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This paper explores the interplay of momentum transfer and nonlinear optical processes through moir\'e phenomena. Momentum transfer plays a crucial role in the interaction between photons and matter. Here, we study stacked metasurfaces with tailored dispersion and rotated against each other with varying twisted angles. The stacking introduces interlayer interactions, which can be controlled by the relative angle between metasurfaces, significantly enriching the resulting response compared to the single layer counterpart. By focusing on second-harmonic generation (SHG) from these twisted metasurfaces, we delve into the realm of nonlinear moir\'e photonics. Through experimental observations, we unveil the emergence of intricate far-field SHG radiation patterns, showing their effective tuning by varying the twisted angles. These findings offer a fresh perspective to explore nonlinear wavefront shaping through moir\'e phenomena, opening new avenues for nonlinear information processing, optical steering, and nonlinear optical switching.
Qu et al. (Thu,) studied this question.