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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 614976, 11 pages
Research Article

Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity

Department of Mathematics and Supercomputing, Penza State University, Krasnaya Street 40, Penza 440026, Russia

Received 12 November 2014; Accepted 22 January 2015

Academic Editor: Ivan Avramidi

Copyright © 2015 E. Yu. Smol’kin and D. V. Valovik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper focuses on the problem of monochromatic electromagnetic TM wave propagation in a two-layer circular cylindrical dielectric waveguide. The space outside the waveguide is filled with isotropic medium having constant permittivity. The inner core of the waveguide is filled with isotropic medium having constant permittivity; the cladding of the core is filled with isotropic inhomogeneous nonlinear permittivity (the nonlinear term is expressed by Kerr law). Existence of guided modes which depend harmonically on z (the waveguide axis coincides with z-axis) is proved and their localization is found. Numerical results including different type of nonlinearities are presented. A comparison with the linear case is given. The existence of a new propagation regime is predicted.