Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance

This paper is concerned with the time-dependent Maxwell’s equations for a plane interface between negative material described by Drude model and vacuum, which fill, respectively, two complementary half-spaces. In first paper, we have constructed generalized Fourier transform diagonalizes Hamiltonian that represents propagation of transverse electric waves. this second use to prove limiting absorption amplitude principles, concern, behavior resolvent near continuous spectrum long time response medium time-harmonic source prescribed frequency. also underlines existence an resonance occurs when there exists particular frequency characterized ratio permittivities permeabilities equal −1 across interface. At frequency, system harmonic forcing term blows up linearly in time. Such unusual wave problem unbounded domains corresponds non-zero embedded eigenvalue infinite multiplicity underlying operator. counterpart ill-posdness corresponding problem.