Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Electronics Vol.E83-C No.2 pp.236-247
- Publication Date
- 2000/02/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Electromagnetic Theory
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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},}
Copy
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 -
English
