Shadow Theory of Diffraction Grating: Reciprocity, Symmetry and Average Filter

Junichi NAKAYAMA; Yasuhiko TAMURA

doi:10.1587/transele.E97.C.1036

Shadow Theory of Diffraction Grating: Reciprocity, Symmetry and Average Filter

Junichi NAKAYAMA, Yasuhiko TAMURA

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In the theory of periodic gratings, there is no method to make up a numerical solution that satisfies the reciprocity so far. On the basis of the shadow theory, however, this paper proposes a new method to obtain a numerical solution that satisfies the reciprocity. The shadow thoery states that, by the reciprocity, the mth order scattering factor is an even function with respect to a symmetrical axis depending on the order m of diffraction. However, a scattering factor obtained numerically becomes an even function only approximately, but not accurately. It can be decomposed to even and odd components, where an odd component represents an error with respect to the reciprocity and can be removed by the average filter. Using even components, a numerical solution that satisfies the reciprocity is obtained. Numerical examples are given for the diffraction of a transverse magnetic (TM) plane wave by a very rough periodic surface with perfect conductivity. It is then found that, by use of the average filter, the energy error is much reduced in some case.

Publication: IEICE TRANSACTIONS on Electronics Vol.E97-C No.10 pp.1036-1040

Publication Date: 2014/10/01

Publicized

Online ISSN: 1745-1353

DOI: 10.1587/transele.E97.C.1036

Type of Manuscript: BRIEF PAPER

Category: Electromagnetic Theory

Authors

Junichi NAKAYAMA
Kyoto Institute of Technology
Yasuhiko TAMURA
Kyoto Institute of Technology

Keyword

wave diffraction, periodic surface, scattering factor, reciprocity, average filter, image integral equation

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Junichi NAKAYAMA, Yasuhiko TAMURA, "Shadow Theory of Diffraction Grating: Reciprocity, Symmetry and Average Filter" in IEICE TRANSACTIONS on Electronics, vol. E97-C, no. 10, pp. 1036-1040, October 2014, doi: 10.1587/transele.E97.C.1036.
Abstract: In the theory of periodic gratings, there is no method to make up a numerical solution that satisfies the reciprocity so far. On the basis of the shadow theory, however, this paper proposes a new method to obtain a numerical solution that satisfies the reciprocity. The shadow thoery states that, by the reciprocity, the mth order scattering factor is an even function with respect to a symmetrical axis depending on the order m of diffraction. However, a scattering factor obtained numerically becomes an even function only approximately, but not accurately. It can be decomposed to even and odd components, where an odd component represents an error with respect to the reciprocity and can be removed by the average filter. Using even components, a numerical solution that satisfies the reciprocity is obtained. Numerical examples are given for the diffraction of a transverse magnetic (TM) plane wave by a very rough periodic surface with perfect conductivity. It is then found that, by use of the average filter, the energy error is much reduced in some case.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/transele.E97.C.1036/_p

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@ARTICLE{e97-c_10_1036,
author={Junichi NAKAYAMA, Yasuhiko TAMURA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Shadow Theory of Diffraction Grating: Reciprocity, Symmetry and Average Filter},
year={2014},
volume={E97-C},
number={10},
pages={1036-1040},
abstract={In the theory of periodic gratings, there is no method to make up a numerical solution that satisfies the reciprocity so far. On the basis of the shadow theory, however, this paper proposes a new method to obtain a numerical solution that satisfies the reciprocity. The shadow thoery states that, by the reciprocity, the mth order scattering factor is an even function with respect to a symmetrical axis depending on the order m of diffraction. However, a scattering factor obtained numerically becomes an even function only approximately, but not accurately. It can be decomposed to even and odd components, where an odd component represents an error with respect to the reciprocity and can be removed by the average filter. Using even components, a numerical solution that satisfies the reciprocity is obtained. Numerical examples are given for the diffraction of a transverse magnetic (TM) plane wave by a very rough periodic surface with perfect conductivity. It is then found that, by use of the average filter, the energy error is much reduced in some case.},
keywords={},
doi={10.1587/transele.E97.C.1036},
ISSN={1745-1353},
month={October},}

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TY - JOUR
TI - Shadow Theory of Diffraction Grating: Reciprocity, Symmetry and Average Filter
T2 - IEICE TRANSACTIONS on Electronics
SP - 1036
EP - 1040
AU - Junichi NAKAYAMA
AU - Yasuhiko TAMURA
PY - 2014
DO - 10.1587/transele.E97.C.1036
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E97-C
IS - 10
JA - IEICE TRANSACTIONS on Electronics
Y1 - October 2014
AB - In the theory of periodic gratings, there is no method to make up a numerical solution that satisfies the reciprocity so far. On the basis of the shadow theory, however, this paper proposes a new method to obtain a numerical solution that satisfies the reciprocity. The shadow thoery states that, by the reciprocity, the mth order scattering factor is an even function with respect to a symmetrical axis depending on the order m of diffraction. However, a scattering factor obtained numerically becomes an even function only approximately, but not accurately. It can be decomposed to even and odd components, where an odd component represents an error with respect to the reciprocity and can be removed by the average filter. Using even components, a numerical solution that satisfies the reciprocity is obtained. Numerical examples are given for the diffraction of a transverse magnetic (TM) plane wave by a very rough periodic surface with perfect conductivity. It is then found that, by use of the average filter, the energy error is much reduced in some case.
ER -