Within the last decades, laser light has advanced from the typical Gaussian beam to structured light fields, spatially varying in its amplitude, phase, and/or polarization beyond the Gaussian shape. In this case, continuously changing light field properties vary around its ‘skeleton’, formed by optical singularities—namely, points, lines, or surfaces in which specific properties of light are undefined. Although optical singularities even appear in natural sunlight, only recently all kinds of singularities, especially in polarization-structured light, have became experimentally accessible. This progress has decisively pushed research in this area, allowing for novel insights into the fundamental nature of singular light and establishing structured singular light as a key tool for advanced applications as high-dimensional quantum key distribution, to name only one. Though research has evolved rapidly from the study of scalar to vectorial, and paraxial to non-paraxial (tightly focused) structured fields, a concise overview on the implemented realizations and analysis approaches is still missing. In this tutorial, we introduce the fundamentals of structured light fields and optical singularities in the paraxial as well as non-paraxial regime, provide the tools for its analysis, and exemplify its customization by holographic approaches.

在过去的几十年里，激光已经从典型的高斯光束发展到结构化光场，其幅度、相位和/或偏振超出高斯形状的空间变化。在这种情况下，连续变化的光场属性围绕其“骨架”变化，由光学奇点形成——即光的特定属性未定义的点、线或表面。尽管光学奇点甚至出现在自然阳光中，但直到最近，各种奇点，尤其是偏振结构光中的奇点，才可以通过实验获得。这一进展决定性地推动了该领域的研究，使人们对奇异光的基本性质有了新的见解，并将结构化奇异光确立为高维量子密钥分布等高级应用的关键工具，仅举一例。尽管研究从标量研究到矢量研究，以及从近轴研究到非近轴（紧密聚焦）结构场的研究迅速发展，但仍然缺少对实现的实现和分析方法的简明概述。在本教程中，我们将介绍近轴和非近轴区域中结构光场和光学奇点的基础知识，提供其分析工具，并通过全息方法举例说明其定制。