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

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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.