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 Zap. Nauchn. Sem. POMI, 2014, Volume 422, Pages 62–89 (Mi znsl5764)

Diffraction by grating consisting of screens with different height: new equations

A. I. Korol'kov, A. V. Shanin

Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia

Abstract: A 2D problem of diffraction of a plane wave by a grating consisting of screens of different heights is studied. The incident wave travels at a grazing incidence angle. The consideration is held in the parabolic approximation. Screens are supposed to be perfectly absorbing. Edge Green's functions of the problem are introduced. Embedding formula and a spectral equation are proven. An OE-equation for the unknown coefficient of spectral equation is derived. An evolution equation which describes dependence of the edge Green's functions on geometrical parameter of problem(screen height) is derived. An asymptotic estimation of the reflection coefficient is obtained by using the evolution equation.

Key words and phrases: diffraction grating, absorbing screens, parabolic equation.

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English version:
Journal of Mathematical Sciences (New York), 2015, 206:3, 270–287

UDC: 534.26

Citation: A. I. Korol'kov, A. V. Shanin, “Diffraction by grating consisting of screens with different height: new equations”, Mathematical problems in the theory of wave propagation. Part 43, Zap. Nauchn. Sem. POMI, 422, POMI, St. Petersburg, 2014, 62–89; J. Math. Sci. (N. Y.), 206:3 (2015), 270–287

Citation in format AMSBIB
\Bibitem{KorSha14} \by A.~I.~Korol'kov, A.~V.~Shanin \paper Diffraction by grating consisting of screens with different height: new equations \inbook Mathematical problems in the theory of wave propagation. Part~43 \serial Zap. Nauchn. Sem. POMI \yr 2014 \vol 422 \pages 62--89 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl5764} \transl \jour J. Math. Sci. (N. Y.) \yr 2015 \vol 206 \issue 3 \pages 270--287 \crossref{https://doi.org/10.1007/s10958-015-2311-y} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953354779} 

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This publication is cited in the following articles:
1. A. I. Korol'kov, A. V. Shanin, “Parabolic equation method and Fresnel approximation in Weinstein's problems”, J. Math. Sci. (N. Y.), 214:3 (2016), 302–321
2. Shanin A.V., Korol'kov A.I., “Wave Reflection From a Diffraction Grating Consisting of Absorbing Screens: Description in Terms of the Wiener-Hopf-Fock Method”, Acoust. Phys., 60:6 (2014), 624–632
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