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Far field patterns and the inverse scattering problem for electromagnetic waves in an inhomogeneous medium

Published online by Cambridge University Press:  24 October 2008

David Colton  and
Lassi Päivärinta
David Colton
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, U.S.A.
Lassi Päivärinta
Affiliation:
Department of Mathematics, University of Helsinki, Helsinki, Finland
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Abstract

We consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support. It is first shown that the set of far field patterns of the electric fields corresponding to incident plane waves propagating in arbitrary directions is complete in the space of square-integrable tangential vector fields defined on the unit sphere. We then show that under certain conditions the electric far field patterns satisfy an integral identity involving the unique solution of a new class of boundary value problems for Maxwell's equations called the interior transmission problem for electromagnetic waves. Finally, it is indicated how this integral identity can be used to formulate an optimization scheme yielding an optimal solution of the inverse scattering problem for electromagnetic waves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 561 - 575
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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