Due to their unique field distribution properties, vectorial optical fields have been extensively researched and applied across various domains. However, traditional methods for controlling optical fields are limited by material properties and physical dimensions, which restrict flexible and efficient dynamic manipulation capabilities. In contrast, metasurfaces overcome these constraints with subwavelength structural designs that provide additional degrees of freedom for independent control over attributes such as amplitude, phase, polarization, and propagation direction of vectorial optical fields. This paper systematically combines foundational theories with recent advancements in domestic and international research on vectorial optical fields to elucidate the fundamental principles and mathematical models underlying them. It particularly focuses on current methodologies using metasurfaces to generate vectorial optical fields, along with specific case studies and innovative outcomes in applications including focusing, orbital angular momentum detection, and high-precision positioning.

In recent years, terahertz waves have garnered significant attention due to their unique properties. Among them, terahertz vector beams with different polarization characteristics exhibit novel spatial distributions and show increasingly broad prospects for applications. This review explores the generation methods of terahertz vector beams, their applications in various fields, and future development directions. Firstly, the methods for generating terahertz vector beams are systematically classified, and the research progress in terahertz vector beam generation is introduced. The principles of these methods and the characteristics of the generated vector beams are elaborated in detail. In addition, typical applications using terahertz vector beams are summarized. Lastly, the challenges and possibilities of terahertz vector field manipulation using different devices are prospected. The review aims to provide a comprehensive understanding of the generation and application of terahertz vector beams and offer guidance for future related research and development.

Structured beams manipulated by single or multiple degrees of freedom (DoFs) present novel physical properties, showing important research significance and practical value. Among them, orbital angular momentum (OAM), as a novel DoF, directly decides the phase and spatial distribution of laser beams. The independent manipulation of OAM or the coupled manipulation with spin angular momentum enables the construction of high-dimensional Hilbert space, which has already found broad applications in domains like ultra-large capacity optical communication, remote sensing detection and quantum communication. On this basis, considering the rapidly evolving application requirements, there is still a significant challenge to integrate the novel degrees of freedom with the traditional degrees of freedom, limiting the extension and expansion of high-dimensional and multi-dimensional structured beams. In this paper, from the perspective of two-degree-of-freedom manipulation methods, a series of structured beams coupled by two intrinsic DoFs is reviewed with emphasis on the vectorial vortex beams. Furthermore, we systematically review the manipulation of complex structured beams with multiple degrees of freedom that overcome the limitations of conventional two-degree-of-freedom. Also, the related work of our team is discussed here.

Holography, which can record and reconstruct all the information of object light waves, has made remarkable progress since its invention. In recent years, the emergence of vectorial holography has brought new developments to this field. Vectorial holography not only inherits the ability to record the amplitude and phase of traditional scalar holography but also introduces the additional control of the polarization dimension, which can significantly improve the density of the recorded information and has been widely used in many fields. This paper discusses vectorial holography in depth from the perspective of polarization modulation. Firstly, the concepts of scalar holography and vectorial holography are introduced, and their advantages and disadvantages are compared. Then, the two polarization modulation methods of vectorial holography are introduced in detail, including the polarization modulation of incident light and output light. Meanwhile, the applications of vectorial holography in the field of 3D display and encryption are described. Finally, the challenges faced by vectorial holography are summarized, and the future development of vectorial holography is expected.

In the past two decades, numerous significant advances have been achieved in the realm of the vector beams. Considering numerous published reviews already covering diverse topics in terms of generating and/or manipulating unprecedented vector beams, we summarize the typical applications of vector vortex beams in the topics of laser micro-nano processing for material modification, subtractive and additive manufactures. This paper reviews part of the critical advances in fabricating micro-nano structures on the surface and inside the materials, optical information storage and rapid fabrication of microstructures with the stereolithography based-on vector vortex beams. Particular cares are focused on the principles and technologies in applications of patterned laser-induced periodic surface structures and rapid two-photon polymerization of three-dimensional microstructures based on customized vector vortex beams. Finally, we summarize the advantages and challenges of vector vortex beams in laser micro-nano processing, and we also anticipate that more vector light fields will enable more complex applications in the future.

Polarization, as one of the basic characteristics of light, is widely utilized in communication, imaging, optical encryption, and other fields. However, traditional polarization devices face numerous problems such as large size and low integration. Due to their unique light field manipulation mechanisms, subwavelength-scale metasurfaces offer innovative solutions for miniaturization and cost reduction of polarization devices. This paper reviews recent advances in metasurface-based polarization devices and fabrication techniques. Starting from the phase manipulation mechanisms of metasurfaces, the article briefly introduces methods for controlling the transmission phase, geometric phase, generalized geometric phase, and resonance phase. The focus is summarizing various metasurface polarization devices and their fabrication, including polarization conversion, polarization beam splitting, vector vortex beam generators, high-order Poincaré sphere optical encryption, polarization multi-channel holography, and polarization detection. Finally, we discuss potential development trends and application prospects in this field.

