Plane Wave Diffraction by a Finite Sinusoidal Grating

Kazuya KOBAYASHI; Toru EIZAWA

Plane Wave Diffraction by a Finite Sinusoidal Grating

Kazuya KOBAYASHI, Toru EIZAWA

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The diffraction of a plane electromagnetic wave by a perfectly-conducting finite sinusoidal grating is analyzed using the Wiener-Hopf technique combined with the perturbation method. Assuming the depth of the grating to be small compared with the wavelength and approximating the boundary condition on the grating surface, the problem is reduced to that of the diffraction by a flat strip with a certain mixed boundary condition. Introducing a perturbation expansion for the unknown scattered field under the small-depth approximation, the problem is formulated in terms of the zero order and the first order Wiener-Hopf equations, which are solved exactly in a formal sense by a factorization and decomposition procedure. Applying a rigorous asymptotics, explicit high-frequency asymptotic solutions are further obtained for the width of the grating large compared with the wavelength. Scattered far field expressions are derived by taking the inverse Fourier transform are applying the saddle point method. Representative numerical examples of the far field patterns are given for various physical parameters, and the scattering characteristics of the grating are discussed.

Publication: IEICE TRANSACTIONS on Electronics Vol.E74-C No.9 pp.2815-2826

Publication Date: 1991/09/25

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Type of Manuscript: Special Section PAPER (Special Issue on OFSET '90)

Category: Grating

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Kazuya KOBAYASHI
Toru EIZAWA

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Kazuya KOBAYASHI, Toru EIZAWA, "Plane Wave Diffraction by a Finite Sinusoidal Grating" in IEICE TRANSACTIONS on Electronics, vol. E74-C, no. 9, pp. 2815-2826, September 1991, doi: .
Abstract: The diffraction of a plane electromagnetic wave by a perfectly-conducting finite sinusoidal grating is analyzed using the Wiener-Hopf technique combined with the perturbation method. Assuming the depth of the grating to be small compared with the wavelength and approximating the boundary condition on the grating surface, the problem is reduced to that of the diffraction by a flat strip with a certain mixed boundary condition. Introducing a perturbation expansion for the unknown scattered field under the small-depth approximation, the problem is formulated in terms of the zero order and the first order Wiener-Hopf equations, which are solved exactly in a formal sense by a factorization and decomposition procedure. Applying a rigorous asymptotics, explicit high-frequency asymptotic solutions are further obtained for the width of the grating large compared with the wavelength. Scattered far field expressions are derived by taking the inverse Fourier transform are applying the saddle point method. Representative numerical examples of the far field patterns are given for various physical parameters, and the scattering characteristics of the grating are discussed.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e74-c_9_2815/_p

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@ARTICLE{e74-c_9_2815,
author={Kazuya KOBAYASHI, Toru EIZAWA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Plane Wave Diffraction by a Finite Sinusoidal Grating},
year={1991},
volume={E74-C},
number={9},
pages={2815-2826},
abstract={The diffraction of a plane electromagnetic wave by a perfectly-conducting finite sinusoidal grating is analyzed using the Wiener-Hopf technique combined with the perturbation method. Assuming the depth of the grating to be small compared with the wavelength and approximating the boundary condition on the grating surface, the problem is reduced to that of the diffraction by a flat strip with a certain mixed boundary condition. Introducing a perturbation expansion for the unknown scattered field under the small-depth approximation, the problem is formulated in terms of the zero order and the first order Wiener-Hopf equations, which are solved exactly in a formal sense by a factorization and decomposition procedure. Applying a rigorous asymptotics, explicit high-frequency asymptotic solutions are further obtained for the width of the grating large compared with the wavelength. Scattered far field expressions are derived by taking the inverse Fourier transform are applying the saddle point method. Representative numerical examples of the far field patterns are given for various physical parameters, and the scattering characteristics of the grating are discussed.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Plane Wave Diffraction by a Finite Sinusoidal Grating
T2 - IEICE TRANSACTIONS on Electronics
SP - 2815
EP - 2826
AU - Kazuya KOBAYASHI
AU - Toru EIZAWA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E74-C
IS - 9
JA - IEICE TRANSACTIONS on Electronics
Y1 - September 1991
AB - The diffraction of a plane electromagnetic wave by a perfectly-conducting finite sinusoidal grating is analyzed using the Wiener-Hopf technique combined with the perturbation method. Assuming the depth of the grating to be small compared with the wavelength and approximating the boundary condition on the grating surface, the problem is reduced to that of the diffraction by a flat strip with a certain mixed boundary condition. Introducing a perturbation expansion for the unknown scattered field under the small-depth approximation, the problem is formulated in terms of the zero order and the first order Wiener-Hopf equations, which are solved exactly in a formal sense by a factorization and decomposition procedure. Applying a rigorous asymptotics, explicit high-frequency asymptotic solutions are further obtained for the width of the grating large compared with the wavelength. Scattered far field expressions are derived by taking the inverse Fourier transform are applying the saddle point method. Representative numerical examples of the far field patterns are given for various physical parameters, and the scattering characteristics of the grating are discussed.
ER -