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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 8, Pages 1437–1450 (Mi zvmmf4736)  

This article is cited in 2 scientific papers (total in 2 papers)

Multilayered model in optics and quantum mechanics

M. D. Kovalev

N. E. Bauman Moscow State Technical University

Abstract: Three types of dispersion equations are analyzed that describe the eigenvalues of the effective refractive index of a multilayer plane optical waveguide and the energy eigenvalues of a quantum particle placed in a piecewise constant potential field. The first equation (D1) is derived by setting to zero the determinant of the system of linear equations produced by matching the solutions in the layers. The second equation (D2) is obtained using the well-known method of characteristic matrices. The third equation has been obtained in the general case by the author and is known as a multilayer equation. Simple relations between the three equations are established. It is shown that the set of roots of D2 exactly coincides with the set of eigenvalues of the multilayer problem, while the roots of D1 and the multilayer equation contain those equal to the refractive index in the optical case (or to the potential in the quantum case) in internal layers of the system, which may be superfluous. Examples are presented.

Key words: TE and TM modes in an optical waveguide, eigenvalues of the effective refractive index of a multilayered planar dielectric waveguide, quantum particle, piecewise constant potential field, steady states, energy levels.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:8, 1369–1381

Bibliographic databases:

UDC: 519.634
Received: 27.11.2008
Revised: 06.04.2009

Citation: M. D. Kovalev, “Multilayered model in optics and quantum mechanics”, Zh. Vychisl. Mat. Mat. Fiz., 49:8 (2009), 1437–1450; Comput. Math. Math. Phys., 49:8 (2009), 1369–1381

Citation in format AMSBIB
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\paper Multilayered model in optics and quantum mechanics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
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\issue 8
\pages 1437--1450
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\jour Comput. Math. Math. Phys.
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\vol 49
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\pages 1369--1381
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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. Kovalev M.D., “Chislo energeticheskikh urovnei kvantovoi chastitsy v kusochno postoyannom potentsialnom pole”, Vestnik moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N.E. Baumana. seriya: estestvennye nauki, 2011, 3–16  mathscinet  zmath  elib
    2. Zhuravleva L.M., Novozhilov A.V., Kruchinin A.S., Loginov D.A., “Proektirovanie izotopicheskikh sverkhreshetok”, Telekommunikatsii, 2013, no. 7, 12–18  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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