Polarization singularities, describing the points where the state of polarization is indeterminate, reveal the polarization topology in vectorial optical fields, which include two-/three-dimensional topologies such as C-points, V-points, L-lines, Möbius strips, links, and knots. Compared with the phase singularities, it has more parameters to manipulate, which bring forth a series of novel optical phenomena and potential applications. In this Perspective, the research progress and development of polarization singularities are reviewed from the mathematical description, generation, detection, propagation dynamics, and related applications. In particular, we focused on the three-dimensional spatial propagation and the topological characteristics of polarization singularities in detail and revealed some basic fundamental physical phenomena and the novel effects of polarization singularities. We aim to touch on the key research studies in this field and provide insight into the current status and the challenges to the research studies. Finally, we outline the exciting prospects for the future that are yet to be realized.

中文翻译：

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极化奇点：进展，基本物理学和前景

偏振奇异性描述了偏振状态不确定的点，揭示了矢量光学场中的偏振拓扑，其中包括二维/三维拓扑，例如C点，V点，L线，莫比乌斯带，链接和结。与相位奇异性相比，它具有更多的可操纵参数，带来了一系列新颖的光学现象和潜在的应用。本文从数学描述，产生，检测，传播动力学及相关应用等方面综述了极化奇异性的研究进展和发展。特别是，我们详细研究了极化奇点的三维空间传播和拓扑特征，并揭示了一些基本的基本物理现象和极化奇点的新颖影响。我们旨在接触该领域的关键研究，并提供有关研究现状和挑战的见解。最后，我们概述了尚未实现的令人兴奋的未来前景。