Polarization singularities are superpositions of orbital angular momentum (OAM) states in orthogonal circular polarization basis. The intrinsic OAM of light beams arises due to the helical wavefronts of phase singularities. In phase singularities, circulating phase gradients and, in polarization singularities, circulating Stokes phase gradients are present. At the phase and polarization singularities, undefined quantities are the phase and Stokes phase, respectively. Conversion of circulating phase gradient into circulating Stokes phase gradient reveals the connection between phase (scalar) and polarization (vector) singularities. We demonstrate this by theoretically and experimentally generating polarization singularities using phase singularities. Furthermore, the relation between scalar fields and Stokes fields and the singularities in each of them is discussed. This paper is written as a tutorial-cum-review-type article keeping in mind the beginners and researchers in other areas, yet many of the concepts are given novel explanations by adopting different approaches from the available literature on this subject.

中文翻译：

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相位奇点到极化奇点

极化奇点是正交圆极化基础上的轨道角动量（OAM）状态的叠加。光束的固有OAM是由于相位奇异性的螺旋波前而产生的。在相位奇异点中，存在循环相位梯度，在极化奇异点中，存在循环斯托克斯相位梯度。在相位和极化奇点处，未定义的量是相位和斯托克斯相。循环相位梯度到循环斯托克斯相位梯度的转换揭示了相位（标量）和极化（矢量）奇点之间的联系。我们通过使用相位奇点在理论上和实验上产生极化奇点来证明这一点。此外，讨论了标量场与斯托克斯场之间的关系以及它们各自的奇异性。本文以兼顾辅导和评论的文章形式撰写，同时牢记其他领域的初学者和研究人员，然而，通过采用与该主题相关的现有文献中的不同方法，对许多概念进行了新颖的解释。