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On the scattering of point‐generated electromagnetic waves by a perfectly conducting sphere, and related near‐field inverse problems
Author(s) -
Athanasiadis C.,
Martin P.A.,
Stratis I.G.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310012
Subject(s) - inverse scattering problem , plane wave , scattering , physics , mathematical analysis , point source , bounded function , inverse , inverse problem , plane (geometry) , electromagnetic radiation , electromagnetic field , mathematics , optics , geometry , quantum mechanics
A spherical electromagnetic wave is scattered by a bounded perfectly conducting obstacle. A generalization of the plane‐wave optical theorem is established. For a spherical scatterer, low frequency results are obtained by approximating the known exact solution (separation of variables). In particular, a closed‐form approximation of the scattered wavefield at the source of the incident spherical wave is obtained. This leads to the solution of a near‐field inverse problem, where both the source and coincident receiver are located at several points in the vicinity of a small sphere. The same inverse problem is also treated from the knowledge of the leading order term in the low‐frequency asymptotic expansion of the scattering cross‐section.