Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer

Affiliation(s)

Department Mathematics and Supercomputer Modeling, Penza State University, Penza, Russia.

Department Mathematics and Supercomputer Modeling, Penza State University, Penza, Russia.

Abstract

The propagation of TM-polarized electromagnetic waves in a dielectric layer filled with lossless, nonmagnetic, and isotropic medium is considered. The permittivity in the layer defines by Kerr law. We look for eigenvalues of the problem and reduce the issue to the analysis of the corresponding dispersion equation. The equivalence of the boundary eigenvalue problem and the dispersion equation is proved. We show that the solution of the problem exists and from dispersion equation it can be numerically obtained. Using this solution the components of electromagnetic field in the layer can be numerically obtained as well. Transition to the limit in the case of a linear medium in the layer is proved. Some numerical results are presented also.

The propagation of TM-polarized electromagnetic waves in a dielectric layer filled with lossless, nonmagnetic, and isotropic medium is considered. The permittivity in the layer defines by Kerr law. We look for eigenvalues of the problem and reduce the issue to the analysis of the corresponding dispersion equation. The equivalence of the boundary eigenvalue problem and the dispersion equation is proved. We show that the solution of the problem exists and from dispersion equation it can be numerically obtained. Using this solution the components of electromagnetic field in the layer can be numerically obtained as well. Transition to the limit in the case of a linear medium in the layer is proved. Some numerical results are presented also.

Keywords

Maxwell Equations, Nonlinear Boundary Eigenvalue Problem, Dispersion Equation, Nonlinear Slab (Film)

Maxwell Equations, Nonlinear Boundary Eigenvalue Problem, Dispersion Equation, Nonlinear Slab (Film)

Cite this paper

nullY. Smirnov and D. Valovik, "Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer,"*Applied Mathematics*, Vol. 1 No. 1, 2010, pp. 29-36. doi: 10.4236/am.2010.11005.

nullY. Smirnov and D. Valovik, "Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer,"

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