Coherent vortex structures are fascinating physical objects that are widespread in nature: from large scale atmospheric phenomena, such as tornadoes and the Great Red Spot of Jupiter to microscopic size topological defects in quantum physics and optics. Unlike classical vortex dynamics in fluids, optical vortices feature new interesting properties. For instance, novel discrete optical vortices can be generated in photonic lattices, leading to new physics. In nonlinear optical media, vortices can be treated as solitons with nontrivial characteristics currently studied under the emerging field of topological photonics. Parallel to theoretical advances, new areas of the engineering applications based on light vortices have emerged. Examples include the possibility of carrying information coded in the vortex orbital angular momentum, understood as a spatial-division-multiplexing scheme, to the creation of optical tweezers for efficient manipulation of small objects. This report presents an overview highlighting some of the recent advances in the field of optical vortices with special attention on discrete vortex systems and related numerical methods for modeling propagation in multi-core fibers.

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具有离散和连续旋转对称性的波导中的光涡流

相干涡旋结构是自然界中广泛存在的迷人物理对象：从大规模大气现象，如龙卷风和木星大红斑，到量子物理和光学中的微观拓扑缺陷。与流体中的经典涡流动力学不同，光学涡流具有新的有趣特性。例如，可以在光子晶格中产生新的离散光学涡流，从而产生新的物理学。在非线性光学介质中，涡流可以被视为具有非平凡特性的孤子，目前正在新兴的拓扑光子学领域进行研究。在理论进步的同时，出现了基于光涡流的工程应用的新领域。例子包括携带编码在涡旋轨道角动量中的信息的可能性，被理解为一种空间分割多路复用方案，用于创建用于有效操纵小物体的光镊。本报告概述了光学涡流领域的一些最新进展，特别关注离散涡流系统和相关的多芯光纤传播建模数值方法。