Knots and links play a fundamental role across a wide range of physical fields, from classical to quantum physics. In optics, structured light fields with multiple controllable degrees of freedom provide a versatile experimental platform for investigating topological properties. Knot theory underpins the topological control of high-dimensional structured light, thereby giving rise to fundamental physical effects and applications. Furthermore, topologically structured light has attracted significant attention for light-matter interaction. Here we review the recent advances in topologically structured light from the perspective of knot theory. Starting from the basics of knots and related braids, we introduce the generation and manipulation of topologically structured light from the purely spatial domain across to the spatiotemporal domain. Moreover, we demonstrate that the particle-like structured light, such as photonic skyrmions and hopfions, can host the topologies of high dimensional space, followed by brief discussions on potential applications as well as an outlook and future trends and challenges in this field.

Spatiotemporal optical vortices (STOVs) possess helical phase singularities distributed jointly in space and time, enabling light to carry transverse orbital angular momentum and offering a fundamentally new degree of freedom for structured light. However, the precise detection of STOVs with fractional topological charges remains highly challenging, as conventional interferometric and diffraction-based techniques suffer from limited resolution and experimental complexity. Here we demonstrate a scattering-assisted detection scheme that enables ultra-high-precision measurement of STOVs with fractional topological charges. By exploiting the sensitivity of random scattering media to the spatiotemporal phase structure of broadband optical fields, we establish a robust mapping between scattered intensity patterns and fractional STOV states. This approach achieves reliable discrimination of fractional topological charges with step sizes down to 0.01, significantly surpassing the resolution of existing methods. Furthermore, we leverage this capability to realize a multi-level free-space optical communication scheme encoded by fractional STOV states, demonstrating enhanced channel capacity within a compact experimental configuration. This work introduces scattering media as a powerful platform for probing spatiotemporal phase singularities, and opens new opportunities for high-dimensional spatiotemporal photonics and optical communications.

Non-diffracting beams are typically confined to a limited set of specific profiles. Existing methods for diversifying these beams face challenges in achieving arbitrarily complex intensity distributions. In this paper, we present a phase engineering approach based on local spatial frequency mapping to construct novel non-diffracting beams. The proposed method facilitates the creation of customized intensity profiles by tailoring and splicing phase modulations in the Fourier domain, enabling the generation of intricate non-diffracting beams, such as those with a Tai Chi shape. We experimentally demonstrate the robust propagation invariance and self-healing capabilities of these novel non-diffracting beams. This approach provides a versatile means for designing structured non-diffracting fields, with potential applications in areas such as precision laser machining, optical trapping, free-space communication, and structured-light imaging.

Rare-earth-doped upconversion nanocrystals (UCNCs), with unique anti-Stokes emission, have been extensively explored, while their performances are hindered by the restriction of parity-forbidden 4f-4f transitions, making their emission difficult to control and resulting in low quantum yields. Current research primarily relies on modifying dopant types and concentrations, matrix composition, particle size, core-shell structures, and surface functional groups, to tune the absorption and emission transitions of 4f electrons. While these methods can effectively adjust emission spectra, reduce defects, and enhance luminescence efficiency, they cannot fundamentally regulate the 4f electron transition process, especially with respect to studying the intrinsic luminescence kinetics of rare earth ions. Therefore, a fundamental understanding of the transition behavior of 4f electrons and the ability to intrinsically control their absorption and emission processes are crucial. By manipulating the local optical field around UCNCs, micro-nano structures offer a powerful means to control their upconversion luminescence, making them an important tool for developing efficient optoelectronic devices for display, lighting, and conversion applications. In this review, we comprehensively expound on the optical engineering for UC luminescence control through micro/nano-optical structures. By utilizing structures such as plasmonic antennas, dielectric superstructures, high Q microcavities, and programmable wavefront shapers, precise control over the interaction between light and matter is achieved at multiple spatial scales. Moreover, we systematically analyze how such structures enhance local excitation fields, amplify spontaneous emission, and direct photon extraction, thereby transcending the inherent limitations of rare-earth emitters. By bridging advances in materials chemistry with nanophotonics design principles, this approach unlocks unprecedented control over UC efficiency, spectral purity, and polarization properties.

Structured light fields are engineered through precise control of their amplitude, phase, polarization, and spatiotemporal properties, which are extensively studied for both scientific and applied purposes, and can offer novel pathways for information processing, quantum communication, and precision measurement. Although the linear manipulation of structured light is already very mature with the help of liquid crystal devices and planar optical elements, nonlinear manipulation remains nascent, despite demonstrating unique potential for critical functionalities such as optical field information exchange. Hence, critical challenges now lie in harnessing nonlinear interactions, between light fields themselves and between light and matter, to achieve on-demand multidimensional control of target optical fields, particularly for spatial modes of light. The advancing nonlinear optics theory, guided by structured light, reveals novel physical phenomena in various nonlinear interactions, and promotes the development of novel applications based on nonlinear light field control technologies. Accordingly, this review systematically summarizes recent advances across key areas, including the nonlinear manipulation of spatial structured light fields, optical information transfer, full-dimensional manipulation theory, field modulation and nonlinear topological frontiers, and three-dimensional (3D) light field manipulation theory, thereby providing a comprehensive perspective on the current state and the emerging trends in this rapidly evolving field.

