Numerical study of propagation of nonlinear coupled surface and leaky electromagnetic waves in a circular cylindrical metal–dielectric waveguide

The problem of propagation of coupled surface (TE) and leaky (TM) polarized electromagnetic waves in a Goubau line (a perfectly conducting cylinder covered with a concentric dielectric layer) filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE–TM wave is characterized by two (independent) frequencies $\omega_E$ and $\omega_M$ and two propagation constants $\hat\gamma_E$ and $\hat\gamma_M$. The physical problem is reduced to a nonlinear two-parameter eigenvalue field-matching problem for a system of nonlinear ordinary differential equations. Two types of solutions are found: nonlinear solutions of the first type correspond to solutions of the linear problems (such solutions become linear when the nonlinearity coefficient tends to zero); solutions of the second type are purely nonlinear, since they do not transform into linear solutions when the nonlinearity coefficient decreases. The results of calculations of coupled propagation constants and coupled eigenmodes are presented.