Mathematical Analysis of Multi-dimensional Topological Edge Modes

多维拓扑边缘模式的数学分析

• 批准号: EP/X027422/1
• 负责人: Richard Craster
• 金额: $ 24.26万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX027422%2F1
• 关键词: Mathematical; Analysis; Multi; dimensional; Topological

The goal of this proposal is to develop novel mathematical techniques for analysing topological edge modes that will inform rapid advancements in metamaterial design. This proposal will yield new analytic methods capable of describing the rich variety of multi-dimensional metamaterial geometries being developed. This will lead to rigorous results relating the properties of topological edge modes (localization strength, robustness, eigenfrequency) with those of the underlying materials (topological indices, symmetry) in multi-dimensional systems. This will reveal fundamental new insight into the fundamental physics and the deliverables (theorems, formulas, codes) will be used to rapidly and accurately guide metamaterial design. It will also overcome the reliance on perturbative methods. This will be achieved by developing approaches for modelling scattering by almost periodic (semi-infinite, randomly perturbed, quasi-periodic) structures with general geometries in dimension greater than one. These will combine my extensive expertise in boundary integral methods with the expertise of the host group (led by Richard Craster, at Imperial College London) in the Wiener-Hopf method. Additionally, input from the unique, world-leading expertise in topological waveguide design possessed by the host group and other members of the Imperial College Centre for Plasmonics and Metamaterials will help guide the project towards achieving high-impact, cutting-edge results. This fellowship will further my career by giving me the opportunity to conduct an independent program of research and to develop high-profile collaborations within the Imperial College Centre for Plasmonics and Metamaterials. I will develop the management, communication and technical skills needed for a career of applied mathematical research and to achieve my goal of becoming a European leader on the mathematical analysis of metamaterials.

该提案的目标是开发用于分析拓扑边缘模式的新颖数学技术，这将为超材料设计的快速进步提供信息。该提案将产生新的分析方法，能够描述正在开发的丰富多样的多维超材料几何形状。这将产生严格的结果，将拓扑边缘模式的属性（定位强度、鲁棒性、本征频率）与多维系统中的基础材料的属性（拓扑指数、对称性）联系起来。这将揭示对基础物理学的基本新见解，并且可交付成果（定理、公式、代码）将用于快速、准确地指导超材料设计。它还将克服对微扰方法的依赖。这将通过开发对维度大于一的一般几何形状的几乎周期性（半无限、随机扰动、准周期性）结构的散射进行建模的方法来实现。这些将把我在边界积分方法方面的广泛专业知识与主办小组（由伦敦帝国理工学院的理查德·克拉斯特领导）在维纳-霍普夫方法方面的专业知识结合起来。此外，主办团队和帝国理工学院等离激元和超材料中心其他成员在拓扑波导设计方面拥有独特的、世界领先的专业知识，他们的投入将有助于指导该项目取得高影响力的尖端成果。该奖学金将让我有机会进行独立的研究项目并在帝国理工学院等离激元和超材料中心开展高调的合作，从而进一步推动我的职业生涯。我将培养应用数学研究职业所需的管理、沟通和技术技能，并实现成为欧洲超材料数学分析领导者的目标。

项目成果

Graded Quasiperiodic Metamaterials Perform Fractal Rainbow Trapping

分级准周期超材料执行分形彩虹捕获

• DOI: 10.1103/physrevlett.131.177001
• 发表时间: 2023
• 期刊: Physical Review Letters
• 影响因子: 8.6
• 作者: Davies B

Code for "Exponentially localised interface eigenmodes in finite chains of resonators"

“有限谐振器链中的指数局部界面本征模式”的代码

• DOI: 10.5281/zenodo.10361316
• 发表时间: 2023
• 作者: Barandun S

Tunable topological edge modes in Su-Schrieffer-Heeger arrays

Su-Schrieffer-Heeger 阵列中的可调谐拓扑边缘模式

• DOI: 10.1063/5.0152172
• 发表时间: 2023
• 期刊: Applied Physics Letters
• 影响因子: 4
• 作者: Chaplain G

Convergence Rates for Defect Modes in Large Finite Resonator Arrays

大型有限谐振器阵列中缺陷模式的收敛率

• DOI: 10.1137/23m1575937
• 发表时间: 2023
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Ammari H

Landscape of wave focusing and localization at low frequencies

• DOI: 10.1111/sapm.12659
• 发表时间: 2023-11-28
• 期刊: STUDIES IN APPLIED MATHEMATICS
• 影响因子: 2.7
• 作者: Davies，Bryn;Lou，Yiqi
• 通讯作者: Lou，Yiqi