The vector light field carrying angular momentum finds wide applications in various fields, such as particle manipulation, optical communication and display, optical information encryption, and high-dimensional quantum information processing. However, the conventional approach to vector light field regulation typically involves a series of cascaded optical elements, such as spiral phase plates, polarizers, quarter wave plates, vortex wave plates, spatial light modulators, etc., resulting in a bulky device that does not meet the requirements for future photonic device integration. The rapid development of metasurfaces offers a transformative solution for realizing integrated meta-devices for vector light field control. In this paper, we summarize the research progress on metasurface-based control and detection of vector light fields. Then, we systematically summarize the current applications of metasurface-based vector light fields in particle manipulation, edge enhancement imaging, holographic display, machine vision, and so on. Finally, we have summarized and discussed the full text as well as the challenges and provided an outlook on this emerging field.

Vector optical field, which have arbitrarily designed wavefronts and polarization state distributions, have attracted widespread attention from scientists over the word due to their high multiplexing dimensions, strong tight focusing ability, flexible light field manipulation capability, and chirality selection. Compared with uniform scalar fields, they have greater control freedom and broader application prospects. Nowadays, the rapid development of micro-nano optics provides new opportunities for expanding the freedom, dimensions, and scales of vector optical field manipulation. The special issue on vector optical field manipulation in 2024 has received 10 manuscripts, including 7 review articles and 3 original articles. It aims to showcase the important research progress and achievements in vector optical field manipulation over recent years, allowing readers to have a deeper understanding of the current status, trends, and application prospects of vector optical field research, and also providing helpful assistance to researchers in related fields.

When a vector optical field acts on the metasurface-based diffractive light sail, the maximum acceleration, self-stabilizing thrust, and attitude controllability of the diffractive light sail can be enhanced. In a vacuum environment, it is important to measure the optical force acting on the diffraction light sail to establish a comprehensive space dynamics model under the influence of vector optical fields. Based on the weak force measurement technique, we have designed an optical force measurement torsion pendulum for both regular and irregular shaped diffraction light sails. The measurement accuracy of regular-shaped light sails can be enhanced by ensuring that the size of the torsion pendulum and relative position errors of each component are strictly controlled. The force measurement has a relative error of 0.55‰. We have also designed a torsion pendulum to measure the optical force of the irregular-shaped light sails, which can hardly calculate the moment of inertia. There are two standard spheres on the torsion pendulum that can be placed or removed at any time. The magnitude of the optical force acting on the complex object can be measured by calculating the moment of inertia of the spheres. This research enhances the efficiency and flexibility of optical force measurement experiments, providing data support for applications such as laser-driven light sail and space debris remediation.

LiDAR currently mainly uses a Dammann grating as the laser beamsplitter. However, as a periodic diffraction optical device, the Dammann grating satisfies the grating equation requiring each diffraction angle's sine value to form an arithmetic progression, which cannot achieve uniform angular beam-splitting. The theoretical diffraction efficiency is also limited. This paper uses the angular spectrum and random search optimization algorithm to design a more flexible non-periodic beamsplitter. Simulations show that the metasurface beamsplitter can achieve a 70-degree field angle of 41 beams with an equal diffraction angle interval. The simulated diffraction efficiency reaches 84% which is higher than the diffraction limit of a binary phase device. In experiments, the metasurface beamsplitter has good beam-splitting uniformity and can promote the development of LiDAR.

When designing metasurface systems, the actual efficiency of the metasurface is much different from the theoretical design efficiency. This can lead to stray light caused by insufficient modulation efficiency of the metasurfaces, which acts as background noise and is magnified in cascaded metasurface systems step by step, affecting system functionality. To reduce the impact of metasurfaces with limited efficiency on system performance, this paper proposes a design method for an orbital angular momentum demultiplexing system based on off-axis cascaded metasurfaces. By incorporating an off-axis phase design, the stray light generated by the reduced efficiency of the metasurface in a cascaded metasurface system is effectively eliminated. Using FDTD (finite difference time domain) simulation software for calculation and validation, the results demonstrate that the off-axis cascaded metasurface system can effectively reduce stray light caused by insufficient modulation efficiency. Compared to the on-axis system, it achieves a maximum reduction in crosstalk of 4.15 dB and an average of 80% stray light elimination, showing a significant performance advantage.