Geodesic
Propagation of TM waves in a layer with arbitrary nonlinearity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1729-1739

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A boundary value problem for Maxwell’s equations describing propagation of TM waves in a nonlinear dielectric layer with arbitrary nonlinearity is considered. The layer is located between two linear semi-infinite media. The problem is reduced to a nonlinear boundary eigenvalue problem for a system of second-order nonlinear ordinary differential equations. A dispersion equation for the eigenvalues of the problem (propagation constants) is derived. For a given nonlinearity function, the dispersion equation can be studied both analytically and numerically. A sufficient condition for the existence of at least one eigenvalue is formulated. 
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     author = {D. V. Valovik},
     title = {Propagation of {TM~waves} in a~layer with arbitrary nonlinearity},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1729--1739},
     publisher = {mathdoc},
     volume = {51},
     number = {9},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a13/}
}
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D. V. Valovik. Propagation of TM waves in a layer with arbitrary nonlinearity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1729-1739. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a13/