论文标题
基于2D微孔晶格的N波段光子HOPF绝缘子
N-Band Photonic Hopf Insulators Based on 2D Microring Lattices
论文作者
论文摘要
HOPF绝缘子是拓扑绝缘子，其拓扑行为是由从3D球到2D球体（称为HOPF地图）的非平凡映射引起的。通常在旋转和天际系统研究中遇到的HOPF地图是由称为HOPF索引的整数不变式对拓扑分类的。在这里，我们表明，由于每个微林内部的光周期性循环，微型谐振器的2D晶格可以模仿具有非平凡HOPF索引的$ n $ band Photonon Hopf绝缘子。特别是，我们通过数值计算和直接的分析证明表明，$ n $ band Hopf索引与绕线数相同。结果表明，HOPF指数是分类2D微林光子晶格的替代拓扑不变，并在Hopf绝缘体相和晶格的异常浮子绝缘体相之间建立对应关系。更普遍的是，我们的工作表明，2D微林格晶格可以为研究非亚洲拓扑光子系统提供多功能的纳米光子平台。
Hopf insulators are topological insulators whose topological behavior arises from the nontrivial mapping from a 3D sphere to a 2D sphere, known as the Hopf map. The Hopf map, typically encountered in the study of spinor and skyrmion systems, is classified topologically by an integer invariant called the Hopf index. Here we show that due to the periodic circulation of light inside each microring, a 2D lattice of microring resonators can emulate an $N$-band photonic Hopf insulator with nontrivial Hopf index. In particular, we show by numerical computation and direct analytical proof that the $N$-band Hopf index of the microring lattice is identical to its winding number. The result shows that the Hopf index is an alternative topological invariant for classifying 2D microring photonic lattices and establishes a correspondence between the Hopf insulator phase and the anomalous Floquet insulator phase of the lattice. More generally, our work shows that 2D microring lattices can provide a versatile nanophotonic platform for studying non-Abelian topological photonic systems.
