Spectral theory for Maxwell's equations at the interface of a metamaterial. Part I: Generalized Fourier transform

Maxence Cassier 1, 2 Christophe Hazard 1 Patrick Joly 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We explore the spectral properties of the time-dependent Maxwell's equations for a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill respectively complementary half-spaces. We construct explicitly a generalized Fourier transform which diagonalizes the Hamiltonian that describes the propagation of transverse electric waves. This transform appears as an operator of decomposition on a family of generalized eigenfunctions of the problem. It will be used in a forthcoming paper to prove both limiting absorption and limiting amplitude principles.
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https://hal-ensta.archives-ouvertes.fr/hal-01379118
Contributeur : Christophe Hazard <>
Soumis le : mardi 11 octobre 2016 - 10:17:26
Dernière modification le : vendredi 17 février 2017 - 16:13:46

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  • HAL Id : hal-01379118, version 1
  • ARXIV : 1610.03021

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Maxence Cassier, Christophe Hazard, Patrick Joly. Spectral theory for Maxwell's equations at the interface of a metamaterial. Part I: Generalized Fourier transform. 34 pages, 8 figures. 2016. <hal-01379118>

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