This article is cited in 9 papers

Propagation of electromagnetic waves in an open planar dielectric waveguide filled with a nonlinear medium II: TM waves

D. V. Valovik

Penza State University, Penza, 440026 Russia

Abstract: A nonlinear eigenvalue problem on an interval is considered. The nonlinearity in the equation is specified by a nonnegative monotonically increasing function, and the boundary conditions nonlinearly depend both on the sought-for functions and on the spectral parameter. The discrete eigenvalues are defined using an additional (local) condition at one end of the interval. This problem describes the propagation of monochromatic (polarized) electromagnetic TM waves in a planar dielectric waveguide filled with a nonlinear medium. The nonlinearity covers a wide range of laws of nonlinear optics corresponding to self-interaction effects. Results on the solvability of the problem and the properties of the eigenvalues are obtained.

Key words: Maxwell’s equations, nonlinear eigenvalue problem, nonlinear Sturm–Liouville problem, asymptotics of eigenvalues, comparison theorem, planar dielectric waveguide, nonlinear permittivity.

UDC: 517.927.4

Received: 13.06.2019
Revised: 13.06.2019
Accepted: 18.11.2019

DOI: 10.31857/S0044466920030163

 English version: Computational Mathematics and Mathematical Physics, 2020, 60:3, 427–447

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