of diffractive nonlocal metasurfaces to nonlinear optics, and pave the way for the development of nanoscale nonlinear devices with unparalleled control over the optical properties of generated light.