Open waveguides in a thin Dirichlet lattice: II. localized waves and radiation conditions

Wave processes localized near an angular open waveguide obtained by thickening two perpendicular semi-infinite rows of ligaments in a thin square lattice of quantum waveguides (Dirichlet problem for the Helmholtz equation) are investigated. Waves of two types are discovered: the first are observed n...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2017-02, Vol.57 (2), p.236-252
Main Author: Nazarov, S. A.
Format: Article
Language:English
Subjects:
Algebraic group theory
Computational mathematics
Computational Mathematics and Numerical Analysis
Dirichlet problem
Eigenvalues
Helmholtz equations
Lattice theory
Lattices (mathematics)
Ligaments
Mathematical models
Mathematics
Mathematics and Statistics
Oscillations
Physics
Radiation
Representations
Rest
Studies
Theorems
Waveguides
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Summary:Wave processes localized near an angular open waveguide obtained by thickening two perpendicular semi-infinite rows of ligaments in a thin square lattice of quantum waveguides (Dirichlet problem for the Helmholtz equation) are investigated. Waves of two types are discovered: the first are observed near the lattice nodes and almost do not affect the ligaments, while the second, on the contrary, excite oscillations in the ligaments, whereas the nodes stay relatively at rest. Asymptotic representations of the wave fields are derived, and radiation conditions are imposed on the basis of the Umov–Mandelstam energy principle.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542517020129