Dynamic tomography of the spin-orbit coupling in nonlinear optics

Spin-orbit coupling (SOC) light fields with spatially inhomogeneous polarization have attracted increasing research interest within the optical community. In particular, owing to their spin-dependent phase and spatial structures, many nonlinear optical phenomena which we have been familiar with up to now are being reexamined; hence there is a revival of research in nonlinear optics. To fully investigate this topic, knowledge on how the topological structure of the light field evolves is necessary, but, as yet, there are few studies that address the structural evolution of the light field. Here, we present a universal approach for theoretical tomographic treatment of the structural evolution of SOC light in nonlinear optics processes. Based on a Gedanken vector second-harmonic generation, a fine-grained slice of evolving SOC light in a nonlinear interaction and the following diffraction propagation are studied theoretically and verified experimentally, which at the same time reveal several interesting phenomena. The approach provides a useful tool for enhancing our capability to obtain a more nuanced understanding of vector nonlinear optics, and sets a foundation for further broad-based studies in nonlinear systems.