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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 3, Pages 460–468 (Mi zvmmf10173)  

This article is cited in 6 scientific papers (total in 6 papers)

Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides

Yu. G. Smirnov

Penza State University, ul. Krasnaya 40, Penza, 440026, Russia

Abstract: Problems on the propagation of surface TE and TM waves in an inhomogeneous anisotropic two-layered planar or cylindrical magneto-dielectric waveguide are considered. The problem is reduced to the analysis of a Sturm–Liouville problem of a special kind with boundary conditions of the third kind, nonlinearly depending on the spectral parameter. The conditions under which TE and TM waves can propagate are obtained, and the regions of localization of the corresponding propagation constants are determined.

Key words: electromagnetic wave propagation, Sturm–Liouville problem, spectral problem, waveguide.

DOI: https://doi.org/10.7868/S0044466915030187

Full text: PDF file (679 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:3, 461–469

Bibliographic databases:

UDC: 519.634
MSC: Primary 78A50; Secondary 34B24, 35P05, 35Q60
Received: 12.02.2014

Citation: Yu. G. Smirnov, “Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015), 460–468; Comput. Math. Math. Phys., 55:3 (2015), 461–469

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Valovik, E. Yu. Smol'kin, “Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide”, Comput. Math. Math. Phys., 57:8 (2017), 1294–1309  mathnet  crossref  crossref  isi  elib
    2. D. V. Valovik, “Nonlinear multi-frequency electromagnetic wave propagation phenomena”, J. Opt., 19:11 (2017), 115502  crossref  mathscinet  isi
    3. Yu. G. Smirnov, D. V. Valovik, “Nonlinear coupled wave propagation in a $n$-dimensional layer”, Appl. Math. Comput., 294 (2017), 146–156  crossref  mathscinet  isi
    4. Yu. Smirnov, E. Smolkin, Yu. Shestopalov, “On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium”, J. Electromagn. Waves Appl., 32:11 (2018), 1389–1408  crossref  isi
    5. T. K. Yuldashev, “Spektralnye osobennosti resheniya odnoi kraevoi zadachi dlya integro-differentsialnogo uravneniya Fredgolma vtorogo poryadka s otrazheniem argumenta”, Izv. IMI UdGU, 54 (2019), 122–134  mathnet  crossref  elib
    6. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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