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Vectorial nonlinear optics refers to the investigation of optical processeswhose nonlinear polarization (NP) undergoes spin-orbit coupling (SOC)interactions where, in general, the driving light field or the new fieldgenerated by the interaction containing the SOC property. To contribute tofundamental knowledge in this domain, we examine the type-II second harmonicgeneration (SHG) induced by vectorial laser modes. First, we provide a generaltheory to analyze the vectorial SHG process. Second, by using two typicalvector modes as examples, we show how the SOC of the pump field dictatesnonlinear interaction. Finally, we corroborate our theoretical predictionsthrough experiments to confirm the crucial role of the SOC in nonlinearinteractions. These results enhance our fundamental understanding ofSOC-mediated nonlinear optics and lay the foundation for further fundamentalstudies as well as possible applications.

Vectorial nonlinear optics: type-II second-harmonic generation driven by spin-orbit coupled fields