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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 1, Pages 144–162 (Mi zvmmf10514)  

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

Open waveguides in a thin Dirichlet ladder: I. Asymptotic structure of the spectrum

S. A. Nazarovabc

a St. Petersburg State Polytechnical University, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
c Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The spectra of open angular waveguides obtained by thickening or thinning the links of a thin square lattice of quantum waveguides (the Dirichlet problem for the Helmholtz equation) are investigated. Asymptotics of spectral bands and spectral gaps (i.e., zones of wave transmission and wave stopping, respectively) for waveguides with variously shaped periodicity cells are found. It is shown that there exist eigenfunctions of two types: localized around nodes of a waveguide and on its links. Points of the discrete spectrum of a perturbed lattice with eigenfunctions concentrated about corners of the waveguide are found.

Key words: square lattice of quantum waveguides, open waveguides, spectrum, asymptotics, spectral gaps, trapped modes.

Funding Agency Grant Number
Saint Petersburg State University 0.38.237.2014


DOI: https://doi.org/10.7868/S0044466917010136

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:1, 156–174

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 24.10.2015

Citation: S. A. Nazarov, “Open waveguides in a thin Dirichlet ladder: I. Asymptotic structure of the spectrum”, Zh. Vychisl. Mat. Mat. Fiz., 57:1 (2017), 144–162; Comput. Math. Math. Phys., 57:1 (2017), 156–174

Citation in format AMSBIB
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\crossref{https://doi.org/10.7868/S0044466917010136}
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\pages 156--174
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    This publication is cited in the following articles:
    1. S. A. Nazarov, “Open waveguides in a thin Dirichlet lattice: II. Localized waves and radiation conditions”, Comput. Math. Math. Phys., 57:2 (2017), 236–252  mathnet  crossref  crossref  isi  elib
    2. Nazarov S.A., Taskinen J., “Essential Spectrum of a Periodic Waveguide With Non-Periodic Perturbation”, J. Math. Anal. Appl., 463:2 (2018), 922–933  crossref  mathscinet  zmath  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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