Modes and resonances of plasmonic scatterers

We present a rigorous full-wave electromagnetic approach to analyze the modes and resonances of dielectric and plasmonic nanoparticles of practically any geometry. Using boundary integral operators, we identify the resonances as inherent properties of the particles and propose a modal expansion for their optical response. We show that the resonance frequencies are isolated points on the complex plane. The approach allows the particles to be analyzed without specifying an incident field, which can be separately tailored for the desired interaction with the modes. We also connect the general theory to the Mie theory in spherical geometry and provide a connection to the quasistatic theory. In comparison to earlier work on modes and resonances of scatterers, our approach has the benefit that modes are defined entirely over a compact boundary surface of the scatterer. Furthermore, the boundary integral operator is of second-kind Fredholm type, enabling the rigorous characterization of the resonances.