By Paolo Franchi
An alternative derivation of the scattering matrix under Kirchhoff approximation in electromagnetics. Fuscaldo, Walter; Di Simone, Alessio; Millefiori, Leonardo; Iodice, Antonio; Braca, Paolo; Willett, Peter K.. CMRE-FR-2018-001. January 2018.
This report furnishes an alternative theoretical framework for the analytical evaluation of the bistatic scattering coefficients, under the Kirchhoff approximation (KA) in electromagnetics. Starting from the KA, specific results under the geometrical optics and physical optics approximations are furnished, along with the backscattering geometry. Comparison with classical results available in the related literature validates the proposed derivation. The main objectives of this report are 1) to provide an explicit formulation of the scattering matrix under KA in terms of the incident and scattered unit wavevectors; 2) to provide a more generic derivation of the scattering matrix under the physical optics approximation by relaxing typical hypotheses regarding the geometry of the scattering problem; 3) to highlight some important symmetries of the scattering matrix under KA. The framework proposed here can be exploited to simplify the evaluation of the electromagnetic scattered fields in complex scenarios where multiple-bounce contributions come into play. Indeed, un-der the KA, it is shown that the scattering matrix can conveniently be expressed in terms of few variables, thus greatly reducing the complexity of the theoretical derivation of the scattering matrix.