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arXiv · 1610.03021

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

Maxence Cassier·Christophe Hazard·Patrick Joly
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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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Maxence Cassier, Christophe Hazard, Patrick Joly. 2016-10-10. Spectral theory for Maxwell's equations at the interface of a metamaterial. Part I: Generalized Fourier transform. https://arxiv.org/abs/1610.03021

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