非厄米光子晶体中拓扑态的理论与实验研究

The information age is enabled by optics, which involves the generation, transmission and detection of light. Exploring a new way to control the flow of light becomes one of the hot research frontiers. Photonic crystal is one type of man-made subwavelength structure with spatial modulated refractive index. Band topological features is recently a new degree of freedom attracting much attention, which gives rise to many novel phenomena such as robust transport of light. Most of the current studies on topological states focus on the Hermitian case without absorption loss. However, most materials have loss more or less and the Hermitian eigenvalue problem is at best an approximation. We proposed to study the influence of non-Hermiticity on the topologically protected transport of light, and explore the new topological phase in non-Hermitian system, including the topological states of non-Hermitian photonic crystals in PT exact phase or PT broken phase and the associated new optical phenomena. On the other hand, most topological phases are derived from the band singularity point, such as 2D Dirac point and 3D Weyl point. Exceptional point is one type of band singularity points which are unique to non-Hermitian systems. We will lift this degeneracy by breaking different symmetries and study the associated topological states. By introducing loss and gain (the imaginary part of refractive index), we will find a new way to manipulate optical field. In addition, optical wave is a good platform to study non-Hermitian physics, our research will have important guiding significance to the non-Hermitian studies in other systems.

光学成就了现今的光信息时代，包括光信号的产生、传输和探测。探索调控光场的新方法，已成为国际上热门的前沿课题。光子晶体是折射率周期调制的亚波长结构，能带的拓扑性质是近年关注的一个新的自由度，它是本征向量的性质，继而实现光抗散射等新奇现象。目前拓扑态研究大多考虑无吸收损耗的厄米体系，然而光学材料或多或少都有吸收，厄米本征值问题只是一个近似。我们将研究厄米性的引入令拓扑保护的光传输带来的影响，探索非厄米体系中新的拓扑相，包括处于PT对称相、破缺相的光子晶体的拓扑态及其相关新光学现象。另一方面，拓扑态的发现多源于能带中本征值简并的奇点，如二维狄拉克点和三维外尔点。奇异点是非厄米体系所独有的一类奇点，我们将通过打破不同对称性打开简并，研究与奇异点相关的拓扑态。通过引入增益损耗（折射率虚部），我们将发现光场调控的新机制、新方法，同时，光波是研究非厄米物理很好的平台，对其他系统的非厄米研究具有指导意义。

项目负责人陈文杰教授围绕非厄米拓扑光学的基础物理等科学问题，以超构材料光学为方向，基于光子晶体等人工亚波长光学结构，研究了PT系统中动量带隙的拓扑性质，在非厄米光子晶体中实现了拓扑保护的时间边缘态。总结了拓扑光学设计新方法，拓宽了光传输/光局域等新型光学行为，解决了高维拓扑态应用到微纳光学器件的难题。本项目已按计划执行，完成了全部的研究目标，具体包括：（1）科学内容层面。研究了光脉冲信号在非厄米拓扑能谷光子晶体波导中的无畸变抗散射传输特性，还进一步研究了基于晶格平移引入的四维合成维度空间中的PT对称拓扑态。研究了一维PT对称光子晶体中动量带隙的拓扑性质及其受拓扑保护的瞬态边缘态，还研究了PT对称破缺系统中奇异链的演化规律及其背后的物理机制。我们在能谷光子中研究了奇异点与拓扑相间的联系，并撰写了能谷光子晶体综述文章，利用三维金属超材料的低频色散模型研究了奇异点的拓扑性质，进而提出一维非厄米光子晶体中的三维奇异环及其拓扑界面态。（2）研究成果层面。在本项目的支持下，项目负责人陈文杰教授获得国家千人计划项目的资助，过去4年发表SCI论文15篇，包括Nature Communications, Physical Review Letters、Physical Review Applied、Light: Sciences & Applications、National Science Review、Nanophotonics和Advanced Optical Materials等。项目执行期间，负责人董建文教授受邀完成了4个邀请报告，并在多个会议上作口头报告。同时，协助举办了2019粤港澳超构材料与微纳光学应用专题研讨会。培养已毕业硕士研究生2名。