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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 1, Pages 144–162
DOI: https://doi.org/10.7868/S0044466917010136 (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
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DOI: https://doi.org/10.7868/S0044466917010136
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
Received: 24.10.2015
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 1, Pages 156–174
DOI: https://doi.org/10.1134/S0965542517010110
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
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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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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