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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.
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10514 https://www.mathnet.ru/eng/zvmmf/v57/i1/p144
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Abstract page: | 365 | Full-text PDF : | 82 | References: | 68 | First page: | 31 |
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