Continuous phase control of second harmonic generation from metasurfaces composed of complementary split ring resonators

We demonstrate the realization of a continuous control over the phase change from zero to 2π for second harmonic generation (SHG) from the complementary split-ring resonators (CSRRs) by adjusting their geometrical parameters and reversing their orientations. We verify this concept by designing and fabricating nonlinear metasurfaces consisting of CSRRs with desired nonlinear phase profiles, which can bend and focus the SHG signals. The ability to provide a continuous and subwavelength phase control of the local second-order nonlinearities makes the CSRRs good candidates for applications, such as nonlinear holograms and integrated nonlinear nanophotonic elements that combine the coherent generation and manipulation of harmonic waves.