Research output: Contribution to journal › Article › peer-review
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.
Original language | English |
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Pages (from-to) | 943-956 |
Number of pages | 14 |
Journal | Siberian Mathematical Journal |
Volume | 57 |
Issue number | 6 |
DOIs | |
State | Published - 1 Nov 2016 |
ID: 34905613