paper 150203131741

Abstract

The propagation of monochromatic electromagnetic TE waves in the Goubau line (conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is considered. Two types of nonlinearity are studied. A physical problem is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation. Eigenvalues of the problem correspond to propagation constants of the waveguide. A method is proposed for finding approximate eigenvalues of the nonlinear problem based on solving an auxiliary Cauchy problem (by the shooting method). The existence of eigenvalues that correspond to a new propagation regime is predicted. A comparison with the linear case is given.

1. Shestopalov, Y., E. Kuzmina, and A. Samokhin, "On a mathematical theory of open metaldielectric waveguides," FERMAT, Vol. 5, 1-9, 2014. Google Scholar

2. Valovik, D. V., Y. G. Smirnov, and E. Y. Smol'kin, "Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides," Computational Mathematics and Mathematical Physics, Vol. 53, 1150-1161, 2013.
doi:10.1134/s096554251307018x Google Scholar

3. Valovik, D. V. and E. Y. Smol'kin, "Calculation of the propagation constants of inhomogeneous nonlinear double-layer circular cylindrical waveguide by means of the Cauchy problem method," Journal of Communications Technology and Electronics, Vol. 58, 759-767, 2013.
doi:10.1134/s1064226913060132 Google Scholar

4. Akhmediev, N. N. and A. Ankevich, Nonlinear Pulses and Beams, Chapman and Hall, London, UK, 1997. Google Scholar

5. Smirnov, Y. G. and D. V. Valovik, Electromagnetic Wave Propagation in Non-linear Layered Waveguide Structures, Penza State University Press, Penza, Russia, 2011. Google Scholar

6. Schuermann, H. W., V. S. Serov, and Y. V. Shestopalov, "TE-polarized waves guided by a lossless nonlinear three layer structure," Phys. Rev. E, Vol. 58, No. 1, 1040-1050, 1998. Google Scholar

7. Smirnov, Y. G., H. W. Schurmann, and Y. V. Shestopalov, "Integral equation approach for the propagation of TE-waves in a nonlinear dielectric cylindrical waveguide," Journal of Nonlinear Mathematical Physics, Vol. 11, No. 2, 256-268, 2004.
doi:10.2991/jnmp.2004.11.2.10 Google Scholar

8. Schurmann, H. W., Y. G. Smirnov, and Y. V. Shestopalov, "Propagation of TE-waves in cylindrical nonlinear dielectric waveguides," Phys. Rev. E, Vol. 71, No. 1, Article ID 016614, 10 Pages, 2005. Google Scholar

9. Smirnov, Y. G., E. Y. Smolkin, and D. V. Valovik, "Nonlinear double-layer bragg waveguide: Analytical and numerical approaches to investigate waveguiding problem," Advances in Numerical Analysis, Vol. 2014, 1-11, 2014.
doi:10.1155/2014/231498 Google Scholar

Yury V. Shestopalov

Eugene Smolkin