Open AccessNONLINEAR PROPAGATION OF LEAKY TE-POLARIZED ELECTROMAGNETIC WAVES IN A METAMATERIAL GOUBAU LINE
Author(s) -
Eugene Smolkin,
Yury Smirnov
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.13077
Subject(s) - mathematical analysis , nonlinear system , physics , boundary value problem , metamaterial , electromagnetic radiation , wave propagation , cauchy distribution , mathematics , optics , quantum mechanics
Propagation of leaky TE-polarized electromagnetic waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear metamaterial medium is studied. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.