Topological Photonic Crystal Fibres

该研究项目的总体目标是制造光子晶体（PhC）光纤，该光纤由于拓扑保护而允许强大的光传播。拓扑学，在数学意义上，是研究在光滑变形下守恒的量，在物理学中，这些守恒量可以在广泛的系统中找到。该项目将专注于使用守恒光子模式来保证由拓扑phc光纤引导的光没有散射损失。减少光纤损耗可以更好地传输微妙的光信号，包括单光子的传输，这在量子光子电路中尤为重要。项目的第一阶段是寻找有效的拓扑保护状态，并对其进行理论研究。我们希望这一过程最好能在项目的前三到四个月内完成。这一步将包括首先在一系列几何中浏览拓扑状态的当前限制。这些前沿的想法将用于我们自己的新几何形状的设计，这将提供拓扑保护模式，可以构建到适当的纤维设计中。一旦我们有了多个新系统，计算模拟就可以开始了。这些模拟将使用COMSOLMultiphysics（一种有限元求解器）来数值验证受保护拓扑状态的存在。它将通过计算系统的拓扑不变量和相关的光子模式来做到这一点。虽然这部分工作将在理论设计之后进行，但一旦每个设计看起来有希望，就可以开始一些几何形状的设置工作。在三到四个月的时间里，我相信设计的几何形状可以进行模拟和计算测试。这个时间表非常依赖于每个设计的成功，在这里很可能出现延迟和不可预见的问题。在推导出成功的理论设计并经过计算验证后，就可以开始制造了。这将涉及使用光子学和光子材料中心（CPPM）光纤制造室来设计复制预测设计的定制预制件。然后将这些预成型物拉入光纤线轴中，在光学实验室中进行研究。这些纤维的性能将被仔细分析，以确认保护模式的存在。我们预见到在制造过程中可能会出现潜在的挑战，如果一个设计看起来太难而无法正确制造，那么它可能不得不被废弃。即使在制造之后，也可能存在设计上的挑战，不能证明拓扑保护状态的存在或强大的光传输。这些都需要仔细考虑，任何有缺陷的设计都需要迭代或完全重新设计

The overall goal of this research project is to fabricate photonic crystal (PhC) fibres that allow for robust lightpropagation due to topological protection. Topology, in the mathematical sense, is the study of quantities which areconserved under smooth deformations and in physics these conserved quantities can be found in a wide range ofsystems. This project would focus on using conserved photonic modes to guarantee that light guided by a topologicalPhC fibre experiences no scattering loss. Reducing loss within the fibre enables better transmission of delicateoptical signals, including the transmission of single photons, which can be of particular importance in quantumphotonic circuitry.The first stage of the project is to find a valid topologically protected state and investigate it theoretically. We hopethis process would ideally be completed within the first three to four months of the project. This step will involve firstreviewing current limitations of topological states in a range of geometries. These cutting-edge ideas will be used toinform the design of our own novel geometries which will provide topologically protected modes that can be built intoan appropriate fibre design.Once we have multiple novel systems, computational simulations can begin. These simulations will use COMSOLMultiphysics (a finite element solver) to numerically verify the presence of protected topological states. It will do thisby computing the system's topological invariants and associated photonic modes. While this part of the project willcome after the theoretical design, some work to setup the geometries can begin as soon as each design lookspromising. Over three/four months I believe the designed geometries can be simulated and computationally tested.This timeline is very dependent on the success of each design, with delays and unforeseen problems highly likelyhere.After a successful theoretical design has been derived and computationally verified, fabrication c an begin. This willinvolve using the Centre for Photonics and Photonic Materials (CPPM) fibre fabrication room to design custompreforms that replicate the predicted designs. These preforms will then be drawn into spools of fibre which can beinvestigated in the optical labs. The performance of these fibres will be carefully analysed, with the intention ofconfirming the presence of protected modes. We foresee potential challenges may occur in fabrication and a designmay have to be scrapped here if it appears too difficult to correctly fabricate. Even after fabrication there may bechallenges with the design not demonstrating the existence of topologically protected states or robust lighttransmission. These will need to be carefully considered and any deficient designs will either need to be iteratedthrough or redesigned entirely