Intrinsic Nonlinear Geometric Phase Driven By Nonlinear Tensor Rotations In Second-Harmonic Generation Processes

We show the intrinsic nonlinear geometric phase acquired by the SHG from AlGaAs film and metasurfaces which is fundamentally different from the one that has been so far observed in nonlinear dielectric, plasmonic, or hybrid metasurfaces. Our results illustrate that this phenomenon is completely transparent to the linear optical response at the pump and harmonic wavelengths, and it introduces a new unexplored richness of achievable phase functions. Furthermore, we explore the interplay between the intrinsic nonlinear geometric phase and the geometric phase induced by nanoresonator rotations. Our results expand the horizons of nonlinear wavefront shaping metasurfaces relying on phase manipulation with novel phenomena that are unique to the nonlinear regime.