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.