The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
La théorie mathématique des ondes électromagnétiques bicomplexes dans les problèmes de diffusion et de diffraction bidimensionnelle est développée. L'expression intégrale de Vekua pour les champs bidimensionnels valable uniquement dans la région fermée sans source est généralisée au champ rayonnant. Les problèmes de valeurs limites pour la diffusion et la diffraction sont formulés dans l'espace bicomplexe. La fonction complexe d'une variable unique, qui obéit aux relations de Cauchy-Riemann et exprime ainsi les aspects basse fréquence du champ proche au niveau d'un coin du diffuseur, est reliée au champ rayonnant par un opérateur intégral ayant un noyau approprié. Les comportements de cette fonction complexe dans tout l'espace sont discutés ainsi que ceux du champ de la zone lointaine ou de l'amplitude du spectre angulaire. Le schéma de factorisation de Hilbert est utilisé pour découvrir une transformation linéaire du champ de zone lointaine vers la fonction à valeur bicomplexe d'une variable unique. Cette transformation s’avère unique. La nouvelle expression intégrale du champ diffusé par une fine bande métallique est également obtenue.
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Masahiro HASHIMOTO, "Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems" in IEICE TRANSACTIONS on Electronics,
vol. E83-C, no. 2, pp. 236-247, February 2000, doi: .
Abstract: The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e83-c_2_236/_p
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@ARTICLE{e83-c_2_236,
author={Masahiro HASHIMOTO, },
journal={IEICE TRANSACTIONS on Electronics},
title={Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems},
year={2000},
volume={E83-C},
number={2},
pages={236-247},
abstract={The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.},
keywords={},
doi={},
ISSN={},
month={February},}
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TY - JOUR
TI - Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems
T2 - IEICE TRANSACTIONS on Electronics
SP - 236
EP - 247
AU - Masahiro HASHIMOTO
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E83-C
IS - 2
JA - IEICE TRANSACTIONS on Electronics
Y1 - February 2000
AB - The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.
ER -