Various manifestations of Wood anomalies in locally distorted quantum waveguides
S. A. Nazarov
St. Petersburg State University, St. Petersburg, Russia
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.
quantum waveguide, regular and singular perturbations of the boundary, asymptotics, resonances, near-threshold frequencies, Wood anomaly.
Computational Mathematics and Mathematical Physics, 2018, 58:11, 1838–1855
S. A. Nazarov, “Various manifestations of Wood anomalies in locally distorted quantum waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018), 1911–1931; Comput. Math. Math. Phys., 58:11 (2018), 1838–1855
Citation in format AMSBIB
\paper Various manifestations of Wood anomalies in locally distorted quantum waveguides
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|