一维石墨烯光栅中的拓扑等离激元及其特性研究

Topological photonics, a new area of the application of general topology concepts in photonics, has been a focus of the photonics field in recent years. This is because specially designed topological photonic systems are able to create topologically protected optical states, which can propagate unidirectionally without any backscattering processes, even in the presence of disorder, defects, and impurities. When such systems are introduced to the field of plasmonics, the concept of topological photonics is then developed to the subwavelength scale. In this project, we propose to extend this concept to surface plasmon polaritons (SPPs) generated on the system of one-dimensional graphene gratings, and investigate in detail its topologically protected localized plasmonic edge states by means of combined rigorous theoretical analyses and advanced numerical simulations. To achieve this, we firstly create the so-called Su-Schrieffer-Heeger (SSH) model with the building blocks of graphene nanoribbons, calculate its plasmonic energy bands and the corresponding Zak phase with plasmon wave functions and Bloch theory, and further make sure the topologically trivial or nontrivial properties of the band structures. Then, by combining two SSH models with different topological invariants (Zak phases), we can construct new graphene gratings to create topologically protected plasmonic edge states, which will be further studied by exploring its field localizations, frequency stabilities, and topological robustness. Finally, the above concepts and methods will be applied to other 1D graphene gratings to further explore and exploit their general topological edge states and other alluring and novel optical properties. Our research extends the family of topological photonics to localized graphene plasmons and represents a simple and versatile platform to demonstrate novel topological concepts, offering a compacted theoretical guidance for designing a new generation of topologically protected graphene plasmonic devices.

拓扑光子学是拓扑学概念渗透到光学形成的一个全新领域，因其鲁棒边界态具有缺陷免疫、背散射抑制等优异特性，已发展成为光学领域的研究热点。当拓扑光子学发展到表面等离激元光学时，拓扑学概念也被引入亚波长尺寸范围。本项目希望把有关研究推广到一维石墨烯光栅结构体系中，通过理论分析与数值仿真相结合的方式探索其局域型表面等离激元拓扑边界态。主要内容包括：1，以石墨烯纳米带为基础建立SSH模型，通过表面等离激元波动方程和布洛赫理论等计算其能带结构和相应的Zak相位，并确定其拓扑平庸或非平庸；2，将拓扑不变量不同的两种纳米带光栅拼接形成新的光栅结构产生拓扑边界态，研究其模式局域性、频率稳定性和鲁棒性；3，将纳米带光栅的研究方法和思路扩展到其他一维石墨烯光栅结构，探索此类结构具有的拓扑边界态及光学新特性。本课题对丰富拓扑表面等离激元光学的内容具有重要意义，为开发新型石墨烯微纳结构光学器件打下理论基础。

由于受拓扑保护的模式具有缺陷免疫、背散射抑制等优异特性，使得拓扑光子学成为近年来光学领域的研究热点。本项目相关研究将拓扑光子学概念进一步扩展到一维石墨烯光栅结构体系中，并通过理论研究和数值仿真预测了其所支持的局域型表面等离激元拓扑边界态。本项目所取得的研究成果主要包括：1，研究了利用石墨烯纳米带建立的SSH模型及其拓扑性质，并分别利用拓扑平庸和非平庸的单元建立了SSH和镜面型m-SSH一维石墨烯纳米带光栅结构，发现在拓扑非平庸的纳米带光栅能带中分别存在两个处于带隙内的拓扑边界态和一个中间态，其能量主要局域在光栅两端和中间边界处，最后验证了拓扑模式的局域能量和频率的鲁棒性。2，研究了利用堆叠石墨烯纳米带构建的一维纳米带光栅结构及其拓扑属性，发现利用拓扑非平庸的SSH模型构建的体系存在两个能量局域在最顶层和最底层纳米带的拓扑表面态。3，研究了利用石墨烯纳米带构建的基于二维SSH模型的光栅结构，并利用二维Zak相位描述其拓扑属性，发现当SSH模型仅在x/y方向为拓扑非平庸时，二维体系仅在左右边界/上下层纳米带存在拓扑边界态/表面态，而当两个方向都是拓扑非平庸时，体系存在拓扑边界态、表面态和角态，并且对于具有Nx和Ny个结构单元的体系，三种模式数量分别为4(Ny-1)个、4(Nx-1)个和4个。本项目的研究内容丰富和完善了拓扑光子学的内涵，并将拓扑模式引入了石墨烯纳米带结构中，为设计受拓扑保护的纳米激光器、传感器和光开光等器件提供理论支持和指导。