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Harmonic spin–orbit angular momentum cascade in nonlinear optical crystals



Optical angular momentum-based photonic technologies demonstrate the key role of the optical spin–orbit interaction that usually refers to linear optical processes in spatially engineered optical materials1. Re-examining the basics of nonlinear optics of homogeneous crystals under circularly polarized light2,3, we report experiments on the enrichment of the spin–orbit angular momentum spectrum of paraxial light. The demonstration is made within the framework of second-harmonic generation using a crystal with three-fold rotational symmetry. Four spin–orbit optical states for the second harmonic field are predicted from a single fundamental state owing to the interplay between linear spin–orbit coupling and nonlinear wave mixing; three of these states are experimentally verified. Besides representing a spin-controlled nonlinear route to orbital angular multiplexing4, modal vortex light sources5,6, high-dimensional parametric processes7 and multi-state optical magnetization8, our findings suggest that the fundamentals of nonlinear optics are worth revisiting through the prism of the spin–orbit interaction of light.

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Fig. 1: Spin-selective second-harmonic generation along the optical axis of a BBO crystal.
Fig. 2: Spin–orbit angular momentum cascade along the optical axis of a BBO crystal with weakly focused pumping light.
Fig. 3: Three-step description of the spin–orbit angular momentum cascade for the second-harmonic generation process.
Fig. 4: Spin–orbit tomography of the second-harmonic field for weakly focused pumping light.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors on reasonable request.


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G.L. is financially supported by the National Natural Science Foundation of China (grant numbers 91950114 and 11774145), a Guangdong Provincial Innovation and Entrepreneurship Project (2017ZT07C071) and the Qiu Shi Science & Technologies Foundation.

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Authors and Affiliations



E.B. and G.L. proposed the idea and designed the experiment. Y.T., K.L., J.D., X.Z. and G.L. conducted the nonlinear optical measurements. E.B., G.L., Y.T. and J.D. wrote the manuscript. All authors participated in the data analysis and discussions. G.L. and E.B. supervised the project.

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Correspondence to Guixin Li or Etienne Brasselet.

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Supplementary Figs. 1–21, Tables 1–8 and discussion.

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Tang, Y., Li, K., Zhang, X. et al. Harmonic spin–orbit angular momentum cascade in nonlinear optical crystals. Nat. Photonics 14, 658–662 (2020).

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