Exploring topological physics with photonics

长期以来，凝聚态物理和光学一直是相互提供新思想和新技术的领域。这种协同作用的一个最近的例子来自拓扑物理学。在适当的条件下，周期系统可以用倒易空间中的非平凡拓扑不变量来表征（如果系统的能带结构平滑变形，该量不会改变）。这导致了具有非常有趣性质的状态的出现，例如存在于体晶体边界的状态。这些国家受到保护，免遭混乱。最近在发现显示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形成的晶体晶格，不能轻易修改。此外，大多数材料都是三维的，因此拓扑物理的一维和二维实验研究具有挑战性。幸运的是，我们有可能构建出具有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，以及非常容易获得的实验，可用于检查拓扑物理中的问题。用光子研究拓扑物理学将提供新的见解，其中一些将直接适用于电子系统，继续在光学和凝聚态物理之间进行新思想的交叉授粉。从应用的角度来看，增加对拓扑光子学的理解将为不受制造缺陷影响的光子器件的设计提供信息。

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.