Electromagnetic wave propagation in media consisting of dispersive metamaterials

Nguyen, Hoai-Minh; Vinoles, Valentin

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

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.

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.

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