Continuous control of the nonlinearity phase for harmonic generations



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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Figure 1: Illustration of geometric-phase-controlled nonlinear metamaterials.
Figure 2: Experimental verification of the nonlinear phase with nonlinear phase gratings.
Figure 3: Diffraction of the fundamental wave on metasurfaces with linear phase gradients.
Figure 4: THG signals from metasurfaces with a phase gradient of the nonlinearity.


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This work was partly supported by EPSRC (EP/J018473/1). T.Z. and S.Z. acknowledge financial support by the European Commission under the Marie Curie Career Integration Program. N.P., B.R. and T.Z. acknowledge the financial support by the DFG Research Center TRR142 ‘Tailored nonlinear photonics’. K.W.C. and E.Y.B.P. acknowledge the support by the Research Grant Council of Hong Kong under Projects HKUST2/CRF/11G and AoE/P-02/12. G.L. acknowledges support from the High Performance Cluster Computing Centre, Hong Kong Baptist University. S.Z. acknowledges financial support from the National Science Foundation of China (grant no. 61328503) and Leverhulme Trust (grant no. RPG-2012-674).

Author information




S.Z. and T.Z. conceived the idea and experiment. B.R., P.W.H.W. and E.Y.B.P. fabricated the samples. G.L., S.C., N.P., K.W.C. and T.Z. performed the measurements. S.C. performed the simulation. G.L., S.Z. and T.Z. wrote the paper. All authors participated in discussions.

Corresponding authors

Correspondence to Kok Wai Cheah or Thomas Zentgraf or Shuang Zhang.

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The authors declare no competing financial interests.

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Li, G., Chen, S., Pholchai, N. et al. Continuous control of the nonlinearity phase for harmonic generations. Nature Mater 14, 607–612 (2015).

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