Mathematical theory of plasmonics: Plasmonic eigenvalues, singular perturbations, microlocal analysis

等离子体激元数学理论：等离子体特征值、奇异扰动、微局域分析

• 批准号: 211072416
• 负责人: Professor Dr. Daniel Grieser
• 金额: --
• 依托单位: Institut für Mathematik (IFM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/211072416?language=en
• 关键词: Mathematical; theory; plasmonics; Plasmonic; eigenvalues

Plasmonics is a novel area of research in physics which studies surface plasmon polaritons, that is, waves arising from the interaction of electromagnetic waves with a metal. If the metal has the shape of a particle which is small in comparison with the wave length, this leads to a spectral problem, the plasmonic eigenvalue problem. The goal of this project is to study the plasmonic eigenvalue problem from a mathematical perspective and to put it into the context of other fields of recent interest, including singular analysis and spectral geometry. By using and refining tools from microlocal analysis, singular perturbation theory and differential geometry we expect to gain qualitative and quantitative insight into the behavior of plasmonic eigenvalues and their associated eigenfunctions. Apart from their mathematical interest the results will justify, generalize and refine predictions made in the physics literature based on physical or numerical experiments, and will also go beyond these and thus provide the basis for further applications in physics.

等离子体激元是物理学中一个新的研究领域，它研究表面等离子体激元，即电磁波与金属相互作用产生的波。如果金属具有与波长相比较小的粒子形状，这将导致光谱问题，即等离子体本征值问题。这个项目的目标是从数学的角度研究等离子体本征值问题，并将其放在最近感兴趣的其他领域的背景下，包括奇异分析和谱几何。通过使用和提炼微局域分析、奇异微扰理论和微分几何的工具，我们期望对等离子体本征值及其相关的本征函数的行为有定性和定量的了解。除了对数学感兴趣外，这些结果还将证明、概括和完善基于物理或数值实验的物理文献中的预测，并将超越这些预测，从而为进一步的物理应用提供基础。