Geodesic
A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 70-74

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We consider the propagation of TM-polarized electromagnetic waves in a nonlinear dielectric layer located between two linear media. The nonlinearity in the layer is described by the Kerr law. We reduce the problem to a nonlinear boundary eigenvalues problem for a system of ordinary differential equations. We obtain a dispersion relation and a first approximation for eigenvalues of the problem. We compare the results with those obtained for the case of a linear medium in the layer.
Mots-clés : dispersion relation
Keywords: boundary value problem, Kerr nonlinearity. 
@article{IVM_2008_10_a7,
     author = {D. V. Valovik and Yu. G. Smirnov},
     title = {A nonlinear boundary eigenvalues problem for {TM-polarized} electromagnetic waves in a nonlinear layer},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {70--74},
     publisher = {mathdoc},
     number = {10},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_10_a7/}
}
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D. V. Valovik; Yu. G. Smirnov. A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 70-74. http://geodesic.mathdoc.fr/item/IVM_2008_10_a7/