Computational Mathematics and Mathematical Physics

, 51:1622

Propagation of TM waves in a layer with arbitrary nonlinearity

Article

DOI: 10.1134/S096554251109017X

Cite this article as:
Valovik, D.V. Comput. Math. and Math. Phys. (2011) 51: 1622. doi:10.1134/S096554251109017X
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Abstract

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.

Keywords

nonlinear boundary eigenvalue problem for Maxwell’s equationsnonlinear layerdispersion equationnumerical-analytical solution method

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Penza State UniversityPenzaRussia