О выборе параметров модели малого окна
https://doi.org/10.17586/2220-8054-2021-12-2-151-155
Аннотация
Рассмотрено рассеяние плоских волн и гауссовых пучков экраном с малым отверстием. Получены асимптотики вдали от препятствия.
Результаты могут быть полезны для описания перфорированных нанослоев и для выбора параметров модели, основанной на теории расширений операторов.
Об авторах
A. S. MelikhovaРоссия
Kroverkskiy pr. 49, St. Petersburg, 197101
M. P. Faleeva
Россия
Kroverkskiy pr. 49, St. Petersburg, 197101
I. Y. Popov
Россия
Kroverkskiy pr. 49, St. Petersburg, 197101
Список литературы
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.
Рецензия
Для цитирования:
Melikhova A.S., Faleeva M.P., Popov I.Y. О выборе параметров модели малого окна. Наносистемы: физика, химия, математика. 2021;12(2):151-155. https://doi.org/10.17586/2220-8054-2021-12-2-151-155
For citation:
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):151-155. https://doi.org/10.17586/2220-8054-2021-12-2-151-155