全息约束的偏振变换
Holonomically constrained polarization transformation
AI总结：
本文提出在拓扑构造上定义全息约束偏振变换，分析光束、元件和球体拓扑参数需满足的条件，并据此为偏振光学引入拓扑指数空间。
摘要：
在偏振光学中，各种拓扑构造，即不同阶的庞加莱球，被用来表示均匀和结构化的偏振分布。类似地，也存在结构化的偏振光学元件。因此，针对结构化光束和元件定义了各种拓扑指数。这些拓扑特性自然地使我们能够基于全息对偏振变换进行分类。本文在拓扑构造上引入了全息约束的偏振变换。详细讨论了光束、元件和球体的拓扑参数为实现全息约束偏振变换所需满足的条件。对全息系统进行拓扑处理是必要的，因为文献中报道的大量关于结构化偏振光束的偏振变换是非全息的。开展这项研究是审慎的，因为不能假设在全息变换与非全息变换之间切换不会影响系统输出。本文展示了这些概念如何使我们能够为偏振光学引入拓扑指数空间。
英文摘要：
In polarization optics, various topological constructs, namely Poincaré spheres of different orders, are used to represent uniform and structured polarization distributions. Similarly, there are also structured polarization optical elements. Consequently, various topological indices are defined for structured beams and elements. These topological aspects naturally allow us to holonomy-based categorization of polarization transformations. In this paper, we introduce holonomically constrained polarization transformations on topological constructs. The conditions on the topological parameters of the beams, elements and spheres to achieve holonomically constrained polarization transformations are discussed in detail. A topological treatment of holonomic systems is needed, since abundant polarization transformations reported in the literature on beams with structured polarization are nonholonomic. It is prudent to carry out this study since it can not be assumed that switching between holonomic and nonholonomic transformations does not affect the system output. It is shown here how these concepts enable us to introduce topological index spaces for polarization optics.
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