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The scattering of an arbitrary incoming electromagnetic wave by an unrestricted scattering object is described in terms of a tensor scattering matrix. General reciprocity relations and the cross-section theorem, including an interesting extension, are established using this representation. The results are related to the special case of plane-wave scattering and the scattering matrix is explicitly exhibited in terms of the plane-wave scattering amplitude for two mutually perpendicular directions of polarization.
David S. Saxon (Thu,) studied this question.