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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 3, Pages 429–450
DOI: https://doi.org/10.31857/S0044466920030163 (Mi zvmmf11046) 		 
This article is cited in 8 scientific papers (total in 8 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
Full-text PDF Citations (8)
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DOI: https://doi.org/10.31857/S0044466920030163
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.
Funding agency Grant number
Russian Science Foundation 18-71-10015
This work was supported by the Russian Science Foundation, project no. 18-71-10015.
Received: 13.06.2019
Revised: 13.06.2019
Accepted: 18.11.2019
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 3, Pages 427–447
DOI: https://doi.org/10.1134/S0965542520030161
Bibliographic databases:
Document Type: Article
UDC: 517.927.4
Language: Russian
Citation: D. V. Valovik, “Propagation of electromagnetic waves in an open planar dielectric waveguide filled with a nonlinear medium II: TM waves”, Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020), 429–450; Comput. Math. Math. Phys., 60:3 (2020), 427–447
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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