Electromagnetic TE- and TM-waves propagation in a plane waveguide covered with graphene characterized by nonlinear conductivity

Background. Guiding properties of waveguiding structures with graphene are of great importance for various applications and have been studied in many papers. In all such studies, graphene was characterized, as a rule, by linear surface conductivity. However, if the intensity of an electromagnetic wave is large enough, the interaction of graphene with the electromagnetic wave becomes nonlinear; in this case, it is more correct to describe graphene by nonlinear conductivity. Aim. This work is aimed at studying the influence of cubic nonlinearity of graphene, corresponding to the so-called self-action effects (not affecting the frequency of the incident wave), on the propagation of TE- and TM-polarized waves in the structure, which is a plain dielectric layer covered on one side by graphene. Methods. In this study, the guiding properties of the waveguide are studied using primarily an analytical approach. Thus, from Maxwell's equations, material equations and boundary conditions, a couple of dispersion equations for TE-and TM-polarized waves is derived and then its solvability is studied. In addition, some numerical experiments are carried out in the study. Results. The dispersion equations of the studied waveguiding structure for TE- and TM-polarized waves are derived in explicit form. Studying analytically obtained equations, conditions for waveguide parameters are found, providing the existence of a given number of waveguide modes. In addition, some numerical results are obtained in the paper, which give an idea of the influence of nonlinear effects on the electromagnetic waves propagating in the structure. Conclusion. The results obtained in this paper reveal two effects related to the cubic nonlinearity of graphene. Firstly, in a plain dielectric layer with graphene coating in the strong nonlinear regime TE-waves with longer wavelength and TM-waves with shorter wavelength propagate compared to electromagnetic waves that propagate in the same structure in the linear regime. Secondly, the strong cubic nonlinearity leads to a greater localization of the electromagnetic wave within the waveguiding structure.