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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 609765, 21 pages
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.
- S. A. Akhmanov and R. V. Khokhlov, Problems of Non-Linear Optics, VINITI, Moscow, Russia, 1964, (in Russian).
- N. Bloembergen, Nonlinear Optics, W. A. Benjamin, New York, NY, USA, 1965.
- N. N. Akhmediev and A. Ankevich, Solitons, Nonlinear Pulses and Beams, Chapman and Hall, London, UK, 1997.
- A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, “Third-order nonlinear electromagnetic TE and TM guided,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, Eds., Elsevier, 1991.
- R. Y. Chiao, E. Garmire, and C. Townes, “Self-trapping of optical beams,” Physical Review Letters, vol. 13, no. 15, pp. 479–482, 1964.
- V. M. Eleonskii, L. G. Oganes’yants, and V. P. Silin, “Cylindrical nonlinear waveguides,” Soviet Journal of Experimental and Theoretical Physics, vol. 35, p. 44, 1972.
- V. M. Eleonskii and V. P. Silin, “Nonlinear theory of penetration of p-polarized waves into a conductor,” Soviet Journal of Experimental and Theoretical Physics, vol. 33, p. 1039, 1971.
- D. V. Valovik and Y. G. Smirnov, “Calculation of the propagation constants and fields of polarized electromagnetic TM waves in a nonlinear anisotropic layer,” Journal of Communications Technology and Electronics, vol. 54, no. 4, pp. 411–417, 2009.
- D. V. Valovik and Y. G. Smirnov, “Calculation of the propagation constants of TM electromagnetic waves in a nonlinear layer,” Journal of Communications Technology and Electronics, vol. 53, no. 8, pp. 934–940, 2008.
- A. Snyder and J. Love, Optical Waveguide Theory, Chapman and Hall, London, UK, 1983.
- R. I. Joseph and D. N. Christodoulides, “Exact field decomposition for TM waves in nonlinear media,” Optics Letters, vol. 12, no. 10, pp. 826–828, 1987.
- K. M. Leung and R. L. Lin, “Scattering of transverse-magnetic waves with a nonlinear film: formal field solutions in quadratures,” Physical Review B, vol. 44, no. 10, pp. 5007–5012, 1991.
- K. M. Leung, “p-polarized nonlinear surface polaritons in materials with intensity-dependent dielectric functions,” Physical Review B, vol. 32, no. 8, pp. 5093–5101, 1985.
- H. W. Schürmann and R. Schmoldt, “Optical response of a nonlinear absorbing dielectric film,” Optics Letters, vol. 21, no. 6, pp. 387–389, 1996.
- H. W. Schürmann, V. S. Serov, Y. V. Shestopalov, et al., “TE-polarized waves guided by a lossless nonlinear three-layer structure,” Physical Review E, vol. 58, no. 1, pp. 1040–1050, 1998.
- D. V. Valovik, “Propagation of electromagnetic waves in a nonlinear metamaterial layer,” Journal of Communications Technology and Electronics, vol. 56, no. 5, pp. 544–556, 2011.
- A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Physical Review A, vol. 35, no. 3, pp. 1159–1164, 1987.
- C. Qin and Z. H. Wang, “Exact dispersion relations for TM waves guided by thin dielectric films bounded by nonlinear media,” Optics Letters, vol. 18, no. 1, pp. 260–262, 1993.
- A. D. Boardman and P. Egan, “S-polarized waves in a thin dielectric film asymmetrically bounded by optically nonlinear media,” IEEE Journal of Quantum Electronics, vol. 21, no. 10, pp. 1701–1713, 1958.
- C. T. Seaton, J. Valera, R. Shoemaker, et al., “Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media,” IEEE Journal of Quantum Electronics, vol. 21, no. 7, pp. 774–783, 1985.
- V. M. Agranovich, V. S. Babichenko, and V. Ya Chernyak, “Nonlinear surface polaritons,” JETP Letters, vol. 32, pp. 532–535, 1980.
- C. T. Seaton, J. D. Valera, B. Svenson, and G. I. Stegeman, “Comparison of solutions for TM-polarized nonlinear guided waves,” Optics Letters, vol. 10, no. 3, pp. 149–150, 1985.
- R. A. Sammut and C. Pask, “Gaussian and equivalent-step-index approximations for nonlinear waveguides,” Journal of the Optical Society of America B, vol. 8, no. 2, pp. 395–402, 1991.
- A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Soviet Physics, JETP, vol. 72, pp. 896–905, 1977.
- U. Langbein, F. Lederer, T. Peschel, and H.-E. Ponath, “Nonlinear guided waves in saturable nonlinear media,” Optics Letters, vol. 10, no. 11, pp. 571–573, 1985.
- W. J. Tomlinson, “Surface wave at a nonlinear interface,” Optics Letters, vol. 5, no. 7, pp. 323–325, 1980.
- D. V. Valovik and Yu. G. Smirnov, “A nonlinear boundary eigenvalue problem for TM-polarized electromagnetic waves in a nonlinear layer,” Russian Mathematics, vol. 52, no. 10, pp. 60–63, 2008.
- D. V. Valovik and Yu. G. Smirnov, “On the propagation of TM-polarized electromagnetic waves in a nonlinear layer with the nonlinearity expressed by the Kerr law,” Journal of Communications Technology and Electronics, vol. 48, no. 12, pp. 2186–2194, 2008.
- Y. G. Smirnov and D. V. Valovik, “Boundary eigenvalue problem for maxwell equations in a nonlinear dielectric laye,” Applied Mathematics, vol. 1, no. 1, pp. 29–36, 2010.
- Y. G. Smirnov, Mathematical Methods for Electromagnetics Problems, Penza State University Press, Penza, Russia, 2010.
- Y. G. Smirnov and D. V. Valovik, Electromagnetic Wave Propagation in Nonlinear Waveguide Structures, Penza State University Press, Penza, Russia, 2011.
- H. W. Schürmann, Y. G. Smirnov, and Y. V. Shestopalov, “Propagation of TE waves in cylindrical nonlinear dielectric waveguides,” Physical Review E, vol. 71, no. 1, part 2, Article ID 016614, 2005.
- Y. G. Smirnov, H. W. Schürmann, and Y. U. 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, pp. 256–268, 2004.
- N. N. Bautin and E. A. Leontovich, Metody i Priemy Kachestvennogo Issledovaniya Dinamicheskikh Sistem na Ploskosti, Nauka, Moscow, Russia, 1990, (in Russian).
- G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book, New York, NY, USA, 1968.