Numerical Methods of Multilayered Dielectric Gratings by Application of Shadow Theory to Middle Regions

Hideaki WAKABAYASHI; Keiji MATSUMOTO; Masamitsu ASAI; Jiro YAMAKITA

doi:10.1587/transele.E95.C.44

Numerical Methods of Multilayered Dielectric Gratings by Application of Shadow Theory to Middle Regions

Hideaki WAKABAYASHI, Keiji MATSUMOTO, Masamitsu ASAI, Jiro YAMAKITA

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In the scattering problem of periodic gratings, at a low grazing limit of incidence, the incident plane wave is completely cancelled by the reflected wave, and the total wave field vanishes and physically becomes a dark shadow. This problem has received much interest recently. Nakayama et al. have proposed “the shadow theory”. The theory was first applied to the diffraction by perfectly conductive gratings as an example, where a new description and a physical mean at a low grazing limit of incidence for the gratings have been discussed. In this paper, the shadow theory is applied to the analyses of multilayered dielectric periodic gratings, and is shown to be valid on the basis of the behavior of electromagnetic waves through the matrix eigenvalue problem. Then, the representation of field distributions is demonstrated for the cases that the eigenvalues degenerate in the middle regions of multilayered gratings in addition to at a low grazing limit of incidence and some numerical examples are given.

Publication: IEICE TRANSACTIONS on Electronics Vol.E95-C No.1 pp.44-52

Publication Date: 2012/01/01

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Online ISSN: 1745-1353

DOI: 10.1587/transele.E95.C.44

Type of Manuscript: Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application)

Category: Periodic Structures

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Hideaki WAKABAYASHI, Keiji MATSUMOTO, Masamitsu ASAI, Jiro YAMAKITA, "Numerical Methods of Multilayered Dielectric Gratings by Application of Shadow Theory to Middle Regions" in IEICE TRANSACTIONS on Electronics, vol. E95-C, no. 1, pp. 44-52, January 2012, doi: 10.1587/transele.E95.C.44.
Abstract: In the scattering problem of periodic gratings, at a low grazing limit of incidence, the incident plane wave is completely cancelled by the reflected wave, and the total wave field vanishes and physically becomes a dark shadow. This problem has received much interest recently. Nakayama et al. have proposed “the shadow theory”. The theory was first applied to the diffraction by perfectly conductive gratings as an example, where a new description and a physical mean at a low grazing limit of incidence for the gratings have been discussed. In this paper, the shadow theory is applied to the analyses of multilayered dielectric periodic gratings, and is shown to be valid on the basis of the behavior of electromagnetic waves through the matrix eigenvalue problem. Then, the representation of field distributions is demonstrated for the cases that the eigenvalues degenerate in the middle regions of multilayered gratings in addition to at a low grazing limit of incidence and some numerical examples are given.
URL: https://globals.ieice.org/en_transactions/electronics/10.1587/transele.E95.C.44/_p

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@ARTICLE{e95-c_1_44,
author={Hideaki WAKABAYASHI, Keiji MATSUMOTO, Masamitsu ASAI, Jiro YAMAKITA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Numerical Methods of Multilayered Dielectric Gratings by Application of Shadow Theory to Middle Regions},
year={2012},
volume={E95-C},
number={1},
pages={44-52},
abstract={In the scattering problem of periodic gratings, at a low grazing limit of incidence, the incident plane wave is completely cancelled by the reflected wave, and the total wave field vanishes and physically becomes a dark shadow. This problem has received much interest recently. Nakayama et al. have proposed “the shadow theory”. The theory was first applied to the diffraction by perfectly conductive gratings as an example, where a new description and a physical mean at a low grazing limit of incidence for the gratings have been discussed. In this paper, the shadow theory is applied to the analyses of multilayered dielectric periodic gratings, and is shown to be valid on the basis of the behavior of electromagnetic waves through the matrix eigenvalue problem. Then, the representation of field distributions is demonstrated for the cases that the eigenvalues degenerate in the middle regions of multilayered gratings in addition to at a low grazing limit of incidence and some numerical examples are given.},
keywords={},
doi={10.1587/transele.E95.C.44},
ISSN={1745-1353},
month={January},}

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TY - JOUR
TI - Numerical Methods of Multilayered Dielectric Gratings by Application of Shadow Theory to Middle Regions
T2 - IEICE TRANSACTIONS on Electronics
SP - 44
EP - 52
AU - Hideaki WAKABAYASHI
AU - Keiji MATSUMOTO
AU - Masamitsu ASAI
AU - Jiro YAMAKITA
PY - 2012
DO - 10.1587/transele.E95.C.44
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E95-C
IS - 1
JA - IEICE TRANSACTIONS on Electronics
Y1 - January 2012
AB - In the scattering problem of periodic gratings, at a low grazing limit of incidence, the incident plane wave is completely cancelled by the reflected wave, and the total wave field vanishes and physically becomes a dark shadow. This problem has received much interest recently. Nakayama et al. have proposed “the shadow theory”. The theory was first applied to the diffraction by perfectly conductive gratings as an example, where a new description and a physical mean at a low grazing limit of incidence for the gratings have been discussed. In this paper, the shadow theory is applied to the analyses of multilayered dielectric periodic gratings, and is shown to be valid on the basis of the behavior of electromagnetic waves through the matrix eigenvalue problem. Then, the representation of field distributions is demonstrated for the cases that the eigenvalues degenerate in the middle regions of multilayered gratings in addition to at a low grazing limit of incidence and some numerical examples are given.
ER -