Optical vortex arrays, with their unique wavefront structures, find extensive applications in fields such as optical communications, trapping, imaging, metrology, and quantum. The methods used to generate these vortex beam arrays are crucial for their applications. In this review, we begin with introducing the fundamental concepts of optical vortex beams. Subsequently, we present three methods for generating them, including diffractive optical elements, metasurfaces, and integrated optical devices. We then explore the applications of optical vortex beam arrays in five different domains. Finally, we conclude with a summary and outlook for the research on optical vortex beam arrays.

The high-power mode-programmable orbital angular momentum (OAM) beam has attracted significant attention in a wide range of applications, such as long-distance optical communication, nonlinear frequency conversion, and beam shaping. Coherent beam combining (CBC) of an optical phased array (OPA) can offer a promising solution for both generating the high-power OAM beam and rapidly switching the OAM modes. However, achieving real-time phase noise locking and formation of desired phase structures in a high-power CBC system faces significant challenges. Here, an internal phase-sensing technique was utilized to generate the high-power OAM beam, which effectively mitigated thermal effects and eliminated the need for large optical devices. An OPA with six elements was employed for experimental demonstration. The first effective generation of over 1.5 kW mode-programmable OAM beam in a continuous-wave domain was presented. Moreover, the results demonstrated that the generated OAM beam could be modulated with multiple dimensions. The topological charge can be switched in real time from -1 to -2. Notably, this OAM beam emitter could function as an OAM beam copier by easily transforming a single OAM beam into an OAM beam array. More importantly, a comprehensive analysis was conducted on power scaling, mode switching speed, and expansion of OAM modes. Additionally, the system’s compact design enabled it to function as a packageable OAM beam emitter. Owing to the advantages of having high power and programmable modes with multiple dimension modulation in phase structures and intensity distribution, this work can pave the way for producing high-power structured light beams and advancing their applications.

用空间光调制器模拟叉形光栅的方式产生高阶和分数阶涡旋光束，分离各阶涡旋光束并探究单级特性，探测其拓扑荷数以验证实验方法的正确性。设计了涡旋光束生成光路，编写了产生叉形光栅全息图的计算机程序，利用透射式空间光调制器模拟叉形光栅，以全息图的方式加载到空间光调制器上。调节参数改变全息光栅图样，得到拓扑荷数从1.0到100.0的整数阶与间隔为0.1的分数阶涡旋光束。利用孔径光阑分离出一级衍射，分析其特性并利用干涉法测量其拓扑荷数。实验发现，整数与分数阶光场分布与拓扑荷数为单调关系，拓扑荷数接近100时光束质量显著下降的特性，利用干涉法测得的拓扑荷数与计算全息图设置的参数完全相同。干涉测量结果验证了计算全息方法的正确性。该方法装置简易、参数可调，可为高阶和分数阶涡旋光的产生和应用提供一定的参考。

Hall effect of light is a result of symmetry breaking in spin and/or orbital angular momentum (OAM) possessing optical system and is caused by e.g. refractive index gradient/interface between media or focusing of a spatially asymmetrical beam, similar to the electric field breaking the symmetry in spin Hall effect for electrons. The angular momentum (AM) conservation law in the ensuing asymmetric system dictates redistribution of spin and orbital angular momentum, and is manifested in spin-orbit, orbit-orbit, and orbit-spin conversions and reorganization, i.e. spin-orbit and orbit-orbit interaction. This AM restructuring in turn requires shifts of the barycenter of the electric field of light. In the present study we show, both analytically and by numerical simulation, how different electric field components are displaced upon tight focusing of an asymmetric light beam having OAM and spin. The relation between field components shifts and the AM components shifts/redistribution is presented too. Moreover, we experimentally demonstrate, for the first time, to the best of our knowledge, the spin-orbit Hall effect of light upon tight focusing in free space. This is achieved using azopolymers as a media detecting longitudinal or z component of the electrical field of light. These findings elucidate the Hall effect of light and may broaden the spectrum of its applications.

We report the experimental and theoretical investigation of tilted spatiotemporal optical vortices with partial temporal coherence. The theoretical study shows that the instantaneous spatiotemporal optical vortex is widely variable with the statistical orbital angular momentum (OAM) direction. While decreasing temporal coherence results in a larger variability of OAM tilt, the average OAM direction is relatively unchanged.

完美涡旋（POV）光束具有光束半径与拓扑荷数无关的特点，与其他涡旋光束相比具有更加稳定的空间强度分布特性。利用多相位屏法和傅里叶变换法，分析了POV光束在大气湍流中的斜程传输特性。采用光束漂移和孔径平均闪烁指数作为大气湍流影响光束质量的评价参数，对比了POV光束与高斯涡旋光束在相同传输条件下的光束质量。结果表明：相比于高斯涡旋光束，POV光束的光束稳定性更好。当拓扑荷数增大或天顶角减小时，POV光束抵抗大气湍流的能力增强。在不改变POV光束拓扑荷数的前提下增大其光束半径，也能提高POV光束对大气湍流的抵抗能力。

A new type of power-exponent-phase vortex-like beams with both quadratic and cubic azimuthal phase gradients is investigated in this work. The intensity and orbital angular momentum (OAM) density distributions are noticeably different when the phase gradient increases or decreases along the azimuth angle, while the orthogonality and total OAM remain constant. The characteristics of the optical field undergo a significant change when the phase shifts from linear to nonlinear, with the variation of the power index having little impact on the beam characteristics under nonlinear phase conditions. These characteristics provide new ideas for applications such as particle manipulation, optical communications, and OAM encryption.

利用Debye积分，研究了三个相互正交的轨道角动量（包括两个正交的横向轨道角动量以及一个纵向轨道角动量）光场在紧聚焦条件下的复杂耦合现象，并演示了焦场中相位奇点在三维时空间中的演化。此外，还研究了具有不同拓扑荷数的纵向轨道角动量对聚焦波包整体轨道角动量指向的影响。数值结果表明，聚焦波包的整体轨道角动量指向可由纵向轨道角动量的拓扑荷数进行调控，进而实现紧聚焦时空波包的轨道角动量指向可控。这种角动量指向可控的时空波包在光学微操作、微纳加工、自旋-轨道耦合以及量子通信等领域具有潜在的应用价值。