Harmonic spin-orbit angular momentum cascade in nonlinear optical crystals

An experimental study of the second-harmonic-generation process in a beta barium borate crystal shows that homogeneous optical crystals can exhibit the rich physics of the spin-orbit angular momentum cascade in the nonlinear optical regime. 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 materials(1). 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 multiplexing(4), modal vortex light sources(5,6), high-dimensional parametric processes(7)and multi-state optical magnetization(8), our findings suggest that the fundamentals of nonlinear optics are worth revisiting through the prism of the spin-orbit interaction of light.