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Nonlinear Goubau line: analytical-numerical approaches and new propagation regimes
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
2017 (English)In: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 31, no 8, 781-797 p.Article in journal (Refereed) Published
Abstract [en]

We consider propagation of surface TE waves in the Goubau line (GL) assuming that the dielectric cover is non-linear and inhomogeneous. The problem at hand is reduced to a non-linear 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 TE waves for the chosen nonlinearity (Kerr law) is proved by the method of contraction. Conditions under which several higher-order waves can propagate are obtained, and the intervals of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiment two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation modes are found.

Place, publisher, year, edition, pages
2017. Vol. 31, no 8, 781-797 p.
Keyword [en]
Goubau line; surface TE waves; non-homogeneous dielectric waveguide; non-linear permittivity; non-linear eigenvalue problem; Green’s function; non-linear integral equation; numerical method
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-24273DOI: 10.1080/09205071.2017.1317036ISI: 000401737300002Scopus ID: 2-s2.0-85018707985OAI: oai:DiVA.org:hig-24273DiVA: diva2:1110398
Note

Funding Agency

University of Gavle  

Swedish Institute within the frames of the project Largescale  

Ministry of Education and Science of the Russian Federation  Grant no: 1.894.2017/Pi 

Available from: 2017-06-15 Created: 2017-06-15 Last updated: 2017-06-16Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf