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The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices.
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