On the choice of parameters for a model of small window
https://doi.org/10.17586/2220-8054-2021-12-2-151-155
Abstract
Scattering of plane waves and Gaussian beams by a screen with small opening is considered. The asymptotics far from the obstacle is obtained.
The results can be useful for description of perforated nanolayers and for fitting the model based on the operator extensions theory.
About the Authors
A. S. Melikhova
ITMO University
Russian Federation
Russian Federation
Kroverkskiy pr. 49, St. Petersburg, 197101
M. P. Faleeva
ITMO University
Russian Federation
Russian Federation
Kroverkskiy pr. 49, St. Petersburg, 197101
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Kroverkskiy pr. 49, St. Petersburg, 197101
References
1. Morse F.M., Feshbach G. Methods of theoretical physics, V. 2. Foreign Literature Publishing House, Moscow, 1960, 986 p.
2. H. Wang, Sh. Zou. Extremely low scattering cross section of a perforated silver film. Appl. Phys. Lett., 2009, 94, P. 073119.
3. Mirin N.A., Ali T.A., Nordlander P., Halas N.J. Perforated semishells: far-field directional control and optical frequency magnetic response. ACS Nano, 2010, 4(5), P. 2701–2712.
4. Kiselev A.A., Pavlov B.S. The eigenfrequencies and eigenfunctions of the Laplace operator of the Neumann problem in a system of two coupled resonators. Theor. Math. Phys., 1994, 100, P. 354–366.
5. Popov I.Yu. The extension theory and localization of resonances for the domain of trap type. Mathematics of the USSR-Sbornik, 1992, 71(1), P. 209–234.
6. Popov I.Yu. The resonator with narrow slit and the model based on the operator extensions theory. J. Math. Phys., 1992, 33(11), P. 3794–3801.
7. Gadyl’shin R.R. Influence of the position of the opening and its shape on the properties of a Helmholtz resonator. Theor. Math. Phys., 1992, 93, P. 1151–1159.
8. Borisov D., Exner P. Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold case. J. Math. Phys., 2006, 47(11), P. 113502(1-24).
9. Vorobiev A.M., Popov I.Y., Trifanova E.S. Resonance asymptotics for a pair quantum waveguides with common semitransparent perforated wall. Nanosystems: Physics, Chemistry, Mathematics, 2020, 11(6), P. 619–627.
10. Kiselev A.A., Popov I.Yu. Indefinite metrics and scattering by a domain with small aperture. Mathematical Notes, 1995, 58(6), P. 1276–1285.
11. Popov I.Yu. Helmholtz resonator and the operator extension theory in a space with an indefinite metrics. Matematicheskii sbornik, 1992, 183(3), P. 2-38; English translation in Russian Acad. Sci. Sb. Math., 1993, 75(2), P. 285–315.
12. Shondin Yu.G. Quantum mechanical models in Rn connected with extensions of the energy operator in a Pontryagin space. Teoret. Mat. Fiz., 1988, 74, P. 331–344. English transl. in Theoret. and Math. Phys., 1988, 74.
13. Faleeva M.P., Popov I.Y. On quantum bit coding by Gaussian beam modes for the quantum key distribution. Nanosystems: Physics, Chemistry, Mathematics, 2020, 11(6), P. 651–658.
14. Vasylyev D.Yu., Semenov A.A., Vogel W. Atmospheric quantum channels with weak and strong turbulence. Phys. Rev. Lett., 2016, 117, P. 090501.
15. Goncharenko A.M. Gaussian Beams of Light. Minsk, Science and Techn, 1977, 144 p.
Review
For citations:
Melikhova A.S., Faleeva M.P., Popov I.Y. On the choice of parameters for a model of small window. Nanosystems: Physics, Chemistry, Mathematics. 2021;12(2):151-156. https://doi.org/10.17586/2220-8054-2021-12-2-151-155
Views:
6
Email this article 