Geodesic
On the problem of propagation of nonlinear coupled TE–TM waves in a layer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3, pp. 504-518
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The problem of simultaneous propagation of two types of electromagnetic waves (TE and TM) in a plane dielectric waveguide filled with a nonlinear medium is considered. These polarized waves have different frequencies and different propagation constants. The physical problem is reduced to a nonlinear two-parameter transmission eigenvalue problem for Maxwell’s equations in a layer. The coupled eigenvalues are coupled propagation constants. A theorem on the existence and localization of coupled eigenvalues corresponding to coupled polarized electromagnetic waves is proved. 
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D. V. Valovik; Yu. G. Smirnov. On the problem of propagation of nonlinear coupled TE–TM waves in a layer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3, pp. 504-518. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a13/

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