The plasmonic eigenvalue problem beyond the quasi-static limit

Abstract

Plasmonic resonances in nanoparticles can be understood in the quasi-static limit as solutions to the plasmonic eigenvalue problem, i.e. solutions to the quasi-static homogeneous Maxwell's equations when considering the permittivity as the eigenvalue; this formulation makes the modes material-independent. In this talk I will consider analogous versions of the plasmonic eigenvalue problem in two scenarios. First, the full wave regime in 2D where the subwavelength assumption on the size of the nanoparticle is abandoned and the wave scattering problem has to be modelled by the Helmholtz equation. Second (time permitting), the nonlocal hydrodynamic Drude model, which describes, qualitatively, the light-matter interactions at scales where the quantum nature of matter becomes apparent. I will present a rigorous spectral analysis of the plasmonic eigenvalue problem in these two scenarios. The main results are the completeness of the material-independent modes for the Helmholtz equation, and the regularizing properties of nonlocality in the nonlocal hydrodynamic Drude model.