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.

The discovery of optical transverse orbital angular momentum (OAM) has broadened our understanding of light and is expected to promote optics and other physics. However, some fundamental questions concerning the nature of such OAM remain, particularly whether they can survive from observed mode degradation and hold OAM values higher than 1. Here, we show that the strong degradation actually origins from inappropriate time-delayedk_x–ωmodulation, instead, for transverse OAM having inherent space-time coupling, immediate modulation is necessary. Thus, using immediatex–ωmodulation, we demonstrate theoretically and experimentally degradation-free spatiotemporal Bessel (STB) vortices with transverse OAM even beyond 10². Remarkably, we observe a time-symmetrical evolution, verifying pure time diffraction on transverse OAM beams. More importantly, we quantify such nontrivial evolution as an intrinsic dispersion factor, opening the door towards time diffraction-free STB vortices via dispersion engineering. Our results may find analogues in other physical systems, such as surface plasmon-polaritons, superfluids, and Bose-Einstein condensates.

Providing additional degrees of freedom to manipulate light, spatiotemporal optical vortex (STOV) beams carrying transverse orbital angular momentum are of fundamental importance for spatiotemporal control of light-matter interactions. Unfortunately, existing methods to generate STOV are plagued by various limitations such as inefficiency, bulkiness, and complexity. Here, we theoretically propose and experimentally demonstrate a microscale singlet platform composed of a slanted nanograting to generate STOV. Leveraging the intrinsic topological singularity induced by C₂ symmetry and z-mirror symmetry breaking of the slanted nanograting, STOV is generated through the Fourier transform of the spiral phase in the momentum-frequency space to the spatiotemporal domain. In experiments, we observe the space-time evolution of STOV carried by femtosecond pulses using a time-resolved interferometry technique and achieve a generation efficiency exceeding 40%. Our work sheds light on a compact and versatile platform for light pulse shaping, and paves the way towards a fully integrated system for spatiotemporal light manipulation.

Planar optical elements incorporating space-varying Pancharatnam-Berry phase have revolutionized the manipulation of light fields by enabling continuous control over amplitude, phase, and polarization. While previous research focusing on linear functionalities using apolar liquid crystals (LCs) has attracted much attention, extending this concept to the nonlinear regime offers unprecedented opportunities for advanced optical processing. Here, we demonstrate the reconfigurable nonlinear Pancharatnam-Berry LC diffractive optics in photopatterned ion-doped ferroelectric nematics. By customizing the spatial phase distribution of efficient second-harmonic excitation, we accomplish programmable beam steering of various optical states towards predefined diffraction directions. Experimental results reveal continuous evolution of diffraction orders, intensity distributions, and polarization states under electrically varying splay conditions, consistent with our theoretical predictions. This work opens new avenues for designing reconfigurable nonlinear beam shaping and steering devices with potential applications in advanced optical and quantum information processing.

In this Letter, we explore the intersection of chirality and recently discovered toroidal spatiotemporal optical vortices (STOVs). We introduce “photonic conchs” theoretically as a new type of toroidal-like state exhibiting geometrical chirality, and experimentally observe these wave packets with controllable topological charges. Unlike toroidal STOVs, photonic conchs exhibit unique chirality-related dynamical evolution in free space and possess an orbital angular momentum correlated with all the dimensions of space-time. This research deepens our understanding of toroidal light states and potentially advances various fields by unveiling similar wave phenomena in a broader scope of physics systems, including acoustics and electronics.

Spatiotemporal (ST) beams—ultrafast optical wavepackets with customized spatial and temporal characteristics—present a significant contrast to conventional spatial-structured light and hold the potential to revolutionize our understanding and manipulation of light. However, progress in ST beam research has been constrained by the absence of a universal framework for its analysis and generation. Here, we introduce the concept of ‘two-dimensional space-time duality’, establishing a foundational duality between spatial-structured light and ST beams. We show that breaking the exact balance between paraxial diffraction and narrow-band dispersion is crucial for guiding the dynamics of ST wavepackets. Leveraging this insight, we pioneer a versatile complex-amplitude modulation strategy, enabling the precise crafting of ST beams with an exceptional fidelity exceeding 97%. Furthermore, we uncover a new range of ST wavepackets by harnessing the exact one-to-one relationship between scalar spatial-structured light and ST beams. Our results expand the toolkit for ST beam research and hold promise for applications across a diverse spectrum of wave-based physical systems.