Bicomplex Waves in Electromagnetic Scattering and Diffraction Problems

Masahiro HASHIMOTO 

Publication
IEICE TRANSACTIONS on Electronics  Vol.E83-C  No.2  pp.236-247
Publication Date: 2000/02/20
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Electromagnetic Theory
Keyword: 
bicomplex,  scattering,  diffraction,  Hilbert's factorization technique,  Vekua's formulas, 

Full Text: PDF

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.