Exploring topological physics with photonics

凝聚态物理学和光学长期以来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（如果系统的能带结构平滑变形，则该量不会改变）来表征。这导致了具有非常有趣性质的状态的出现，例如存在于大块晶体边界的状态。这些国家受到保护，不受混乱的影响。最近在发现显示拓扑行为的材料方面的重要进展为阐明它们的性质和开发它们的应用提供了令人兴奋的机会。拓扑材料仅限于天然存在的晶格，不能轻易修改。此外，大多数材料都是三维的，因此在1D和2D中进行拓扑物理的实验研究具有挑战性。幸运的是，有可能构造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，以及非常容易的实验，可以用来研究拓扑物理学中的问题。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，继续光学和凝聚态物理学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为光子器件的设计提供信息，这些光子器件不受制造缺陷的影响。我的研究计划的长期目标是利用光学技术开发多功能实验平台，研究具有拓扑特征的1D和2D系统。利用这些平台，我们将实验性地探索拓扑物理学中难以在材料中研究的问题。在这一保护伞下的关键短期项目是：（i）设计，制造和表征具有边缘状态的1D拓扑结构，（ii）研究2D拓扑光子绝缘体中边缘状态的光传输，以及（iii）利用拓扑特性开发在不完美的结构中操纵光的方法。从这里提出的研究拓扑光子学的预期进展将是一个双重的好处：（i）一个更好的理解晶格系统的物理（本质上是系统相关的凝聚态物理），和（ii）新的光子器件将被设计，将是强大的制造缺陷。值得注意的是，（i）也可以在微波范围内进行研究，但（ii）需要使用近红外或可见光。我们提出的平台将允许直接探索，使用标准的电信或可见激光，在1D和2D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.