Three-level approach to graphene metamaterials: Electron density waves and linear and nonlinear electrodynamics

We propose “three-level” approach to graphene metamaterials including “metamaterial treatment” of electron density waves in graphene. First, we determined the characteristics of electron wave transport in graphene layer, accounting for applied external electric and magnetic fields, exchange and spin-orbit interactions. The new system of equations for 2D electron beam in graphene layer with a 2D inhomogeneity is derived and the special method for a solution of such a system is developed. W search a possibility of “capturing” by the “magnetic ring resonator” of an electron beam. Then we propose the paradigm of “solid state graphene electron optics”. This approach includes different ways of control over characteristics of a propagation of electron density waves, passive components, typical for electron optics and nanoelectronics, such as waveguides, lenses, diffraction gratings. Finally, the new equations are derived, to model linear (with great slowdown) and nonlinear (with electronic nonlinearity) electromagnetic waves in graphene layered lossy structures.