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 light^2,3, 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 sources^5,6, 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.

基于光学角动量的光子技术证明了光学自旋-轨道相互作用的关键作用，这种相互作用通常是指空间工程光学材料中的线性光学过程¹。重新审视圆偏振光下均匀晶体的非线性光学基础^2,3，我们报告了近轴光自旋轨道角动量谱富集的实验。该演示是在二次谐波产生的框架内使用具有三重旋转对称性的晶体进行的。由于线性自旋轨道耦合和非线性波混合之间的相互作用，可以从一个基本状态预测出用于二次谐波场的四个自旋轨道光学状态。这些状态中的三个已通过实验验证。除了表示到轨道角度多路复用⁴的自旋控制非线性路径之外，模态涡旋光源^5,6，高维参数过程⁷和多态光磁化强度⁸，我们的发现表明，非线性光学的基本原理值得通过光的自旋轨道相互作用的棱镜进行回顾。