+7 (495) 957-77-43
Контакты

Article 7-8-2019

Извините, этот техт доступен только в “Американский Английский”. For the sake of viewer convenience, the content is shown below in the alternative language. You may click the link to switch the active language.

USE OF PATTERN EQUATION METHOD FOR THE ANALYSIS
OF SCAT-TERING ON A THIN DIELECTRIC CYLINDER

Dmitry B. Demin, Moscow Technical University of Communications and Informatics, Moscow, Russia, dbdemin@gmail.com
Andrey I. Kleev,  P.L. Kapitza Institute for Physical Problems, Russian Academy of Sciences, Moscow, Russia, kleev@kapitza.ras.ru
Alexander G. Kyurkchyan,  Moscow Technical University of Communications and Informatics; Kotel’nikov Institute of Radio Engineering and Electronics,
Fryazino Branch; Central Research Institute of Communication FSUE, Moscow, Russia, agkmtuci@yandex.ru

 

Abstract
Electromagnetic scattering by small particles is an important key problem of the diffraction theory. From the moment of occurrence of the first papers on this subject and up to now, the most widely used mathematical model, applied for solution to a problem of scattering on small objects, is dipole approximation (Rayleigh approximation). This approach is quite detailed for particular cases of scattering on spheres and ellipsoids when solution to an associated electrostatic problem can be obtained explicitly. It should be noted that problem solution in electrostatic approximation in a general case is a complicated problem in itself and labor input for its solution is comparable to the labor input for solution of an initial wave problem. The existing methods for its solution have a range of fundamental limitations. This paper develops methodology based on the use of pattern equation method (PEM) which was initially proposed in 1992. It was clearly demonstrated in a significant number of publications that PEM has important advantages over multiple alternative methods and is quite efficient for solving a wide range of problems. While building up a new approach to the analysis of scattering on small bodies, we used a high convergence of PEM, established in the above papers. Indeed, as was demonstrated by previous works of the authors of the given article, in order to solve a problem of scat-tering on impedance bodies, the typical size of which is comparable to the primary field wavelength, it is sufficient to consider one to three summands in the scattering pattern decomposition, depending on polarization of an incident field. This circumstance allowed obtaining explicit formulas for integrated scattering characteristics, applicable for impedance scatterers of complex shape. This paper develops approximated method of calculation of integrated characteristics of scattering on thin dielectric cylinders, based on the use of PEM. Explicit formulas were obtained for integrated scattering characteristics, which are applied to dielectric cylinders with arbitrary cross section. Applicability of the obtained ratios is analyzed by a range of examples: scattering on an elliptic cylinder and scattering on a cylinder, the cross section of which has a shape of superellipse. As shown by the presented re-sults, the obtained approximated relations are quite accurate in a wide range of problem parameters.

Keywords:Light scattering by small particles, Rayleigh approximation, Pattern Equation Method, electromagnetic scattering, numerical methods in diffraction theory.

References

 

  1. Landau L.D. and Lifshitz E.M. (1984). Electrodynamics of Continuous Media. Pergamon, Oxford and New York. 460 p.
  2. van de Hulst H.C. (1957). Light scattering by small particles. New York (John Wiley and Sons), London (Chapman and Hall. 470 p.
  3. Bohren C.F., Huffman D.R. (1998). Absorption and Scattering of Light by Small Particles. New York (John Wiley and Sons). 544 p.
  4. Mishchenko M.I., Hovenier J.W., Travis L.D. (2000). Light Scattering by Nonspherical Particles. San Diego: Academic Press. 690 p.
  5. Farafonov V.G., Ustimov V.I. (2015). Analysis of the extended boundary condition method: an electrostatic problem for Chebyshev particles. Optics and Spectroscopy. Vol. 118. No. 3, р 445-459.
  6. Kyurkchan A.G. (1992). A new integral equation in the diffraction theory. Soviet Physics-Doklady, vol. 37, no 7, pp. 338-340.
  7. Kyurkchan A.G. (1994). On a method of solution to the problem of wave diffraction by finite-size scatterers. Physics-Doklady,
    39, no 8, pp. 546-549.
  8. Kyurkchan A.G., Kleev A.I. (1995). Solution of the Problems of Wave Diffraction on Finite Scatterers with the Method of Diagram Equations. Radiotekhnika i elektronika. Vol. 40. No. 6. Pp. С. 897-
  9. Kyurkchan A.G., Smirnova N.I. (2015). Mathematical Modeling in Diffraction Theory Based on A Priori Information on the Analytic Properties of the Solution. Amsterdam: Elsevier. 280 p.
  10. Kleev A.I., A.B. Manenkov A.B. (1986). Adaptive Collocation Method in 2D Diffraction Problems. Radiophysics and Quantum. Vol. 29. No. 5. Pp. 557-565.
  11. Dmitriev V.I., Zakharov E.V. (1987). Integral Equations in Boundary Problems of Electrodynamics. Мoscow: MSU Publishing House.
  12. Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, Ed. By M. Abramovitz and I.A. Stegun (Dover, New York, 1964) 1046 p.
  13. Demin D.B., Kleev A.I., Kyurkchan A.G. (2016). Use of Pattern Equation Method for Analysis of Scattering on Small Particles of a Complex Shape. T-Comm. 10, No. 10, рp. 38-42.
  14. Demin D.B., Kleev A.I., Kyurkchan A.G. (2017). Modeling of electromagnetic scattering by thin cylinders using Pattern Equation Method. Journal of Quantitative Spectroscopy and Radiative Transfer. Vol. 187, No. 1, р 287-292.
  15. Demin D.B., Kleev A.I., Kyurkchan A.G. (2018). Application of the Pattern Equation Method to the Analysis of Electromagnetic Wave Scattering by a Thin Cylinder of an Arbitrary Cross Section. Journal of Communication Technology and Electronics. 63, No. 6, рp. 505-512.
  16. Demin D.B., Kleev A.I., Kyurkchan A.G. (2017). Solution of Electromagnetic Problems of Diffraction on Small Particles of a Complex Shape Using Pattern Equation Method. T-Comm. 11, No. 5, рp. 26-32.
  17. Demin D.B., Kleev A.I., Kyurkchan A.G.(2019). Construction of the Approximate Solution to the Problems of Diffraction of Electromagnetic Waves by Small Particles with the Use of the Pattern Equation Method. Journal of Communication Technology and Electronics. Vol. 64, No. 1, р 13-19.
  18. Farafonov V.G. (2000). Light scattering by multilayer ellipsoid in the Rayleigh approximation. Optics and Spectroscopy. Vol. 88. No. 3, р 441-443.
  19. Farafonov V.G. (2001). New recursive solution of the problem of scattering of electromagnetic radiation by multilayer spheroidal particles. Optics and Spectroscopy. Vol. 90. No. 5, р 743-752.
  20. Posselt В., Farafonov V.G., Il’in V.B., ProkopjevaM.S. (2002). Light scattering by multi-layered ellipsoidal particles in the quasistatic approximation. Sci. Technol. Vol. 13,
    рр. 256-262.

Information about authors:
Dmitry B. Demin, Moscow Technical University of Communications and Informatics, Associate Professor, Cand. Sc., Moscow, Russia
Andrey I. Kleev, P.L. Kapitza Institute for Physical Problems, Russian Academy of Sciences, Moscow, Russia
Alexander G. Kyurkchyan, Moscow Technical University of Communications and Informatics; Kotel’nikov Institute of Radio Engineering and Electronics, Fryazino Branch; Central Research Institute of Communication FSUE, Head of Chair, Doctor of Science, Moscow, Russia