Full complex-amplitude modulation of second harmonic generation with nonlinear metasurfaces

Metasurfaces have shown unprecedented capabilities and flexibilities for optical wave manipulation, which provide a powerful platform for the integration and minimization of multifunctional optical devices. However, the realization of the multidimensional manipulation of harmonic waves generated by nonlinear metasurfaces is still a challenge due to the lack of a theoretical guidance. Here, an efficient design strategy of nonlinear metasurfaces based on the hydrodynamic model of the free electron dynamics is demonstrated to realize the full complex-amplitude modulation of the second harmonic generation (SHG). As a proof concept, three multifunctional nonlinear metasurfaces are designed, in which both the amplitude and the phase of the SHG waves are efficiently and independently manipulated. With numerical and experimental validations, the proposed nonlinear metasurfaces can realize the spin-selective SHG optical vortices with independent topological charges. The design strategy of nonlinear metasurfaces shall boost the applications of nonlinear metasurfaces in optical information, optical multifunctional integration, and so on.