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

等离子体激元学是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）的物理学新领域。如果金属具有与波长相比很小的颗粒形状，这将导致光谱问题，即等离子体本征值问题。该项目的目标是从数学角度研究等离子体本征值问题，并将其纳入最近感兴趣的其他领域的背景下，包括奇异分析和光谱几何。通过使用和细化工具，从微局部分析，奇异摄动理论和微分几何，我们期望获得定性和定量的洞察等离子体本征值及其相关的本征函数的行为。除了他们的数学兴趣的结果将证明，推广和完善的预测，在物理文献的基础上物理或数值实验，也将超越这些，从而为进一步的应用在物理学的基础。

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.