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Diffraction by a Grating Consisting of Absorbing Screens of Different Height. New Equations

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The problem of diffraction of a plane wave by a grating consisting of absolutely absorbing screens of different height is studied. It is assumed that the angle of incidence is small. The problem is considered in the parabolic approximation. Edge Green functions are introduced. An embedding formula and a spectral equation for the edge Green functions are derived. An OE-equation for the coefficients of the spectral equation is constructed. The latter is solved numerically. The evolution equation describing the dependence of the edge Green functions on a geometric parameter (the height of the screens) is proved. Using this equation, the asymptotics of the reflection coefficient is calculated for the principal mode.

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Authors and Affiliations

  1. Moscow Lomonosov State University, Moscow, Russia

    A. I. Korolkov & A. V. Shanin

Authors
  1. A. I. Korolkov
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  2. A. V. Shanin
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Correspondence to A. I. Korolkov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 422, 2014, pp. 62–89.

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Korolkov, A.I., Shanin, A.V. Diffraction by a Grating Consisting of Absorbing Screens of Different Height. New Equations. J Math Sci 206, 270–287 (2015). https://doi.org/10.1007/s10958-015-2311-y

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  • DOI: https://doi.org/10.1007/s10958-015-2311-y

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