A Note on Bicomplex Representation for Electromagnetic Fields in Scattering and Diffraction Problems and Its High-Frequency and Low-Frequency Approximations

Masahiro HASHIMOTO

A Note on Bicomplex Representation for Electromagnetic Fields in Scattering and Diffraction Problems and Its High-Frequency and Low-Frequency Approximations

Masahiro HASHIMOTO

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A bicomplex representation for time-harmonic electromagnetic fields appearing in scattering and diffraction problems is given using two imaginary units i and j. Fieldsolution integral-expressions obtained in the high-frequency and low-frequency limits are shown to provide the new relation between high-frequency diffraction and low-frequency scattering. Simple examples for direct scattering problems are illustrated. It may also be possible to characterize electric or magnetic currents induced on the obstacle in terms of geometrical optics far-fields. This paper outlines some algebraic rules of bicomplex mathematics for diffraction or scattering fields and describes mathematical evidence of the solutions. Major discussions on the relationship between high-frequency and low-frequency fields are relegated to the companion paper which will be published in another journal.

Publication: IEICE TRANSACTIONS on Electronics Vol.E80-C No.11 pp.1448-1456

Publication Date: 1997/11/25

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Type of Manuscript: Special Section PAPER (Special Issue on Electromagnetic TheoryScattering and Diffraction)

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Masahiro HASHIMOTO, "A Note on Bicomplex Representation for Electromagnetic Fields in Scattering and Diffraction Problems and Its High-Frequency and Low-Frequency Approximations" in IEICE TRANSACTIONS on Electronics, vol. E80-C, no. 11, pp. 1448-1456, November 1997, doi: .
Abstract: A bicomplex representation for time-harmonic electromagnetic fields appearing in scattering and diffraction problems is given using two imaginary units i and j. Fieldsolution integral-expressions obtained in the high-frequency and low-frequency limits are shown to provide the new relation between high-frequency diffraction and low-frequency scattering. Simple examples for direct scattering problems are illustrated. It may also be possible to characterize electric or magnetic currents induced on the obstacle in terms of geometrical optics far-fields. This paper outlines some algebraic rules of bicomplex mathematics for diffraction or scattering fields and describes mathematical evidence of the solutions. Major discussions on the relationship between high-frequency and low-frequency fields are relegated to the companion paper which will be published in another journal.
URL: https://globals.ieice.org/en_transactions/electronics/10.1587/e80-c_11_1448/_p

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@ARTICLE{e80-c_11_1448,
author={Masahiro HASHIMOTO, },
journal={IEICE TRANSACTIONS on Electronics},
title={A Note on Bicomplex Representation for Electromagnetic Fields in Scattering and Diffraction Problems and Its High-Frequency and Low-Frequency Approximations},
year={1997},
volume={E80-C},
number={11},
pages={1448-1456},
abstract={A bicomplex representation for time-harmonic electromagnetic fields appearing in scattering and diffraction problems is given using two imaginary units i and j. Fieldsolution integral-expressions obtained in the high-frequency and low-frequency limits are shown to provide the new relation between high-frequency diffraction and low-frequency scattering. Simple examples for direct scattering problems are illustrated. It may also be possible to characterize electric or magnetic currents induced on the obstacle in terms of geometrical optics far-fields. This paper outlines some algebraic rules of bicomplex mathematics for diffraction or scattering fields and describes mathematical evidence of the solutions. Major discussions on the relationship between high-frequency and low-frequency fields are relegated to the companion paper which will be published in another journal.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - A Note on Bicomplex Representation for Electromagnetic Fields in Scattering and Diffraction Problems and Its High-Frequency and Low-Frequency Approximations
T2 - IEICE TRANSACTIONS on Electronics
SP - 1448
EP - 1456
AU - Masahiro HASHIMOTO
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E80-C
IS - 11
JA - IEICE TRANSACTIONS on Electronics
Y1 - November 1997
AB - A bicomplex representation for time-harmonic electromagnetic fields appearing in scattering and diffraction problems is given using two imaginary units i and j. Fieldsolution integral-expressions obtained in the high-frequency and low-frequency limits are shown to provide the new relation between high-frequency diffraction and low-frequency scattering. Simple examples for direct scattering problems are illustrated. It may also be possible to characterize electric or magnetic currents induced on the obstacle in terms of geometrical optics far-fields. This paper outlines some algebraic rules of bicomplex mathematics for diffraction or scattering fields and describes mathematical evidence of the solutions. Major discussions on the relationship between high-frequency and low-frequency fields are relegated to the companion paper which will be published in another journal.
ER -