Control of harmonic orbital angular momentum in second-harmonic generation of perfect vortices

Nonlinear interaction between orbital angular momentum (OAM) modes has interesting effects and tremendous applications in both classical and quantum realms. Here we propose a strategy of using perfect vortices, which not only overcomes the spatial mode matching problem of nondegenerate OAM modes, but also reveals the OAM-only influence on the momentum matching by tuning the OAMs of the fundamental wave. We use perfect vortices of degenerate and nondegenerate OAM modes to clearly demonstrate the flexible control of OAM modes on nonlinear interaction by carefully exploring second-harmonic generation (SHG) in periodically poled crystal. We generate second-harmonic perfect vortices with the OAM order up to 40. Based on the observed phase-matching temperature shift caused by OAMs, we also use the SHG nonlinear process to distinctly confirm the OAM-only-induced subluminal effect. Our results pave the way toward unveiling the underlying physics behind nonlinear process of OAM modes and building high-capacity quantum links between systems operating at various wavelengths. The inverse process of SHG we developed, perfect-vortex-based spontaneous parametric down-conversion, may provide a promising solution for high-dimensional OAM entangled source.