Reshaping and capturing nonlinear electromagnetic and linear electron 2D waves in lossy graphene metamaterials. Graphene solid-state electron optics

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 (EM) waves in graphene-dielecric (GD) multlayered structres. This approach can lead, in particular, to the development of graphene metamaterial solid-state electron optics (GMEO). A possibility of resonant behavior of the components of the electron disribution function in 2D “diffraction grating”, with quasi 1D periodicity along a direction of beam propagation, is shown, and capturing electron beams by magnetic ring resonator is shown The theory of 2D EM pulse propagation through multilayered (GD) structure with electron nonlinearity in the strongly nonlinear “above threshold” regime is developed and new nonlinear 2D phenomena of a competition between “longitudinal” and “transfer” focusing is proposed. It is found that some critical value of losses exists. When the parameter of losses ν is equal to or less than 1.5×10¹² s^-1, nonlinear switching of a pulse to “predominantly transmission” regime can be observed. The critical value of ν can be easily achieved in real experimental situation.