Pancharatnam-Berry metasurfaces with giant nonlinear response

We show that a generalization of the Pancharatnam-Berry phase approach can be applied to realize metasurfaces with giant nonlinear response, enabling a unique control of the generated nonlinear wavefront. We apply this approach to design and realize a nonlinear metasurface for efficient second-harmonic generation, which may independently tailor the radiated beam into right-handed and left-handed polarized components propagating with arbitrarily patterned wavefronts.