Electron beams in 2D inhomogeneous graphene and nonlinear electrodynamics properties of graphene-dielectric multilayered metamaterials

We develop farther our “three-level” approach to graphene metamaterials including “metamaterial treatment” of 2D beams of electron (BE) in graphene with 2D inhomogeneous and nonlinear electromagnetic waves in graphene-dielecric multlayered structres. A possibility of resonant behaviour of the components of the electron disrribution function in 2D “diffraction grating”, with 1D periodicity along a direction of beam propagation, is shown, first. The theory of 2D electromagnetic (EM) pulse propagation through multilayered graphene-dielectric structure with electron nonlinearity and “transmission bistability” is developed.