Resonance modes of plasmonic nanoparticles

The concept of resonances and modes for the description of particle plasmons, these are coherent electron charge oscillations at the interface between a metallic nanoparticle and a dielectric environment, has recently received great interest in the field of plasmonics, both in the context of efficient simulations as well as for an intuitive interpretation in physical terms. In this project we plan to investigate resonance modes using a boundary element method approach and to compare different resonance concepts introduced in the literature, with main focus on the analysis and numerical approximations of plasmonic resonance problems in the framework of the analytic Fredholm theory. We will also seek for an efficient computation using a recently developed nonlinear eigenmode solver, and will apply our results to plasmon field tomography based on electron energy loss spectroscopy.

The project "Resonance modes for plasmonic nanoparticles" was dedicated to the analysis and the numerical simulation of surface plasmons of metallic nanoparticles. Surface plasmons are coherently electron oscillations on the surface of metallic nanostructures. When light hits the surface of metallic nanoparticles then under certain circumstances coherently electron oscillations may occur. There are different applications which are based on the excitation of surface plasmons, for example the so-called surface plasmon resonance spectroscopy which can be utilized to determine the thickness of thin films of materials. One important aim of the project was to extend the classical mathematical and physical concept of resonance modes such that it can be applied to surface plasmons. A direct application of the classical resonance concept for the analysis of surface plasmons is from a mathematical but also from a physical point of view not possible since surface plasmons can not be described within the framework of finite closed systems. For surface plasmons the framework of open systems has to be used for which the classical resonance concept is not applicable. The chosen mathematical description of surface plasmons in the project enabled us to resort to a mathematical theory which is an extension of the classical resonance concept. This allowed us to describe oscillations of surface plasmons in terms of resonances and resonance modes. In particular a formula could be established which represent oscillations of surface plasmons as superposition of resonance modes. A further focus of the project was the development and analysis of numerical methods for the computation and simulation of surface plasmons and resonance modes. In the project it could be shown how available numerical methods can be combined to compute surface plasmons and resonance modes in a reliable way. Within the project a software (Matlab toolbox) was developed for the computation of surface plasmons and resonance modes which is freely available under https://github.com/uhohenester/nanobem22. A further topic of the project was the application of the resonance concept of surface plasmons to tomography. In different papers it could be shown how the resonance concept of surface plasmons can be used for the tomography of quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic excited system.