Tailoring Spin-Orbit Interaction in High Harmonic Generation via Geometric Phase.

Intense light fields with spatiotemporally structured wave fronts open new avenues for exploring nonlinear light-matter interactions in ultrafast spectroscopy and photonic technologies. Here, we report the observation of geometric phase induced spin-orbit interaction (SOI) in high harmonic generation from crystalline solids. The geometric phase imprinted on the high-order harmonics originates from spin flips driven by crystal anisotropy. By employing a specially designed metasurface, the conversion from spin to orbital angular momentum can be achieved, sculpting the wave front of harmonics into arbitrary vortex structures. Furthermore, the SOI enables the realization of vectorial shaping, giant photonic spin Hall effects, and metalenses for high-harmonic light.