文章被PRA接收并发表。（PRA.100, 053840 (2019)）
Vectorial nonlinear optics refers to the investigation of optical processes whose nonlinear polarization (NP) undergoesspin-orbit coupling (SOC) interactions where, in general, the driving light field or the new field generated by the interaction contains the SOC property. To contribute to fundamental knowledge in this domain, we examine the type-II second-harmonic generation (SHG) induced by vectorial laser modes. First, we provide ageneral theory to analyze the vectorial SHG process. Second, by using two typical vector modes as examples, we show how the SOC of the pump field dictates nonlinear interaction. Finally, we corroborate our theoretical predictions through experiments to confirm the crucial role of the SOC in nonlinear interactions. These results enhance our fundamental understanding of SOC-mediated nonlinear optics and lay the foundation for further fundamental studies as well as possible applications.