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Spectral analysis of polygonal cavities containing a negative-index material

Christophe Hazard 1 Sandrine Paolantoni 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : The purpose of this paper is to investigate the spectral effects of an interface between vacuum and a negative-index material (NIM), that is, a dispersive material whose electric permittivity and magnetic permeability become negative in some frequency range. We consider here an elementary situation, namely, 1) the simplest existing model of NIM : the non dissipative Drude model, for which negativity occurs at low frequencies; 2) a two-dimensional scalar model derived from the complete Maxwell’s equations; 3) the case of a simple bounded cavity: a polygonal domain partially filled with a portion of Drude material. Because of the frequency dispersion (the permittivity and permeability depend on the frequency), the spectral analysis of such a cavity is unusual since it yields a nonlinear eigenvalue problem. Thanks to the use of an additional unknown, we linearize the problem and we present a complete description of the spectrum. We show in particular that the interface between the NIM and vacuum is responsible for various resonance phenomena related to various components of an essential spectrum.
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https://hal-ensta-paris.archives-ouvertes.fr//hal-01626868
Contributor : Christophe Hazard <>
Submitted on : Thursday, November 26, 2020 - 10:07:51 AM
Last modification on : Friday, November 27, 2020 - 3:30:59 AM

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Christophe Hazard, Sandrine Paolantoni. Spectral analysis of polygonal cavities containing a negative-index material. Annales Henri Lebesgue, UFR de Mathématiques - IRMAR, 2020, 3, pp.1161-1193. ⟨10.5802/ahl.58⟩. ⟨hal-01626868v2⟩

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