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Nonlocal material response distinctively changes the optical properties ofnano-plasmonic scatterers and waveguides. It is described by the nonlocalhydrodynamic Drude model, which -- in frequency domain -- is given by a coupledsystem of equations for the electric field and an additional polarizationcurrent of the electron gas modeled analogous to a hydrodynamic flow. Recentworks encountered difficulties in dealing with the grad-div operator appearingin the governing equation of the hydrodynamic current. Therefore, in thesestudies the model has been simplified with the curl-free hydrodynamic currentapproximation; but this causes spurious resonances. In this paper we present arigorous weak formulation in the Sobolev spaces $H(\mathrm{curl})$ for theelectric field and $H(\mathrm{div})$ for the hydrodynamic current, whichdirectly leads to a consistent discretization based on N\'ed\'elec's finiteelement spaces. Comparisons with the Mie theory results agree well. We alsodemonstrate the capability of the method to handle any arbitrary shapedscatterer.

Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using N\'ed\'elec finite elements