Surface waves in a Goubau line filled with nonlinear anisotropic inhomogeneous medium

Abstract

The propagation of monochromatic nonlinear symmetric hybrid surface waves in a cylindrical nonlinear anisotropic inhomogeneous metal-dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The setting is reduced to a new type of nonlinear eigenvalue problem and an analytical method of its solution is developed. The propagation modes are found that have not been previously reported in the literature. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Keywords:

• Goubau Line
• non-polarized azimuthal-symmetric electromagnetic waves
• Kerr nonlinearity
• nonlinear inhomogeneous waveguide
• Maxwell's equations
• two-parameter eigenvalue problem
• numerical method

2010 Mathematics Subject Classifications:

• 78A60
• 34B15
• 34L16

Acknowledgments

This work was supported by the Russian Science Foundation, project no. 20-11-20087.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Russian Science Foundation, project no. 20-11-20087.