%0 Journal Article
%T Spectral analysis of polygonal cavities containing a negative-index material
%T Analyse spectrale de cavités polygonales contenant un matériau d'indice négative
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%A Hazard, Christophe
%A Paolantoni, Sandrine
%< avec comité de lecture
%@ 2644-9463
%J Annales Henri Lebesgue
%I UFR de Mathématiques - IRMAR
%V 3
%P 1161-1193
%8 2020
%D 2020
%R 10.5802/ahl.58
%K dispersion
%K Drude model
%K essential spectrum
%K resonance
%Z Mathematics [math]/Analysis of PDEs [math.AP]
%Z Mathematics [math]/Spectral Theory [math.SP]Journal articles
%X The purpose of this paper is to investigate the spectral effects of an interface between vacuumand a negative-index material (NIM), that is, a dispersive material whose electric permittivity andmagnetic permeability become negative in some frequency range. We consider here an elementarysituation, namely, 1) the simplest existing model of NIM : the non dissipative Drude model, for whichnegativity occurs at low frequencies; 2) a two-dimensional scalar model derived from the completeMaxwell’s equations; 3) the case of a simple bounded cavity: a polygonal domain partially filled witha portion of Drude material. Because of the frequency dispersion (the permittivity and permeabilitydepend on the frequency), the spectral analysis of such a cavity is unusual since it yields a nonlineareigenvalue problem. Thanks to the use of an additional unknown, we linearize the problem and wepresent a complete description of the spectrum. We show in particular that the interface betweenthe NIM and vacuum is responsible for various resonance phenomena related to various componentsof an essential spectrum.
%G English
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-01626868v2/document
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-01626868v2/file/AHL_2020__3__1161_0.pdf
%L hal-01626868
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-01626868
%~ ENSTA
%~ CNRS
%~ INRIA
%~ INRIA-SACLAY
%~ INSMI
%~ INRIA_TEST
%~ TESTALAIN1
%~ UMA_ENSTA
%~ INRIA2
%~ TDS-MACS
%~ UNIV-PARIS-SACLAY
%~ IP_PARIS
%~ IP_PARIS_COPIE
%~ GS-COMPUTER-SCIENCE
%~ INRIAARTDOI