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The plane H-polarized electromagnetic wave scattering by pre-fractal grating of impedance strips

Published online by Cambridge University Press:  01 June 2020

George I. Koshovy Open the ORCID record for George I. Koshovy [Opens in a new window]
George I. Koshovy*
Affiliation:
Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, Vul. Proskury 12, Kharkiv61085, Ukraine
*
Author for correspondence: George I. Koshovy, E-mail: gikosh@gmail.com
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Abstract

The problem of the plane H-polarized electromagnetic wave scattering by flat pre-fractal impedance strips' gratings is examined. For this purpose, a mathematical model in the form of the first kind singular integral equation system is modified for correct usage. Considerable attention is focused on the asymptotic model of the H-polarized electromagnetic wave scattering by sparsely filled grating, which has an explicit solution. The scattered electromagnetic field in the far-zone is considered in details. Dependences of scattering integral characteristics on values of the strip impedance and angles of the plane H-polarized electromagnetic wave incidence upon the grating are studied.

Keywords

Analytical methodselectromagnetic wave scatteringpre-fractal modeling
Type
Research Paper
Information
International Journal of Microwave and Wireless Technologies , Volume 12 , Special Issue 10: EuMCE 2019 Special Issue (Part II) , December 2020 , pp. 969 - 975
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Copyright
Copyright © Cambridge University Press and the European Microwave Association 2020

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References

Honl, H, Maue, AW and Westpfahl, K (1961) Theorie der Beugung. Berlin: Springer Verlag.Google Scholar
Sologub, VG (1971) Solution of an integral equation of the convolution type with finite limits of integration. USSR Computational Mathematics and Mathematical Physics 4, 33–52.CrossRefGoogle Scholar
Sologub, VG (1975) A method for investigating the problem of diffraction by a finite number of strips located within a single plane. Dopovidi Akademii Nauk Ukrainy, Series A 6, 549–552.Google Scholar
Borzenkov, AV and Sologub, VG (1975) Scattering of a plane wave by two strip resonators. Radio Engineering and Electron Physics 20, 20–38.Google Scholar
Kvach, NV and Sologub, VG (1982) Scattering of a plane Е-polarized wave by a finite number of strips located within a single plane. Radio Engineering and Electronic Physics 27, 2031–2034.Google Scholar
Panasyuk, VV, Savruk, MP and Nazarchuk, ZT (1984) Singular Integral Equation Technique in Two-Dimensional Diffraction Problems. Kiev: Naukova Dumka Publ.Google Scholar
Boltonosov, AI and Sologub, VG (1986) On scattering of a plane wave by two ribbons of different width in one plane. Journal of Communications Technology and Electronics 31, 179–181.Google Scholar
Shapoval, OV and Nosich, AI (2013) Finite gratings of many thin silver nanostrips: optical resonances and role of periodicity. AIP Advances 3, 042120/13.CrossRefGoogle Scholar
Kostenko, AV (2014) Numerical method for the solution of a hyper singular integral equation of second kind. Ukrainian Mathemetical Journal 65, 1373–1383.CrossRefGoogle Scholar
Kaliberda, ME, Lytvynenko, LM and Pogarsky, SA (2018) Modeling of graphene planar grating in the THz range by the method of singular integral equations. Frequenz 72, 277–284.CrossRefGoogle Scholar
Mandelbrot, BB (1983) The Fractal Geometry of Nature. New York: W.H. Freeman and Company.CrossRefGoogle Scholar
Barnsley, MF (1993) Fractals Everywhere. New York: Academic Press Professional.Google Scholar
Schroeder, M (1998) Fractals, Chaos, Power Laws. New York: W.H.Freeman and Company.Google Scholar
Edgar, GA (2008) Measure, Topology and Fractal Geometry. New York: Springer.CrossRefGoogle Scholar
Koshovy, GI (2011) Wave's diffraction by pre-fractal system of splits in a plane screen. Journal of Nano- and Electronic Physics 3, 66–72.Google Scholar
Koshovy, GI (2012) Systems approach to investigating pre-fractal diffraction gratings. Telecommunications and Radio Engineering 71, 487–500.CrossRefGoogle Scholar
Koshovy, GI (2016) Pre-fractal gratings of PEC strips: general mathematical models of wave scattering, Proceedings on the International Conference of Mathematical Methods in Electromagnetic Theory (MMET-2016), Lviv, Ukraine.CrossRefGoogle Scholar
Koshovy, GI (2017) Diffraction of H-polarized electromagnetic wave by pre-fractal system of slots in PEC screen, Proc. IEEE First Ukraine Conference on Electrical and Computer Engineering (UCRCON-2017), Kyiv, Ukraine.Google Scholar
Koshovy, GI (2018) Rigorous asymptotic models of wave scattering by finite flat gratings of electrically narrow impedance strips, Proceedings of the International Conference on Mathematical Methods in Electromagnetic Theory (MMET-2018), Kyiv, Ukraine.CrossRefGoogle Scholar
Koshovy, GI (2016) Asymptotic models of weakly filled PFSG, Proc. Int. Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2016), Tbilisi, Georgia.Google Scholar
Koshovy, GI (2012) Scattering of the H-polarized wave by pre-fractal diffraction gratings. Telecommunications and Radio Engineering 71, 961–973.CrossRefGoogle Scholar
Koshovy, GI (2017) Mathematical models of acoustic wave scattering by impedance strip, Proc. of Int. Seminar/Workshop on Direct and Inverse Problems Electromagnetic and Acoustic Wave Theory (DIPED-2017), Dnipro, Ukraine.CrossRefGoogle Scholar
Gakhov, FD (1977) Boundary-Value Problems. Oxford: Pergamon Press.Google Scholar
Muskhelishvili, NI (1953) Singular Integral Equations. Groningen: Noordhoff Publishers.Google Scholar
Koshovy, GI and Nosich, AI (2018) Mathematical Models of Acoustic Wave Scattering by a Finite Flat Impedance Strip Grating, Proc. of Int. Seminar/Workshop on Direct and Inverse Problems Electromagnetic and Acoustic Wave Theory (DIPED-2018), Tbilisi, Georgia.Google Scholar
Andriychuk, MI, Indranto, SW and Ramm, AG (2012) Electromagnetic wave scattering by a small impedance particle: theory and modeling. Optics Communications 285, 1684–1691.Google Scholar
Ishimaru, A (1978) Wave Propagation and Scattering in Random media, vol. 1, Single scattering and transport theory, Academic press.Google Scholar