RECIPROCITY THEOREM APPLIED TO THE COMPUTATION OF FUNCTIONAL DERIVATIVES OF THE SCATTERING MATRIX

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Abstract
The paper presents a general reciprocity theorem which is valid for any couple of fields and scatterers ; especially, the surfaces of the scatterers in the two configurations may be different. The theorem is demonstrated from Maxwell equations in the sense of distributions, which permits one to take automatically into account the boundary conditions. Then, several classical relations are derived from the theorem, for two dimensional as well as three dimensional scatterers : classical reciprocity, optical theorem, relation between far scattered field and near field. Moreover, very simple expressions are found for the functional derivatives of the elements of the scattering matrices, which constitute powerful tools for the numerical solving of inverse scattering problems.

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