光学体系中几何相位诱导的界面态的研究

With the development of topological states in electronic systems, people can use the geometric phase of the bulk band to study the existence of topological states. Recently, inspired by the topological states in electronic systems, the topological states in photonic systems, which are immune to impurities and disorders, have attracted much attention. It is known that interface states include topological states and non-topological states. The geometric phase of the bulk band can be also used to investigate the non-topological interface states. This extends the correspondence between the geometric phase of the bulk band and the interface states. The key points of this proposal are to find new topological states and reveal the new physical mechanism for the non-topological states. In this proposal, we will use the theoretical and numerical methods to study the geometric phase induced interface states in optical systems. This proposal includes three parts. In the first part, we will to study the non-topological interface states in photonic crystals at high frequency. At high frequency, the high order diffractions influence the surface impedance. We will reveal the relationship between the surface impedance and the geometric phase of the bulk band. In the second part, we will use the spatial symmetry to search the new topological and non-topological interface states in three-dimensional systems. In the last part, using the concept of non-local geometric phase, we will study the interface states in quasicrystal systems, and find the new physical mechanism. The implementation of this proposal will help us to understand the new physical mechanism of the interface states and to develop the low-loss and high-performance optical communication devices.

电子拓扑态的兴起，使得人们可以利用体能带的几何相位来研究拓扑态的存在性。受到电子拓扑态的启发，对不受杂质和无序影响的光学拓扑态的研究引起了广泛的关注。体系的界面态可以分为拓扑态和非拓扑态。体能带的几何相位同样可以用来研究非拓扑的界面态。这就拓展了体能带几何相位与界面态的对应关系。发现新型的拓扑态，揭示非拓扑界面态的新物理机理是本项目的研究重点。本项目拟采用解析、数值仿真的方法，开展光学体系中由几何相位诱导的界面态的研究。研究内容包括：（1）研究高频时光子晶体的非拓扑界面态，通过研究高频引起的高阶衍射对表面阻抗的影响，揭示表面阻抗与体能带几何相位之间的新对应关系；（2）利用三维体系的空间对称性，探索新型的拓扑与非拓扑界面态；（3）利用局域几何相位的概念来研究准晶，发现新的界面态物理机理。本项目的实施，将对界面态的物理机理有新的认识，对推动低损耗高性能的光通信器件的设计具有实际的应用价值。

伴随着电子体系和经典波体系中狄拉克点和外尔点的实验验证，经典波中由几何相位导致的拓扑态的研究引起人们的广泛兴趣。根据能带拓扑交点的维度，三维拓扑半金属可以分为点拓扑半金属和线拓扑半金属。点拓扑半金属是指其能带结构中能带相交于一点。典型的点拓扑半金属包括狄拉克半金属、外尔半金属。除了点拓扑半金属，线拓扑半金属则是指其能带结构中能带相交于一条线，根据能带构型的不同，如：环状线接触、链状线接触和嵌套的环状线接触，线拓扑半金属还可以分成不同的种类。谷态是指处在色散关系极值位置的模态。由于不同的谷态可以作为一个新的自由度来调控波的传播行为，因此，无论在凝聚态体系还是人工周期结构体系中，谷态的研究正引起越来越多的关注。鉴于经典波体系具有宏观的实际结构，加工和测量都比较容易，这为研究并发现新型的拓扑态提供了一个良好的平台，同时，经典波中拓扑态的研究存在诸多空白与不足。. 本项目主要研究内容包括：(a)通过打破空间反演不变性，实验验证声学外尔点的存在，及其连接不同手征性外尔点的费米弧和表面态的抗散射传输；(b)拓展了三角和蜂窝晶格中谷拓扑材料的概念，实现正方晶格中的声学谷拓扑材料，发现谷拓扑界面态的有趣传播行为，如：负折射和分流现象；(c)实现弹性波中谷拓扑边缘态，观测弹性波谷拓扑界面态的抗散射传输，实现界面态按不同比例分配能量的分流器；(d)通过对称性的设计，实现拓扑线声子晶体，实验证实鼓膜色散的表面态，验证了表面态抗干扰输运。. 在项目的资助下，项目负责人2018年8月参加了8th International Multidisciplinary Conference on Optofluidics (IMCO 2018)国际会议，并作邀请报告；2019年6月参加了Progress In Electromagnetics Research Symposium (PIERS)国际会议。取得的研究成果如下：以共同第一作者在Nature Physics上发表论文1篇，以第二、三、四、五作者在Nature Materials、Physical Review Applied、Nature Communications、Optics Letters和Acta Physica Sinica上发表论文各1篇。