Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2012/609765 |
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| _version_ | 1832567788424658944 |
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| author | Yu G. Smirnov D. V. Valovik |
| author_facet | Yu G. Smirnov D. V. Valovik |
| author_sort | Yu G. Smirnov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-48fbf0e073d74d799247840fac189446 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-48fbf0e073d74d799247840fac1894462025-02-03T01:00:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392012-01-01201210.1155/2012/609765609765Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr NonlinearityYu G. Smirnov0D. V. Valovik1Department of Mathematics and Supercomputer Modeling, Penza State University, Krasnaya Street 40, Penza 440026, RussiaDepartment of Mathematics and Supercomputer Modeling, Penza State University, Krasnaya Street 40, Penza 440026, RussiaThe 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.http://dx.doi.org/10.1155/2012/609765 |
| spellingShingle | Yu G. Smirnov D. V. Valovik Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity Advances in Mathematical Physics |
| title | Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity |
| title_full | Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity |
| title_fullStr | Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity |
| title_full_unstemmed | Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity |
| title_short | Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity |
| title_sort | nonlinear effects of electromagnetic tm wave propagation in anisotropic layer with kerr nonlinearity |
| url | http://dx.doi.org/10.1155/2012/609765 |
| work_keys_str_mv | AT yugsmirnov nonlineareffectsofelectromagnetictmwavepropagationinanisotropiclayerwithkerrnonlinearity AT dvvalovik nonlineareffectsofelectromagnetictmwavepropagationinanisotropiclayerwithkerrnonlinearity |