This tutorial provides an overview of the local description of polarization for nonparaxial light, for which all Cartesian components of the electric field are significant. The polarization of light at each point is characterized by a three-component complex vector in the case of full polarization and by a 3 × 3 polarization matrix for partial polarization. Standard concepts for paraxial polarization such as the degree of polarization, the Stokes parameters, and the Poincaré sphere then have generalizations for nonparaxial light that are not unique and/or not trivial. This work aims to clarify some of these discrepancies, present some new concepts, and provide a framework that highlights the similarities and differences with the description for the paraxial regimes. Particular emphasis is placed on geometric interpretations.

中文翻译：

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非近轴光偏振的几何描述：教程

本教程概述了非近轴光偏振的局部描述，其中电场的所有笛卡尔分量都很重要。在全偏振的情况下，每个点处的光的偏振由三分量复矢量表征，在部分偏振的情况下由 3 × 3 偏振矩阵表征。近轴偏振的标准概念，如偏振度、斯托克斯参数和庞加莱球，然后对非近轴光进行了概括，这些概念不是唯一的和/或不是微不足道的。这项工作旨在澄清其中一些差异，提出一些新概念，并提供一个框架来突出与近轴区域描述的异同。特别强调几何解释。