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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 3, Pages 429–450 (Mi zvmmf11046)  

This article is cited in 1 scientific paper (total in 1 paper)

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: MaxwellТs 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.


DOI: https://doi.org/10.31857/S0044466920030163


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

Bibliographic databases:

UDC: 517.927.4
Received: 13.06.2019
Revised: 13.06.2019
Accepted:18.11.2019

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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\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 60
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\pages 429--450
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\crossref{https://doi.org/10.31857/S0044466920030163}
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\vol 60
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\pages 427--447
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Valovik, “On the integral characteristic function of the Sturm-Liouville problem”, Sb. Math., 211:11 (2020), 1539–1550  mathnet  crossref  crossref  mathscinet  isi  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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