Open waveguides in doubly periodic junctions of domains with different limit dimensions

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Open waveguides in doubly periodic junctions of domains with different limit dimensions. / Bakharev, F. L.; Nazarov, S. A.

In: Siberian Mathematical Journal, Vol. 57, No. 6, 01.11.2016, p. 943-956.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{f904d6a2e75143379adaafba8d15f90b,

title = "Open waveguides in doubly periodic junctions of domains with different limit dimensions",

abstract = "Considering the spectral Neumann problem for the Laplace operator on a doubly periodic square grid of thin circular cylinders (of diameter ε ≪ 1) with nodes, which are sets of unit size, we show that by changing or removing one or several semi-infinite chains of nodes we can form additional spectral segments, the wave passage bands, in the essential spectrum of the original grid. The corresponding waveguide processes are localized in a neighborhood of the said chains, forming I-shaped, V-shaped, and L-shaped open waveguides. To derive the result, we use the asymptotic analysis of the eigenvalues of model problems on various periodicity cells.",

keywords = "doubly periodic grid, localized waves, open waveguides, spectral Neumann problem",

author = "Bakharev, {F. L.} and Nazarov, {S. A.}",

note = "Bakharev, F.L., Nazarov, S.A. Open waveguides in doubly periodic junctions of domains with different limit dimensions. Sib Math J 57, 943–956 (2016). https://doi.org/10.1134/S0037446616060021",

year = "2016",

month = nov,

day = "1",

doi = "10.1134/S0037446616060021",

language = "English",

volume = "57",

pages = "943--956",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - Open waveguides in doubly periodic junctions of domains with different limit dimensions

AU - Bakharev, F. L.

AU - Nazarov, S. A.

N1 - Bakharev, F.L., Nazarov, S.A. Open waveguides in doubly periodic junctions of domains with different limit dimensions. Sib Math J 57, 943–956 (2016). https://doi.org/10.1134/S0037446616060021

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Considering the spectral Neumann problem for the Laplace operator on a doubly periodic square grid of thin circular cylinders (of diameter ε ≪ 1) with nodes, which are sets of unit size, we show that by changing or removing one or several semi-infinite chains of nodes we can form additional spectral segments, the wave passage bands, in the essential spectrum of the original grid. The corresponding waveguide processes are localized in a neighborhood of the said chains, forming I-shaped, V-shaped, and L-shaped open waveguides. To derive the result, we use the asymptotic analysis of the eigenvalues of model problems on various periodicity cells.

AB - Considering the spectral Neumann problem for the Laplace operator on a doubly periodic square grid of thin circular cylinders (of diameter ε ≪ 1) with nodes, which are sets of unit size, we show that by changing or removing one or several semi-infinite chains of nodes we can form additional spectral segments, the wave passage bands, in the essential spectrum of the original grid. The corresponding waveguide processes are localized in a neighborhood of the said chains, forming I-shaped, V-shaped, and L-shaped open waveguides. To derive the result, we use the asymptotic analysis of the eigenvalues of model problems on various periodicity cells.

KW - doubly periodic grid

KW - localized waves

KW - open waveguides

KW - spectral Neumann problem

UR - http://www.scopus.com/inward/record.url?scp=85007110004&partnerID=8YFLogxK

U2 - 10.1134/S0037446616060021

DO - 10.1134/S0037446616060021

M3 - Article

AN - SCOPUS:85007110004

VL - 57

SP - 943

EP - 956

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -

ID: 34905613