Kotelnikov Institute of Radio Engineering and Electronics of RAS Русский Sign in Submit a paper
Journal of Radio Electronics Online scientific journal · eISSN 1684-1719
2026, № 2 · ELECTRODYNAMICS

A technique for obtaining a high-precision heuristic solution to the problem of diffraction on a half-plane with non-ideal boundary conditions

M.V. Vesnik1

1 Kotelnikov IRE RAS, Moscow, Russia
Full text DOI: 10.30898/1684-1719.2026.2.13 UDC 537.874.6 EDN TPMXJK

Abstract

A new technique for obtaining a precise heuristic formula for solving the problem of diffraction of an electromagnetic wave on a half-plane with non-ideal boundary conditions employing the recently developed method of fundamental components is proposed. As a primary heuristic formula, we take a combination of the reflection and transmission coefficients for an infinite plane with non-ideal boundary conditions and the known expression for the diffraction coefficient of a perfectly conducting half-plane. The technique for refining the primary heuristic formula represents a linear combination of two types of heuristic formulas in order to zero the scattering pattern at the margins while retaining the previously found values at the singularity points. The effectiveness of this method of refining is illustrated by solving the problem of diffraction of an electromagnetic wave on a half-plane with generalized two-sided impedance boundary conditions.

  • boundary value problems
  • electromagnetic diffraction
  • heuristic approaches in diffraction theory
  • impedance boundary conditions
  • physical theory of diffraction
  • surface impedance
Аннотация (на русском)

Методика получения уточненного эвристического решения в задаче дифракции на полуплоскости с неидеальными граничными условиями

Предложена новая методика получения уточненной эвристической формулы для решения задачи дифракции электромагнитной волны на полуплоскости с неидеальными граничными условиями с использованием недавно разработанного метода фундаментальных компонент. В качестве основной эвристической формулы берем комбинацию коэффициентов отражения и пропускания для бесконечной плоскости с неидеальными граничными условиями и известное выражение для коэффициента дифракции идеально проводящей полуплоскости. Методика уточнения первичной эвристической формулы представляет собой линейную комбинацию двух типов эвристических формул с целью обнуления диаграммы рассеяния на краях при сохранении ранее найденных значений в сингулярных точках. Эффективность этого метода уточнения иллюстрируется решением задачи дифракции электромагнитной волны на полуплоскости с обобщенными двусторонними импедансными граничными условиями.

For citation

Vesnik M.V. A technique for obtaining a high-precision heuristic solution to the problem of diffraction on a half-plane with non-ideal boundary conditions // Journal of Radio Electronics. – 2026. – No. 2. https://doi.org/10.30898/1684-1719.2026.2.13

