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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, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
2 Department of Mathematics of the University of Utah
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.
Keywords : Maxwell equations Negative Index Materials (NIMs) Drude model Generalized eigenfunctions
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Journal articles
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https://hal-ensta-paris.archives-ouvertes.fr//hal-01379118
Contributor : Christophe Hazard <>
Submitted on : Tuesday, October 11, 2016 - 10:17:26 AM
Last modification on : Friday, January 22, 2021 - 11:34:04 AM

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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. Communications in Partial Differential Equations, Taylor & Francis, 2017, 42 (11), pp.1707-1748. ⟨hal-01379118⟩

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