Intrinsic nonlinear geometric phase in SHG from zincblende crystal symmetry media.

We demonstrate that AlGaAs thin films and metasurfaces generate a distinct intrinsic nonlinear geometric phase in their second harmonic signals, differing significantly from previous studies on nonlinear dielectric, plasmonic, or hybrid metasurfaces. Unlike conventional observations, our study reveals that the second harmonic phase remains unaffected by the linear optical response at both pump and harmonic wavelengths, introducing a novel realm of achievable phase functions yet to be explored. Furthermore, we explore the interplay between this intrinsic nonlinear geometric phase and the geometric phase induced by rotations of nanoresonators within metasurface arrangements. Our findings extend the capabilities of nonlinear wavefront shaping metasurfaces, exploiting phase manipulation to uncover unique phenomena exclusive to the nonlinear regime.