# A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects

## Abstract

The interaction of light with metallic nanostructures is increasingly attracting interest because of numerous potential applications. Sub-wavelength metallic structures, when illuminated with a frequency close to the plasma frequency of the metal, present resonances that cause extreme local field enhancements. Exploiting the latter in applications of interest requires a detailed knowledge about the occurring fields which can actually not be obtained analytically. For the latter mentioned reason, numerical tools are thus an absolute necessity. The insight they provide is very often the only way to get a deep enough understanding of the very rich physics at play. For the numerical modeling of light-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 equations coupled to Maxwell's equations. However, recent experiments have shown that the repulsive interaction between electrons inside the metal makes the response of metals intrinsically non-local and that this effect cannot generally be overlooked. Technologicalmore »

- Authors:

- Inria, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France)
- (TEMF), Schlossgartenstr. 8, 64289 Darmstadt (Germany)
- (France)
- Institut Pascal, Université Blaise Pascal, 24, avenue des Landais, 63171 Aubière Cedex (France)

- Publication Date:

- OSTI Identifier:
- 22572323

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 316; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INTERACTIONS; LANGMUIR FREQUENCY; NANOSTRUCTURES; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; PLASMA; SIMULATION; WAVELENGTHS

### Citation Formats

```
Schmitt, Nikolai, Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder, Scheid, Claire, University of Nice – Sophia Antipolis, Mathematics laboratory, Parc Valrose, 06108 Nice, Cedex 02, Lanteri, Stéphane, E-mail: Stephane.Lanteri@inria.fr, Moreau, Antoine, and Viquerat, Jonathan.
```*A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.04.020.

```
Schmitt, Nikolai, Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder, Scheid, Claire, University of Nice – Sophia Antipolis, Mathematics laboratory, Parc Valrose, 06108 Nice, Cedex 02, Lanteri, Stéphane, E-mail: Stephane.Lanteri@inria.fr, Moreau, Antoine, & Viquerat, Jonathan.
```*A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects*. United States. doi:10.1016/J.JCP.2016.04.020.

```
Schmitt, Nikolai, Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder, Scheid, Claire, University of Nice – Sophia Antipolis, Mathematics laboratory, Parc Valrose, 06108 Nice, Cedex 02, Lanteri, Stéphane, E-mail: Stephane.Lanteri@inria.fr, Moreau, Antoine, and Viquerat, Jonathan. Fri .
"A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects". United States.
doi:10.1016/J.JCP.2016.04.020.
```

```
@article{osti_22572323,
```

title = {A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects},

author = {Schmitt, Nikolai and Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder and Scheid, Claire and University of Nice – Sophia Antipolis, Mathematics laboratory, Parc Valrose, 06108 Nice, Cedex 02 and Lanteri, Stéphane, E-mail: Stephane.Lanteri@inria.fr and Moreau, Antoine and Viquerat, Jonathan},

abstractNote = {The interaction of light with metallic nanostructures is increasingly attracting interest because of numerous potential applications. Sub-wavelength metallic structures, when illuminated with a frequency close to the plasma frequency of the metal, present resonances that cause extreme local field enhancements. Exploiting the latter in applications of interest requires a detailed knowledge about the occurring fields which can actually not be obtained analytically. For the latter mentioned reason, numerical tools are thus an absolute necessity. The insight they provide is very often the only way to get a deep enough understanding of the very rich physics at play. For the numerical modeling of light-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 equations coupled to Maxwell's equations. However, recent experiments have shown that the repulsive interaction between electrons inside the metal makes the response of metals intrinsically non-local and that this effect cannot generally be overlooked. Technological achievements have enabled the consideration of metallic structures in a regime where such non-localities have a significant influence on the structures' optical response. This leads to an additional, in general non-linear, system of partial differential equations which is, when coupled to Maxwell's equations, significantly more difficult to treat. Nevertheless, dealing with a linearized non-local dispersion model already opens the route to numerous practical applications of plasmonics. In this work, we present a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell's equations coupled to a linearized non-local dispersion model relevant to plasmonics. While the method is presented in the general 3D case, numerical results are given for 2D simulation settings.},

doi = {10.1016/J.JCP.2016.04.020},

journal = {Journal of Computational Physics},

number = ,

volume = 316,

place = {United States},

year = {Fri Jul 01 00:00:00 EDT 2016},

month = {Fri Jul 01 00:00:00 EDT 2016}

}