Method of Image Green's Function in Grating Theory

Junichi NAKAYAMA; Yasuhiko TAMURA

doi:10.1587/transele.E95.C.93

Method of Image Green's Function in Grating Theory

Junichi NAKAYAMA, Yasuhiko TAMURA

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This paper deals with the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface by an integral method. However, it is known that a conventional integral method does not work for a critical angle of incidence, because of divergence of a periodic Green's function (integral kernel). To overcome such a divergence difficulty, we introduce an image Green's function which is physically defined as a field radiated from an infinite phased array of dipoles. By use of the image Green's function, it is newly shown that the diffracted field is represented as a sum of radiation from the periodic surface and its image surface. Then, this paper obtains a new image integral equation for the basic surface current, which is solved numerically. A numerical result is illustrated for a very rough sinusoidal surface. Then, it is concluded that the method of image Green's function works practically even at a critical angle of incidence.

Publication: IEICE TRANSACTIONS on Electronics Vol.E95-C No.1 pp.93-96

Publication Date: 2012/01/01

Publicized

Online ISSN: 1745-1353

DOI: 10.1587/transele.E95.C.93

Type of Manuscript: BRIEF PAPER

Category: Periodic Structures

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Junichi NAKAYAMA, Yasuhiko TAMURA, "Method of Image Green's Function in Grating Theory" in IEICE TRANSACTIONS on Electronics, vol. E95-C, no. 1, pp. 93-96, January 2012, doi: 10.1587/transele.E95.C.93.
Abstract: This paper deals with the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface by an integral method. However, it is known that a conventional integral method does not work for a critical angle of incidence, because of divergence of a periodic Green's function (integral kernel). To overcome such a divergence difficulty, we introduce an image Green's function which is physically defined as a field radiated from an infinite phased array of dipoles. By use of the image Green's function, it is newly shown that the diffracted field is represented as a sum of radiation from the periodic surface and its image surface. Then, this paper obtains a new image integral equation for the basic surface current, which is solved numerically. A numerical result is illustrated for a very rough sinusoidal surface. Then, it is concluded that the method of image Green's function works practically even at a critical angle of incidence.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/transele.E95.C.93/_p

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@ARTICLE{e95-c_1_93,
author={Junichi NAKAYAMA, Yasuhiko TAMURA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Method of Image Green's Function in Grating Theory},
year={2012},
volume={E95-C},
number={1},
pages={93-96},
abstract={This paper deals with the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface by an integral method. However, it is known that a conventional integral method does not work for a critical angle of incidence, because of divergence of a periodic Green's function (integral kernel). To overcome such a divergence difficulty, we introduce an image Green's function which is physically defined as a field radiated from an infinite phased array of dipoles. By use of the image Green's function, it is newly shown that the diffracted field is represented as a sum of radiation from the periodic surface and its image surface. Then, this paper obtains a new image integral equation for the basic surface current, which is solved numerically. A numerical result is illustrated for a very rough sinusoidal surface. Then, it is concluded that the method of image Green's function works practically even at a critical angle of incidence.},
keywords={},
doi={10.1587/transele.E95.C.93},
ISSN={1745-1353},
month={January},}

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TY - JOUR
TI - Method of Image Green's Function in Grating Theory
T2 - IEICE TRANSACTIONS on Electronics
SP - 93
EP - 96
AU - Junichi NAKAYAMA
AU - Yasuhiko TAMURA
PY - 2012
DO - 10.1587/transele.E95.C.93
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E95-C
IS - 1
JA - IEICE TRANSACTIONS on Electronics
Y1 - January 2012
AB - This paper deals with the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface by an integral method. However, it is known that a conventional integral method does not work for a critical angle of incidence, because of divergence of a periodic Green's function (integral kernel). To overcome such a divergence difficulty, we introduce an image Green's function which is physically defined as a field radiated from an infinite phased array of dipoles. By use of the image Green's function, it is newly shown that the diffracted field is represented as a sum of radiation from the periodic surface and its image surface. Then, this paper obtains a new image integral equation for the basic surface current, which is solved numerically. A numerical result is illustrated for a very rough sinusoidal surface. Then, it is concluded that the method of image Green's function works practically even at a critical angle of incidence.
ER -