Various Manifestations of Wood Anomalies in Locally Distorted Quantum Waveguides View Full Text


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Article Info

DATE

2018-11

AUTHORS

S. A. Nazarov

ABSTRACT

Anomalies of the diffraction pattern at near-threshold frequencies of the continuous spectrum of a cylindrical quantum waveguide with regular (smooth gentle) or singular (small cavities and bumps) perturbations of the boundary are studied. Wood anomalies are characterized by rapid variations in the scattering matrix near the thresholds. Conditions under which a Wood anomaly is absent, appears, and enhances are obtained by constructing asymptotics of solutions to the Dirichlet problem for the Helmholtz equation. The results are obtained by analyzing an artificial object—the augmented scattering matrix—and involve only operations with real values of the spectral parameter, but the relation between Wood anomalies and complex resonance points is also considered. Generated by almost standing waves, threshold resonances that cause near-threshold anomalies of other types are discussed. More... »

PAGES

1838-1855

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s096554251811009x

DOI

http://dx.doi.org/10.1134/s096554251811009x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110397546


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