Conformal frequency conversion for arbitrary vectorial structured light

Vectorial structured light with spatially varying amplitude, phase, and polarization is reshaping many areas of modern optics, including nonlinear optics, as diverse parametric processes can be used to explore interactions between such complex vector fields, extending the frontiers of optics to new physical phenomena. However, the most basic nonlinear application (i.e., frequency conversion), still remains challenging for vectorial structured light since parametric processes are polarization dependent, leading to a change in the spatial topological structure of signals. In this work, to break this fundamental limit, we propose a conformal frequency conversion scheme that allows the full spatial structure of vectorial structured light to be maintained in the conversion. We systematically examine its spatial polarization independence based on nondegenerate sum-frequency generation with type-0 phase matching. This proof-of-principle demonstration paves the way for a wide range of applications that require conformal frequency conversion, and, particularly, to implement frequency interfaces with multimodal communications channels, high-dimensional quantum states, and polarization-resolved upconversion imaging.