On the Ability of TE- and TM-waves Propagation in a Dielectric Layer Covered with Nonlinear Graphene

The paper focuses on the problems of monochromatic terahertz TE- and TM-polarized waves propagation in a plane dielectric layer covered with a layer of graphene. The study has two important features. On the one hand, energy losses both in dielectric and graphene are neglected. It is reasonable in the terahertz range of electromagnetic radiation (which the paper focuses on) where graphene has a strong plasmonic response and much less loss. On the other hand, in the study third-order nonlinearity of graphene affecting the electromagnetic wave propagation is taken into account. The problems on wave propagation are reduced to eigenvalue problems where one of the boundary conditions is nonlinear with respect to a sought-for function. The main result of the paper is a couple of dispersion equations allowing for a waveguide of a given thickness to determine a set of its propagation constants and, consequently, a set of its TE- and TM-eigenwaves. Studying the dispersion equations, sufficient conditions for existence of several TE- and TM-eigenwaves are obtained in the paper. In addition, the paper contains some numerical results.