References

  1. Vesnik M.V. The method of the generalized Eikonal: new approaches in the diffraction theory. Berlin: Walter de Gruyter; 2015. https://doi.org/10.1515/9783110311297
  2. Hönl H., Maue A.W., Westpfahl K. Theory of diffraction / in: S Flügge, editor. Handbuch der Physik. Berlin: Springer-Verlag; 1961. p. 218-573.
  3. Kravtsov Y.A., Zhu N.Y. Theory of diffraction: heuristic approaches. Oxford: Alpha Science Int.; 2010. ISBN 978-1-84265-372-2
  4. Born M., Wolf E. Principles of optics. Oxford, London: Pergamon Press: 1968.
  5. Keller J.B. Geometrical theory of diffraction // J Opt Soc Am. 1962;52(2):116-130. https://doi.org/10.1364/JOSA.52.000116
  6. James G.L. Geometrical Theory of Diffraction for Electromagnetic Waves. London: Peter Peregrinus Ltd.; 1976.
  7. Borovikov V.A., Kinber B.E. Geometrical Theory of Diffraction. London, UK: IEE; 1994.
  8. Ufimtsev P.Y. Method of edge waves in the physical theory of diffraction. Moscow: Sovetskoe Radio; 1962; US Air Force Foreign Technology Division, 1-1154.
  9. Ufimtsev P.Y. Theory of Edge Diffraction in Electromagnetics. Encino, California: Tech Science Press; 2003.
  10. Ufimtsev P.Y. Fundamentals of the Physical Theory of Diffraction. Hoboken, N.J.: John Wiley & Sons, Inc.; 2007.
  11. Pelosi G., Rahmat-Samii Y., Volakis J.L. High-Frequency Techniques in Diffraction Theory: 50 Years of Achievements in GTD, PTD, and Related Approaches // IEEE Antennas Propag. Magazine, Vol. 55, Issue 3, June 2013 https://doi.org/10.1109/MAP.2013.6586620
  12. Vesnik M.V. Physical interpretation of strict solutions of diffraction problems by heuristic relations // J Math Sci. Vol. 239, pp. 751-770, May 2019, https://doi.org/10.1007/s10958-019-04324-8
  13. Senior T.B.A. Half plane edge diffraction. Radio Sci., Vol. 10(6), p. 645, 1975.
  14. Senior T.B.A. Diffraction tensors for imperfectly conducting edges. Radio Sci., Vol.10(10), p. 911, 1975.
  15. Voitovich N.N., Katsenelenbaum B.Z., Korshunova E.N., et al. Electromagnetics of antennas with semitransparent surfaces. A method of constructive synthesis. Moscow: Nauka; 1989.
  16. Bankov S.E.Integrated Microwave Optics. Moscow: Fizmatlit; 2018.
  17. Klionovski K., Bankov S. Electromagnetic wave scattering by a half-plane with generalized semitransparent boundary conditions // Waves in Random and Complex Media, Vol. 32, no. 5, pp. 2245-2256, 2022. https://doi.org/10.1080/17455030.2020.1849867
  18. Vesnik M.V. Using the method of base components for a heuristic solution to the diffraction problem on a half-plane with nonideal boundary conditions // J Commun Technol Electron. Vol. 64, pp.1211-1217, Nov. 2019 https://doi.org/10.1134/S106422691911024X
  19. Bankov S.E., Vesnik M.V., Kravchenko V.F. Heuristic solution to the diffraction problem on a superconducting half-plane // J Commun Technol Electron., Vol. 65(4), pp. 398-405, May 2020 https://doi.org/10.1134/S1064226920040014
  20. Vesnik M.V. On the Possibility of Employing Heuristic Approaches to Obtain Highly Accurate Analytical Solutions // IEEE 8th All-Russian Microwave Conference (RMC), Moscow, Russian Federation. pp. 322-325, 2022, https://doi.org/10.1109/RMC55984.2022.10079524
  21. Vesnik M.V., Bankov S.E. Heuristic solution to the problem of diffraction of a TE-polarized electromagnetic wave on a semitransparent half-plane // Waves in Random and Complex Media. 2021. https://doi.org/10.1080/17455030.2021.1951888
  22. Vesnik M.V. Physical Interpretation of the Solution to the Problem of Diffraction on the Impedance Half-plane // 7th All-Russian Microwave Conference (RMC), Moscow, Russia. 2020. pp. 200-202, https://doi.org/10.1109/RMC50626.2020.9312342
  23. Vesnik M.V. Physical Interpretation of the Solution to the Problem of Diffraction on a Half-plane with Non-Ideal Boundary Conditions // Journal of Engineering Research and Sciences. 2022. vol. 1, no. 3, pp. 52-58 https://doi.org/10.55708/js0103006
  24. Vesnik M.V. New Possibilities for Constructing Heuristic Solutions to Problems of Electromagnetic Diffraction // MDPI, Eng. 2022, 3, 27-41. https://doi.org/10.3390/eng3010004
  25. Vesnik M.V. A technique for obtaining analytical heuristic solutions in problems of diffraction on two-dimensional semi-infinite objects with non-ideal boundary conditions // Waves in Random and Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2108160
  26. Vesnik M.V. Refinement of the Heuristic Solution for the Problem of TE-Polarized Electromagnetic Wave Diffraction on a Half-Plane with Two-Sided Impedance Boundary Conditions // MDPI, Eng., Vol. 4, Issue 1, 404-415, 2023, https://doi.org/10.3390/eng4010024
  27. Vesnik M.V., Bankov S.E. Heuristic solution to the problem of diffraction of a TE-polarized electromagnetic field on a half-plane with generalized two-sided impedance boundary conditions // Waves in Random and Complex Media. 1-17. https://doi.org/10.1080/17455030.2024.2366848
  28. Vesnik M.V., Bankov S.E. Heuristic solution to the problem of diffraction of a TH-polarized electromagnetic field on a half-plane with generalized two-sided impedance boundary conditions // Waves in Random and Complex Media, https://doi.org/10.1080/17455030.2024.2433624
  29. Maliuzhinets G.D. Excitation, reflection and emission of surface waves from a wedge with given face impedances // Sov Phys Doklady, Vol. 3, pp. 752-755, 1958.
  30. Norris A.N., Osipov A.V. Far-field analysis of the Malyuzhinets solution for plane and surface waves diffraction by an impedance wedge // Wave motion, Vol. 30(1): pp. 69-89, 1999. https://doi.org/10.1016/S0165-2125(98)00049-3
  31. Luebbers R.J. Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss // IEEE Trans Antennas Propag., Vol. 32, pp. 70-76, 1984. https://doi.org/10.1109/TAP.1984.1143189
  32. Holm P.D. A new heuristic UTD diffraction coefficient for nonperfectly conducting wedges // IEEE Trans. Antennas Propag., Vol. 48(8), pp. 1211 - 1219, 2000. https://doi.org/10.1109/8.884489
  33. El-Sallabi H.M., Rekanos I.T., Vainikainen P. A new heuristic diffraction coefficient for lossy dielectric wedges at normal incidence // IEEE Antennas Wirel. Propag. Lett., Vol. 1, pp. 165-168, 2002 https://doi.org/10.1109/LAWP.2002.807566
  34. Soni S., Bhattacharya A. New heuristic diffraction coefficient for modeling of wireless channel // Progr. Electromagn. Res.C. Vol. 12, pp.125-137. 2010 https://doi.org/10.2528/PIERC10010301
  35. Klionovski K., Bankov S. The solution of the problem of scattering by a semitransparent half-plane using the Malyuzhinets method // J.Commun. Technol. Electron., Vol. 66, no. 4, pp. 391-396, Apr. 2021. https://doi.org/10.1134/S1064226921040069