Exploring topological physics with photonics

长期以来，凝聚态物理和光学一直是相互补充新思想和新技术的领域。最近这种协同效应的一个例子来自拓扑物理。在适当的条件下，周期系统可以用倒易空间中的一个非平凡拓扑不变量来刻画(如果系统的能带结构光滑变形，这个量不变)。这导致了具有非常有趣的性质的态的出现，例如存在于大块晶体边界的那些态。这些州受到保护，不会出现混乱。最近在发现具有拓扑行为的材料方面取得的重要进展为阐明其性质和开发其应用提供了令人兴奋的机会。拓扑材料仅限于自然产生的晶格，不容易修改。此外，大多数材料是三维的，因此一维和二维拓扑物理的实验研究是具有挑战性的。幸运的是，有可能构建出表现出拓扑行为的光学系统。光学系统提供了设计任意周期晶格的自由，以及非常容易进行的实验，这些实验可以用来研究拓扑物理中的问题。用光子研究拓扑物理将提供新的见解，其中一些将直接适用于电子系统，继续光学和凝聚态物理之间新思想的交叉授粉。从应用的角度来看，增加对拓扑光子学的理解将有助于设计不受制造缺陷影响的光子器件。我的研究计划的长期目标是利用光学技术开发通用的实验平台，以研究具有拓扑特征的一维和二维系统。利用这些平台，我们将对材料中难以研究的拓扑物理问题进行实验探索。在这一框架下的主要短期项目是：(I)具有边缘状态的一维拓扑结构的设计、制造和表征，(Ii)研究2D拓扑光子绝缘体中边缘状态下的光传输，以及(Iii)利用拓扑性质来开发在不完美结构中操纵光的方法。这里提出的研究在拓扑光子学方面的预期进展将有两方面的好处：(I)更好地理解晶格系统(本质上与凝聚态物理相关的系统)的物理，以及(Ii)将设计出对制造缺陷具有健壮性的新的光子器件。值得注意的是，(I)也可以在微波条件下研究，但(Ii)需要在近红外或可见光下工作。我们建议的平台将允许使用标准电信或可见光激光直接探索一维和二维的拓扑现象。

Condensed matter physics and optics have long been fields that feed each other with new ideas and techniques. A recent example of this synergy comes from topological physics. Under the right conditions, periodic systems can be characterized by a non-trivial topological invariant in reciprocal space (a quantity that does not change if the band structure of the system is smoothly deformed). This leads to the appearance of states with very interesting properties, such as those existing at the boundaries of bulk crystals. These states are protected against disorder. Important recent advances in discovering materials that display topological behaviour provide exciting opportunities to elucidate their properties and exploit their applications. Topological materials are restricted to naturally occurring crystal lattices, which cannot be easily modified. In addition, most materials are three-dimensional, so the experimental study of topological physics in 1D and 2D is challenging. Fortunately, it is possible to construct optical systems that show topological behaviour. Optical systems offer the freedom to design arbitrary periodic lattices, as well as very accessible experiments, which can be used to examine issues in topological physics. Studying topological physics with photons will provide novel insights, some that will be directly applicable to electronic systems, continuing the cross-pollination of new ideas between optics and condensed matter physics. From the applications point of view, increased understanding of topological photonics will inform the design of photonic devices that are immune to fabrication imperfections. The long-term aim of my research program is to exploit optical techniques to develop versatile experimental platforms to study 1D and 2D systems that possess topological features. Using these platforms, we will experimentally explore problems in topological physics that are hard to study in materials. Key short-term projects under this umbrella are: (i) The design, fabrication, and characterization of 1D topological structures with edge states, (ii) the study of light transport in edge states in 2D topological photonic insulators, and (iii) the exploitation of the topological properties to develop ways to manipulate light in structures that are imperfect. The anticipated advances in topological photonics from the research proposed here will be of a two-fold benefit: (i) An improved understanding of the physics of lattice systems (essentially systems relevant to condensed matter physics), and (ii) new photonic devices will be designed that will be robust against fabrication imperfections. Notably, (i) can also be investigated in the microwave regime, but (ii) requires working with near infrared or visible light. Our proposed platforms will allow straightforward exploration, using standard telecommunication or visible lasers, of topological phenomena in 1D and 2D.