论文标题
教程：拓扑，波和折射率
Tutorial: Topology, waves, and the refractive index
论文作者
论文摘要
本教程分为两个部分：第一个检查拓扑在波物理学中的问题。回顾了Chern数的起源，其中表明这计算了表面上复杂切线矢量场的临界点的数量。然后，我们表明，当计算任何线性系统中模式的分散体时，自然就会出现此数量，并给出了其应用的示例以找到一个线性 - 在连续材料和周期性材料中传播界面模式。 第二部分为Chern数字提供了物理解释，这是基于以下想法：它记录的关键点可以理解为折射率消失的点。使用晶体光学的理论，我们表明，当折射率沿复杂的有价值方向消失时，波浪仅在一种意义上被迫循环，这就是拓扑界面状态的单向传播的起源。我们结论说，可以将“零折射率”的这种概念用作捷径，以找到支持单向界面状态的声学和电磁材料。
This tutorial is divided into two parts: the first examines the application of topology to problems in wave physics. The origins of the Chern number are reviewed, where it is shown that this counts the number of critical points of a complex tangent vector field on the surface. We then show that this quantity arises naturally when calculating the dispersion of modes in any linear system, and give examples of its application to find one--way propagating interface modes in both continuous and periodic materials. The second part offers a physical interpretation for the Chern number, based on the idea that the critical points which it records can be understood as points where the refractive index vanishes. Using the theory of crystal optics, we show that when the refractive index vanishes in a complex valued direction, the wave is forced to circulate in only one sense, and this is the origin of the one-way propagation of topological interface states. We conclude by demonstrating that this idea of `zero refractive index in a complex direction' can be used as a shortcut to find acoustic and electromagnetic materials supporting one-way interface states.
