%0 Journal Article
%T Spectral theory for Maxwell's equations at the interface of a metamaterial. Part I: Generalized Fourier transform
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%+ Department of Mathematics of the University of Utah
%A Cassier, Maxence
%A Hazard, Christophe
%A Joly, Patrick
%< avec comité de lecture
%@ 0360-5302
%J Communications in Partial Differential Equations
%I Taylor & Francis
%V 42
%N 11
%P 1707-1748
%8 2017-10-11
%D 2017
%Z 1610.03021
%K Negative Index Materials (NIMs)
%K Drude model
%K Maxwell equations
%K Generalized eigenfunctions
%Z Mathematics [math]/Analysis of PDEs [math.AP]
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Computer Science [cs]/Numerical Analysis [cs.NA]Journal articles
%X 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.
%G English
%L hal-01379118
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-01379118
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