Nonlinear Coupled Surface TE and Leaky TM Electromagnetic Waves

Nonlinear coupled electromagnetic surface TE and leaky TM wave propagation in a cylindrical nonlinear inhomogeneous metal-dielectric waveguide (Goubau line) with circular cross section is considered. Physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. For the numerical solution, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. The coupled TE-TM waves propagating in GL are determined numerically.