Efficient nonlinear wavefront shaping by dielectric metasurfaces

Dielectric metasurfaces provide a unique platform for efficient harmonic generation and optical wavefront manipulation at the nanoscale. Tailoring phase and amplitude of a nonlinearly generated wave with a high emission efficiency using resonance-based metasurfaces is a challenging task which often requires state-of-the-art numerical methods. Here, we propose a simple yet effective approach combining a sampling method with a Monte Carlo approach to design the third-harmonic wavefront generated by all-dielectric metasurfaces composed of elliptical silicon nanodisks. Using this approach, we demonstrate the full nonlinear $2\pi$ phase control with a uniform and highest possible amplitude allowing us to design metasurfaces operating as third harmonic beam deflectors capable of steering light into a desired direction with high emission efficiency. The high amplification of the third-harmonic intensity emitted at the first diffraction order by a factor up to $\sim 500$ is achieved as compared to the best results reported for silicon-based metasurfaces so far. We anticipate that the proposed approach will be widely applied as alternative to commonly used optimization algorithms with higher complexity and implementation effort for the design of metasurfaces with other holographic functionalities.