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Journal Articles Communications in Partial Differential Equations Year : 2017

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

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.

Dates and versions

hal-01379118 , version 1 (11-10-2016)

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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, 2017, 42 (11), pp.1707-1748. ⟨hal-01379118⟩
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