Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with a Nonlinear Medium II: TM Waves

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 d...

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Bibliographic Details
Published inComputational mathematics and mathematical physics Vol. 60; no. 3; pp. 427 - 447
Main Author Valovik, D. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2020
Springer Nature B.V
Subjects
Boundary conditions
Computational Mathematics and Numerical Analysis
Dielectric waveguides
Eigenvalues
Electromagnetic radiation
Mathematics
Mathematics and Statistics
Nonlinear optics
Nonlinearity
Wave propagation
nonlinear permittivity
planar dielectric waveguide
Maxwell’s equations
asymptotics of eigenvalues
nonlinear Sturm–Liouville problem
nonlinear eigenvalue problem
comparison theorem
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542520030161