Electromagnetic wave propagation in media consisting of dispersive metamaterials

Hoai-Minh Nguyen; Valentin Vinoles

doi:10.1016/j.crma.2018.05.012

Partial differential equations/Functional analysis

Electromagnetic wave propagation in media consisting of dispersive metamaterials

Presented by: Jean-Michel Coron

Hoai-Minh Nguyen ¹; Valentin Vinoles ¹

¹ Department of Mathematics, EPFL SB CAMA, Station 8, CH-1015 Lausanne, Switzerland

Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 757-775.

Abstract
Résumé

We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials obeying Drude's and Lorentz' models. The causality and the passivity are the two main assumptions and play a crucial role in the analysis. It is worth noting that by contrast the well-posedness in the frequency domain is not ensured in general. We also provide some numerical experiments using the Drude's model to illustrate its dispersive behaviour.

Nous montrons que les équations de Maxwell dans un milieu constitué de métamatériaux dispersifs (dépendant de la fréquence) forment un problème bien posé, à vitesse de propagation finie et satisfaisant un résultat de régularité. Deux exemples typiques de tels métamatériaux sont les matériaux régis par les modèles de Drude et de Lorentz. La causalité et la passivité sont les deux hypothèses principales ; elles jouent un rôle essentiel dans l'analyse. Il vaut la peine de remarquer qu'en revanche, rien n'assure, en général, le caractère bien posé dans le domaine des fréquences. Nous présentons également quelques résultats numériques utilisant le modèle de Drude, afin d'illustrer le comportement dispersif.

Received: 2017-10-24
Accepted: 2018-05-22
Published online: 2018-05-31

DOI: 10.1016/j.crma.2018.05.012

Author's affiliations:

Hoai-Minh Nguyen ¹; Valentin Vinoles ¹

¹ Department of Mathematics, EPFL SB CAMA, Station 8, CH-1015 Lausanne, Switzerland

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     title = {Electromagnetic wave propagation in media consisting of dispersive metamaterials},
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Hoai-Minh Nguyen; Valentin Vinoles. Electromagnetic wave propagation in media consisting of dispersive metamaterials. Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 757-775. doi : 10.1016/j.crma.2018.05.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.05.012/

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