Numerical Study of the Spectrum of TE-Polarized Electromagnetic Waves of a Goubau Line Coated with Graphene

The problem of TE-polarized waves in a Goubau line (a perfectly conducting cylinder covered by a concentric layer) coated with graphene is studied. The classification of the waves existing in a Goubau line is carried out. The physical problem is reduced to solving a transmission eigenvalue problem for an ordinary differential equation. The conjugation conditions contain the conductivity of graphene. In this work, we take into account the nonlinearity of graphene. Spectral parameters of the problem are the propagation constants of the waveguide. The article proposes a numerical method for calculating the propagation constants of such waves. A number of numerical experiments were carried out with a Goubau line filled with a dielectric, inhomogeneous dielectric, dielectric with losses, and metamaterial.