This article is cited in 3 papers

On the problem of propagation of nonlinear coupled TE–TM waves in a layer

D. V. Valovik, Yu. G. Smirnov

Penza State University, ul. Krasnaya 40, Penza, 440026, Russia

Abstract: 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.

Key words: Maxwell’s equations, coupled TE-TM wave, nonlinear two-parameter eigenvalue problem, layered dielectric waveguide, Kerr nonlinearity.

UDC: 519.634

Received: 15.03.2013

DOI: 10.7868/S0044466914030181

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:3, 522–536

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