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Advances in Mathematical Physics
Volume 2012, Article ID 609765, 21 pages
Research Article

Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity

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

Received 1 March 2012; Accepted 9 May 2012

Academic Editor: Vladimir B. Taranov

Copyright © 2012 Yu G. Smirnov 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 problem of electromagnetic TM wave propagation through a layer with Kerr nonlinearity is considered. The layer is located between two half-spaces with constant permittivities. This electromagnetic problem is reduced to the nonlinear boundary eigenvalue problem for ordinary differential equations. It is necessary to find eigenvalues of the problem (propagation constants of an electromagnetic wave). The dispersion equation (DE) for the eigenvalues is derived. The DE is applied to nonlinear metamaterial as well. Comparison with a linear case is also made. In the nonlinear problem there are new eigenvalues and new eigenwaves. Numerical results are presented.