论文标题
几何和拓扑光子学
Geometry and Topological photonics
论文作者
论文摘要
拓扑光子学提供了一个有力的框架，可以描述和理解复杂电磁平台中许多非平凡波浪现象。物理系统的拓扑指数是一种抽象的全球属性，取决于描述Bloch波传播的操作员家族。在这里，我们强调说，拓扑物理学与数学表面拓扑理论之间存在着深远的几何联系。我们表明，拓扑结构理论可以理解为表面拓扑理论的概括，并且表面的属可以视为在表面上定义的合适操作员的Chern数量。我们指出拓扑问题在辐射问题的背景下对拓扑的某些非平地含义，并讨论了为什么拓扑指数通常与散装对应关系有关。
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on the family of operators that describes the propagation of Bloch waves. Here, we highlight that there is a profound geometrical connection between topological physics and the topological theory of mathematical surfaces. We show that topological band theory can be understood as a generalization of the topological theory of surfaces and that the genus of a surface can be regarded as a Chern number of a suitable operator defined over the surface. We point out some nontrivial implications of topology in the context of radiation problems and discuss why for physical problems the topological index is often associated with a bulk-edge correspondence.
