电磁体系中几何位相及拓扑性质的研究

The novel topological properties of electromagnetic systems have attracted remarkable research interest in recent years. Many intriguing concepts in electronic systems, such as quantum-Hall-effect edge states and topological insulators, have been introduced to electromagnetic systems. Therefore, a new branch bridging topology and photonics named “topological photonics” emerges. It is worth considering whether there are some intrinsic or unique geometrical/topological properties in electromagnetic systems compared with those in electronic systems. A novel example is that a rigorous relation between the surface impedance of a one-dimensional photonic crystal and its bulk properties has been shown through the geometrical (Zak) phases of the bulk bands. Subtle links between Zak phases and topological phase transition are revealed. In general, there is a topological phase transition near the critical point in the parameter space where accidental degeneracies occur. In the periodic array of graphene layers, we have identified the accidental degeneracy of plasmon modes and photon modes. However, in order to investigate the interrelationship between accidental degeneracies and Zak phases, some crucial and fundamental questions are to be answered. In this proposal, we will study geometrical phases and possible associated topological properties starting from low dimensional systems. We will further investigate the accidental degeneracies and geometrical phases systematically in the long wavelength limit and under the approximation of non-local dielectric functions by introducing chiral or other materials with specific magneto-electric effects. Meanwhile, to observe the properties of geometric phases and topological excitations, “spoof” surface plasmon polaritons supported on comb-shaped ultrathin metal strips are employed. Experiments will be conducted in the microwave regime by adopting a near field scanning method. Our work may provide a new aspect to both fundamental researches and applications of topological properties which are unique and intrinsic in electromagnetic systems.

最近，电磁系统中的拓扑性质受到了国际学术界的广泛关注。量子霍尔效应边缘态、拓扑绝缘体等诸多电子系统中的概念都被引入电磁系统，形成了“拓扑光子学”。电磁系统中的拓扑相比电子系统有其独特之处。例如，最新研究发现一维光子晶体能带的几何位相（Zak位相）与阻抗有严格的关系。Zak位相与拓扑相变有很微妙的联系。一般来说，拓扑相变发生在参数空间偶然简并点处。在石墨烯周期阵列中，我们发现了等离激元和普通光学模式的偶然简并。但是，如何把它和Zak位相联系起来，还有很多重要的问题亟需解决。本项目拟从低维结构出发，研究其中的几何位相及伴随的拓扑性质。进一步在长波极限和非局域介电函数近似下，引入手性或有特殊磁电效应的材料，系统研究偶然简并和贝利位相的行为。我们将同时开展实验，研究人工表面等离激元中几何位相和拓扑元激发的性质。这些工作将为电磁系统中固有的拓扑性质的研究及应用开拓新的思路。

电磁和光学系统中的拓扑性质近几年受到了国际学术界的广泛关注，形成了“拓扑光子学”这一分支。电磁系统中的拓扑性质相比电子系统有其独特之处。针对电磁体系的特点，在本项目支持下，根据计划我们开展了四个方面的工作：(1) 在二维人工表面等离激元体系中，我们结合光子晶体和人工表面等离激元的特性，在国际上首次观测到了微波系统中的“能谷”偏振的拓扑边界态。这种“能谷”偏振和传播方向锁定，因此界面态的传播具有单向性。该文章发表于Nat. Commun. 8: 1304 (2017)，两年来该工作已被他引62次，被选为SCI高被引论文。(2) 在一维周期人工表面等离激元体系中，我们利用扫场方法研究了该体系拓扑界面态的场分布、局域长度和带隙的关系等等。该文发表于Opt. Lett. 41(16): 3698 (2016)，并被选为Editors' Pick。(3) 在一维周期性石墨烯阵列中，我们系统研究了Zak位相的随着波矢平行分量的演化性质，发现了在光子模式和表面等离激元模式的偶然简并点处，Zak位相会发生一个\pi的跳变。我们对由此导致的拓扑界面态的存在条件进行了分类。该文章发表于J. Opt. 19 06LT02 (2017)，并被选为Paper of the Week。(4) 我们对光子晶体中反对称模式的研究，导致新的研究方向——连续谱中的束缚态的开展。我们近来在平板光子晶体和周期性的表面等离激元体系都开展了连续谱中的束缚态的工作，取得较好的成果，发表论文Phys. Rev. B Rapid Commun. 98. 081405 (2018)和Phys. Rev. A 100. 023810 (2019).