Nonlinear optical generation has been a well-established way to realize frequency conversion in nonlinear optics, whereas previous studies were just focusing on the scalar light fields. Here we report a concise yet efficient experiment to realize frequency conversion from vector fields to vector fields based on the vectorial nonlinear optical process, e.g., the second-harmonic generation. Our scheme is based on two cascading type-I phase-matching BBO crystals, whose fast axes are configured elaborately to be perpendicular to each other. Without loss of generality, we take the full Poincare beams as the vectorial light fields in our experiment, and visualize the structured features of vectorial second-harmonic fields by using Stokes polarimetry. The interesting doubling effect of polarization topological index, i.e., a low-order full Poincare beam is converted to a high-order one are demonstrated. However, polarization singularities of both C-points and L-lines are found to keep invariant during the SHG process. Our scheme can be straightforwardly generalized to other nonlinear optical effects. Our scheme can offer a deeper understanding on the interaction of vectorial light with media and may find important applications in optical imaging, optical communication and quantum information science.
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