Investigation of problems of electromagnetic wave scattering by conductive strip gratings using integral equation method

George Koshovy; Andrew Koshovy; Oksana Ahapova

doi:10.3103/S0735272723080022

Authors

George Koshovy O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine https://orcid.org/0000-0001-7991-8591
Andrew Koshovy O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine
Oksana Ahapova O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine

DOI:

https://doi.org/10.3103/S0735272723080022

Keywords:

electromagnetic wave scattering, analytical and asymptotic methods, strip gratings, integral equations

Abstract

A detailed study of the problem of scattering of a plane-polarized electromagnetic wave by systems of conductive strips with impedance forming a plane grating is carried out. Two correct general mathematical models of scattering by conductive gratings were developed in a system of singular integral equations. The first modification of the method of integral equations is related to the simpler case of scattering of an E-polarized wave by a conducting strip grating. A simple and correct mathematical model of scattering in the form of a system of singular integral equations was obtained. The diagonal kernel functions of this system have a logarithmic feature, which is considered weak. The second modification is developed for the more complicated case of H-polarized wave scattering by a conducting strip grating. A more complex mathematical model of scattering in the form of a system of integral equations was obtained. The diagonal kernel functions of this system have a strong or Cauchy-type singularity. In this polarization case, two sets of additional conditions arise to ensure the correctness of the mathematical model. In order to check the correctness of the solution of electromagnetic wave scattering problems, it is important to obtain it in an explicit analytical form, even under certain assumptions that narrow the frequency range of the application of mathematical models. The asymptotic models of wave scattering by a single narrow strip with impedance and a weakly filled grating were developed. To show the asymptotic model effectiveness, the algorithms for calculating the directional characteristics are developed and simulations were performed.

References

V. P. Shestopalov, L. N. Lytvynenko, S. A. Masalov, V. G. Sologub, Wave Diffraction by Gratings, [in Ukrainian]. Kharkiv: Vyd-vo Khark. Derzh. Un-ta, 1973.

V. P. Shestopalov, A. A. Kyrylenko, S. A. Masalov, Y. K. Syrenko, “Diffraction Gratings, Vol. 1,” in Resonance Wave Scattering, Kiev: Naukova Dumka, 1986.

M. I. Andriychuk, S. W. Indratno, A. G. Ramm, “Electromagnetic wave scattering by a small impedance particle: Theory and modeling,” Opt. Commun., vol. 285, no. 7, pp. 1684–1691, 2012, doi: https://doi.org/10.1016/j.optcom.2011.12.055.

Y. V. Gandel’, V. D. Dushkin, “Mathematical model of scattering of polarized waves on impedance strips located on a screened dielectric layer,” J. Math. Sci., vol. 212, no. 2, pp. 156–166, 2016, doi: https://doi.org/10.1007/s10958-015-2656-2.

M. E. Kaliberda, L. M. Lytvynenko, S. A. Pogarsky, “Modeling of graphene planar grating in the THz range by the method of singular integral equations,” Frequenz, vol. 72, no. 5–6, pp. 277–284, 2018, doi: https://doi.org/10.1515/freq-2017-0059.

D. Colton, R. Kress, Integral Equation Methods in Scattering Theory. New York et al.: John Wiley & Sons, 1983.

Y. V. Gandel’, “Boundary-value problems for the Helmholtz equation and their discrete mathematical models,” J. Math. Sci., vol. 171, no. 1, pp. 74–88, 2010, doi: https://doi.org/10.1007/s10958-010-0127-3.

H. Hönl, A. W. Maue, K. Westpfahl, “Theorie der Beugung,” in Encyclopedia of Physics, Vol 5 / 25 / 1, Berlin, Heidelberg: Springer, 1987, pp. 218–573.

H. J. Eom, Electromagnetic Wave Theory for Boundary-Value Problems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004, doi: https://doi.org/10.1007/978-3-662-06943-1.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves. Wiley-IEEE Press, 2001.

G. I. Koshovy, A. G. Koshovy, “The Carleman regularization technique in the modelling of the plane E‐polarized electromagnetic wave scattering by a flat system of impedance strips,” IET Microwaves, Antennas Propag., vol. 15, no. 10, pp. 1218–1224, 2021, doi: https://doi.org/10.1049/mia2.12156.

G. I. Koshovy, “The plane H-polarized electromagnetic wave scattering by pre-fractal grating of impedance strips,” Int. J. Microw. Wirel. Technol., vol. 12, no. 10, pp. 969–975, 2020, doi: https://doi.org/10.1017/S1759078720000598.

G. I. Koshovy, “The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips,” IET Microwaves, Antennas Propag., vol. 15, no. 10, pp. 1310–1317, 2021, doi: https://doi.org/10.1049/mia2.12167.

F. D. Gakhov, Boundary-Value Problems. Oxford: Pergamon Press, 1977.

N. I. Muskhelishvili, Singular Integral Equations. Groningen: Noordhoff Publ., 1953.

V. V. Panasiuk, M. P. Savruk, Z. T. Nazarchuk, Method of Special Integral Equations in Two-Dimensional Diffraction Problems, [in Ukrainian]. Kyiv: Naukova Dumka, 1984.

Z. T. Nazarchuk, Numerical Investigation of Wave Diffraction by Cylindrical Structures, [in Ukrainian]. Kyiv: Naukova Dumka, 1989.

I. K. Lifanov, Singular Integral Equations and Discrete Vortices. Utrecht: De Gruyter, 1996, doi: https://doi.org/10.1515/9783110926040.

G. I. Koshovy, “Asymptotic models of weakly filled PFSG,” in 2016 XXIst International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2016, pp. 169–172, doi: https://doi.org/10.1109/DIPED.2016.7772247.

M. Andriychuk, “Asymptotic regularisation of the solution to the problem of electromagnetic field scattering from a set of small impedance particles,” IET Microwaves, Antennas Propag., vol. 15, no. 10, pp. 1330–1346, 2021, doi: https://doi.org/10.1049/mia2.12171.

G. I. Koshovy, A. G. Koshovy, “The regularization technique in modeling of the plane E-polarized EM wave scattering by coplanar system of electrically conducting flat strips,” Appl. Sci., vol. 13, no. 9, p. 5488, 2023, doi: https://doi.org/10.3390/app13095488.

O. O. Ahapova, G. I. Koshovy, “On EM wave scattering by coplanar system of flat impedance strips,” in 2020 IEEE 40th International Conference on Electronics and Nanotechnology (ELNANO), 2020, pp. 34–37, doi: https://doi.org/10.1109/ELNANO50318.2020.9088752.

G. I. Koshovy, A. G. Koshovy, O. O. Ahapova, “On the plane E-polarized EM wave scattering by flat impedance strip gratings,” in 2022 IEEE 41st International Conference on Electronics and Nanotechnology (ELNANO), 2022, pp. 43–46, doi: https://doi.org/10.1109/ELNANO54667.2022.9926997.