The development of surface-enhanced Raman scattering (SERS) technology is critically reliant on the effective modulation of the electromagnetic mechanism and chemical mechanism. In this paper, we conduct a systematic review of the recent advancements in the modulation of SERS by multi-physical fields (light field, magnetic field, and electric field) and their cooperative modulation. Light field modulation enhances the intensity and area of hotspots by optimizing the matching between the local surface plasmon resonance of nanostructures and the parameters of incident light (wavelength, polarization, and pulse). Moreover, the photo-induced plasmonic thermal effect dynamically regulates the phase transition between the nanogap and the material, achieving the synergistic enhancement of SERS. Magnetic field modulation capitalizes on the magnetic induction of magnetic materials and the magnetic resonance behavior of non-magnetic structures. It enables an external magnetic field to control the aggregation and spatial organization of nanoparticles, thereby generating high-density hotspots and enhancing the detection sensitivity and selectivity. Electric field modulation can adjust the band structure, carrier density, and molecular orientation of the substrate through an external electric field or the spontaneous electric field of functional materials (such as piezoelectric, triboelectric, thermoelectric, and pyroelectric materials), thus enhancing the charge transfer efficiency and the local electromagnetic field strength. The multi-field cooperative modulation strategy overcomes the static limitations of traditional SERS substrates and further provides a crucial theoretical and technical approach for realizing a high-performance, intelligent, and reconfigurable SERS sensing platform.

Twisted photonic lattices have recently emerged as a promising platform for opto-twistronics, enabling the exploration of moiré-induced photonic phenomena. Despite significant progress, the implications of non-Hermitian effects within these systems remain largely unexplored. In this work, we theoretically propose and experimentally demonstrate a non-Hermitian twisted photonic lattice with dynamically tunable gain-loss modulation, realized in a four-level atomic medium through the twisted superposition of two stripe fields. By adjusting the frequency detuning, a local flat band is introduced into the photonic band structure, leading to the directional localization of light in momentum space. The degree of localization can be further controlled by varying the laser power, while the direction of localization is reconfigured in real time by tuning the twist angle. Our work uncovers an intriguing interplay between non-Hermitian band reconstruction and geometric twisting by means of reconfigurable photonic lattice, and it provides a versatile platform for studying light manipulation in twisted configurations.

Optical vortices, characterized by their central singularities and spiral phase wavefront, have gained widespread attention in light manipulation and diverse applications. With their topological order being extended from integer to fraction, more unique properties have sprung out, such as continuous topological charges, fractional spiral-phase, expanded orbital angular momentum spectrum, and slit openings. These features have facilitated applications in areas such as optical tweezers, direction-selective edge enhancement imaging, robust rotational Doppler metrology, free-space communication, displacement sensing, and high-dimensional quantum entanglement. In recent years, advances in metasurface-based optical control, spatiotemporal pulse shaping, holographic imaging, and deep learning have spurred rapid innovation in the modeling, generation, and measurement of fractional vortex beams. This review begins with the fundamental theory of fractional vortex beams and surveys the latest developments in this rapidly evolving field. The scope of research has also expanded beyond optical vortices to include acoustic vortices. The growing interest in fractional vortex beams, coupled with ongoing technological innovations, is expected to pave the way for further advancements in this promising area of research.

Topology, a cornerstone of modern condensed matter physics, has in the past decade played a crucial role in diverse wave systems. As a powerful wave system, light can be sculpted into an even richer variety of topological structures, including vortices, skyrmions, Möbius strips, etc., leading to advanced photonic technologies from optical trapping to imaging, across quantum and classical regimes. A recent breakthrough demonstrated that topologically structured water waves can manipulate particles with intricate spin-orbital motion, and similar principles have enabled topological control in acoustofluidics, opening new insights in wave-matter interactions. Therefore, we argue that topological light waves possess an analogous potential, offering a route beyond the scalar-field limitations of conventional optical tweezers and establishing a new paradigm of multidimensional, vectorial control over matter. This article starts with brief introductions to optical tweezer technologies and topological light waves, then focuses on their emerging combination: particle trapping and sorting. It follows with perspectives on how topologies can couple to new degrees of freedom for manipulating complex particle motions previously inaccessible, and finally discusses potential applications.