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We explore the spectral properties of the time-dependent Maxwell's equationsfor a plane interface between a metamaterial represented by the Drude model andthe vacuum, which fill respectively complementary half-spaces. We constructexplicitly a generalized Fourier transform which diagonalizes the Hamiltonianthat describes the propagation of transverse electric waves. This transformappears as an operator of decomposition on a family of generalizedeigenfunctions of the problem. It will be used in a forthcoming paper to proveboth limiting absorption and limiting amplitude principles.

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