Open waveguides in doubly periodic junctions of domains with different limit dimensions
- Authors: Bakharev F.L.1, Nazarov S.A.2
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Affiliations:
- St. Petersburg State University
- Institute of Problems of Mechanical Engineering
- Issue: Vol 57, No 6 (2016)
- Pages: 943-956
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170818
- DOI: https://doi.org/10.1134/S0037446616060021
- ID: 170818
Cite item
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.
About the authors
F. L. Bakharev
St. Petersburg State University
Author for correspondence.
Email: f.bakharev@spbu.ru
Russian Federation, St. Petersburg
S. A. Nazarov
Institute of Problems of Mechanical Engineering
Email: f.bakharev@spbu.ru
Russian Federation, St. Petersburg