DGTD method for a non-local Drude model

For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local Drude dispersion model. In a preliminary study, we restricted on a two-dimensional setting.

Local Drude model	Non-local Drude model

Module of the Fourier transformed field plot of E_x computed with the DGTD-P₂ method

Ex component	Ey component

Field solution computed with the DGTD-P₂ method for a nanodisk dimer (radius of a disk is 2 nm)

Ex component	Ey component

Field solution computed with the DGTD-P₂ method for a square dimer (edge length is 4 nm)

Related publications

N. Schmitt, C. Scheid, S. Lanteri, J. Viquerat and A. Moreau
A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects
Available as INRIA RR-8726 on Hyper Article Online (2015)