Topological solitons with topologically protected spin texture are of fundamental interest in exploring fascinating physical phenomena and nonlinear field theories.¹ In particular, numerous low-dimensional topological solitonic textures have been extensively studied in recent years, such as one-dimensional magnetic domain walls and magnetic skyrmions,^{2 – 4} as well as two-dimensional (2D) electromagnetic skyrmions,^{5 – 8} merons, and bimerons.^{9 – 11} Their sophisticated topological structures have been considered promising information carriers in the next generation of data storage and communication devices.^{12 – 15} 3D topological textures have also been attracting considerable interest in condensed matter physics and optics, and, following their theoretical introduction, extending the frontiers of topological field manipulation.^{13,16 – 18}

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.

Simultaneous manipulation of multiple degrees of freedom of light lies at the heart of photonics. Nonlinear wavefront shaping offers an exceptional way to achieve this goal by converting incident light into beams of new frequencies with spatially varied phase, amplitude, and angular momenta. Nevertheless, the reconfigurable control over structured light fields for advanced multimode nonlinear photonics remains a grand challenge. Here, we propose the concept of nonlinear geometric phase in an emerging ferroelectric nematic fluid, of which the second-order nonlinear susceptibility carries spin-dependent nonlinearity phase. A case study with photopatterned q-plates demonstrates the generation of second-harmonic optical vortices with spin-locked topological charges by using cascaded linear and nonlinear optical spin-orbit interactions. Furthermore, we present the dynamic tunability of second-harmonic structured light through temperature, electric field, and twisted elastic force. The proposed strategy opens new avenues for reconfigurable nonlinear photonics, with potential applications in optical communications, quantum computing, high-resolution imaging, etc.

Vectorial nonlinear optics refers to the investigation of optical processes whose nonlinear polarization (NP) undergoes spin-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 a general 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.

Exploring the physics and potential applications of vectorially structured light with propagation-invariant transverse structures has benefited many areas of modern optics and photonics. In this paper, we investigate the noneigenvector modes of paraxial light fields, focusing on the propagation variations and revivals of their transverse structures, including both spatial and polarization structures. We show that the physical mechanism behind the variations and revivals of their transverse structure is linked to the evolution of the intramodal phases between the constituting spatial modes. Such evolution originates from fractional Gouy phases, or rather, geometric-phase difference between spatial modes with different orders under a same unitary transformation. This underlying principle provides a general guideline for shaping vectorially structured light with custom propagation-evolution properties, and may also inspire a wide variety of new applications based on structured light.