Optical beams carrying orbital angular momentum (optical vortices) are sought for various applications, such as optical communications, optical trapping and manipulation, and material processing. Many of these applications involve the propagation of such beams; therefore, the knowledge of various aspects such as beam size and beam divergence, as well as the effect of beam obstruction, is required. In this paper, we present a numerical study on the generation of high-power discrete vortices by phase locking a 1D ring array of lasers in a degenerate cavity that involves spatial Fourier filtering with a specifically designed amplitude mask. Further, we show that, for a given system size (number of lasers) and fixed distance between the nearest-neighbor lasers, the size of a discrete vortex and its divergence upon propagation do not depend on the orbital angular momentum (topological charge), as opposed to a continuous vortex (Laguerre–Gaussian/Bessel–Gauss beams). We also investigate the self-healing of a discrete vortex by obstructing it at the waist plane ($z = 0$) as well as propagation plane ($z \gt 0$), and we show that a discrete vortex possesses good self-healing abilities. The propagation of a truncated discrete vortex has enabled us to identify an unknown topological charge and the rotation dynamics of intensity in a discrete vortex.

中文翻译：

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锁相激光器形成的离散涡流的发散和自愈

携带轨道角动量（光学涡流）的光束被用于各种应用，例如光通信、光捕获和操纵以及材料加工。其中许多应用涉及此类光束的传播；因此，需要了解光束尺寸和光束发散度等各个方面的知识，以及光束障碍的影响。在本文中，我们通过在简并腔中锁相一维激光环形阵列来生成高功率离散涡流，该研究涉及使用专门设计的幅度掩模进行空间傅立叶滤波。此外，我们表明，对于给定的系统尺寸（激光器数量）和最近邻激光器之间的固定距离，离散涡旋的大小及其传播发散不取决于轨道角动量（拓扑电荷），与连续涡旋（拉盖尔-高斯/贝塞尔-高斯光束）相反。我们还通过在腰部平面阻碍离散涡旋来研究它的自愈（$z = 0$）以及传播平面（$z \gt 0$），我们表明离散涡旋具有良好的自愈能力。截断离散涡旋的传播使我们能够识别未知的拓扑电荷和离散涡旋中强度的旋转动力学。