Numerical solution of nonlocal hydrodynamic Drude model for arbitrary   shaped nano-plasmonic structures using N\'ed\'elec finite elements
  Nonlocal material response distinctively changes the optical properties of nano-plasmonic scatterers and waveguides. It is described by the nonlocal hydrodynamic Drude model, which -- in frequency domain -- is given by a coupled system of equations for the electric field and an additional polarization current of the electron gas modeled analogous to a hydrodynamic flow. Recent works encountered difficulties in dealing with the grad-div operator appearing in the governing equation of the hydrodynamic current. Therefore, in these studies the model has been simplified with the curl-free hydrodynamic current approximation; but this causes spurious resonances. In this paper we present a rigorous weak formulation in the Sobolev spaces $H(\mathrm{curl})$ for the electric field and $H(\mathrm{div})$ for the hydrodynamic current, which directly leads to a consistent discretization based on N\'ed\'elec's finite element spaces. Comparisons with the Mie theory results agree well. We also demonstrate the capability of the method to handle any arbitrary shaped scatterer. 
Kirankumar R. Hiremath, Lin Zschiedrich, Frank Schmidt
physics.comp-ph math.NA physics.optics