Scattering of Electromagnetic Plane Waves by a Grating Composed of Two Arbitrarily Oriented Conducting Strips in One Period

Michinari SHIMODA; Tokuya ITAKURA

Scattering of Electromagnetic Plane Waves by a Grating Composed of Two Arbitrarily Oriented Conducting Strips in One Period

Michinari SHIMODA, Tokuya ITAKURA

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The two-dimensional scattering problem of electromagnetic waves by a grating composed of two arbitrarily oriented strips in one period is analyzed by means of the formulation using the mutual field. A formulation is presented for the analysis of multiple scattering by the grating by means of the representation of the scattered field by a grating composed of one strip in one period. The Wiener-Hopf equations to be satisfied by each scattered field and the representation of scattered wave based on the solution to these equation are obtained. Since the width of the strips in the grating is finite, it is difficult to carry out rigorously the decomposition in the solution of the Wiener-Hopf equations. The characteristic of the sampling function is used for expansion of the unknown function into a series so that the Wiener-Hopf equations are reduced to a set of simultaneous equations. For evaluation of the convergence and the errors in the results, the relative error with respect to the extrapolated value and the square error for satisfaction of the boundary condition are numerically computed. From numerical comparison of the present method with other various methods, it is found that the present method provides us accurate results. Some numerical examples on the reflection coefficient are presented for the reflection and transmission gratings.

Publication: IEICE TRANSACTIONS on Electronics Vol.E74-C No.8 pp.2398-2409

Publication Date: 1991/08/25

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Type of Manuscript: PAPER

Category: Electromagnetic Theory

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Michinari SHIMODA
Tokuya ITAKURA

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Michinari SHIMODA, Tokuya ITAKURA, "Scattering of Electromagnetic Plane Waves by a Grating Composed of Two Arbitrarily Oriented Conducting Strips in One Period" in IEICE TRANSACTIONS on Electronics, vol. E74-C, no. 8, pp. 2398-2409, August 1991, doi: .
Abstract: The two-dimensional scattering problem of electromagnetic waves by a grating composed of two arbitrarily oriented strips in one period is analyzed by means of the formulation using the mutual field. A formulation is presented for the analysis of multiple scattering by the grating by means of the representation of the scattered field by a grating composed of one strip in one period. The Wiener-Hopf equations to be satisfied by each scattered field and the representation of scattered wave based on the solution to these equation are obtained. Since the width of the strips in the grating is finite, it is difficult to carry out rigorously the decomposition in the solution of the Wiener-Hopf equations. The characteristic of the sampling function is used for expansion of the unknown function into a series so that the Wiener-Hopf equations are reduced to a set of simultaneous equations. For evaluation of the convergence and the errors in the results, the relative error with respect to the extrapolated value and the square error for satisfaction of the boundary condition are numerically computed. From numerical comparison of the present method with other various methods, it is found that the present method provides us accurate results. Some numerical examples on the reflection coefficient are presented for the reflection and transmission gratings.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e74-c_8_2398/_p

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@ARTICLE{e74-c_8_2398,
author={Michinari SHIMODA, Tokuya ITAKURA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Scattering of Electromagnetic Plane Waves by a Grating Composed of Two Arbitrarily Oriented Conducting Strips in One Period},
year={1991},
volume={E74-C},
number={8},
pages={2398-2409},
abstract={The two-dimensional scattering problem of electromagnetic waves by a grating composed of two arbitrarily oriented strips in one period is analyzed by means of the formulation using the mutual field. A formulation is presented for the analysis of multiple scattering by the grating by means of the representation of the scattered field by a grating composed of one strip in one period. The Wiener-Hopf equations to be satisfied by each scattered field and the representation of scattered wave based on the solution to these equation are obtained. Since the width of the strips in the grating is finite, it is difficult to carry out rigorously the decomposition in the solution of the Wiener-Hopf equations. The characteristic of the sampling function is used for expansion of the unknown function into a series so that the Wiener-Hopf equations are reduced to a set of simultaneous equations. For evaluation of the convergence and the errors in the results, the relative error with respect to the extrapolated value and the square error for satisfaction of the boundary condition are numerically computed. From numerical comparison of the present method with other various methods, it is found that the present method provides us accurate results. Some numerical examples on the reflection coefficient are presented for the reflection and transmission gratings.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Scattering of Electromagnetic Plane Waves by a Grating Composed of Two Arbitrarily Oriented Conducting Strips in One Period
T2 - IEICE TRANSACTIONS on Electronics
SP - 2398
EP - 2409
AU - Michinari SHIMODA
AU - Tokuya ITAKURA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E74-C
IS - 8
JA - IEICE TRANSACTIONS on Electronics
Y1 - August 1991
AB - The two-dimensional scattering problem of electromagnetic waves by a grating composed of two arbitrarily oriented strips in one period is analyzed by means of the formulation using the mutual field. A formulation is presented for the analysis of multiple scattering by the grating by means of the representation of the scattered field by a grating composed of one strip in one period. The Wiener-Hopf equations to be satisfied by each scattered field and the representation of scattered wave based on the solution to these equation are obtained. Since the width of the strips in the grating is finite, it is difficult to carry out rigorously the decomposition in the solution of the Wiener-Hopf equations. The characteristic of the sampling function is used for expansion of the unknown function into a series so that the Wiener-Hopf equations are reduced to a set of simultaneous equations. For evaluation of the convergence and the errors in the results, the relative error with respect to the extrapolated value and the square error for satisfaction of the boundary condition are numerically computed. From numerical comparison of the present method with other various methods, it is found that the present method provides us accurate results. Some numerical examples on the reflection coefficient are presented for the reflection and transmission gratings.
ER -