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I. T. Gokhberg and M. G. Krein, “Introduction in the Theory of Linear Nonselfadjoint Operators in Hilbert Space,” American Mathematical Society, Providence, 1969.

has been cited by the following article:

• TITLE: Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer

  AUTHORS: Yury G. Smirnov, Dmitry V. Valovik

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

  JOURNAL NAME: Applied Mathematics, Vol.1 No.1, June 2, 2010

  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.