Spectral theory for Maxwell's equations at the interface of a metamaterial. Part I: Generalized Fourier transform
Provides a mathematical foundation for analyzing wave propagation at metamaterial interfaces, which is important for applications in photonics and electromagnetics.
The authors construct an explicit generalized Fourier transform that diagonalizes the Hamiltonian for transverse electric waves at a metamaterial-vacuum interface, enabling future proofs of limiting absorption and amplitude principles.
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.