Nonlinear propagation of coupled surface TE and leaky TM electromagnetic waves

ABSTRACT

Propagation of the coupled electromagnetic wave, which is a superposition of TE surface and TM leaky waves, in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is studied (if the permittivity is linear, the coupled wave does not exist). Nonlinear coupled TE–TM wave is characterised by two (independent) frequencies and two (coupled) propagation constants (propagation constants). The physical problem is reduced to a nonlinear two-parameter transmission eigenvalue problem for Maxwell's equations. Existence of coupled TE–TM waves is proved. Intervals of localisation of propagation constants are found.

KEYWORDS:

• Nonlinear coupled TE–TM waves
• Kerr nonlinearity
• nonlinear waveguide
• Maxwell's equations
• coupled propagation constants
• two-parameter eigenvalue problem

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47J10
• 78A60

Acknowledgments

The reported study was funded by RFBR, project number 19-31-51004.

Disclosure statement

No potential conflict of interest was reported by the authors.