We review the characteristic current decomposition, first introduced by Garbacz (1968, A generalized expansion for radiated and scattered field. Ph.D. Dissertation, Ohio State University, Columbus) and then by Harrington & Mautz (1971, Theory of characteristic modes for conducting bodies. IEEE Trans. Antennas Propag., AP-19, 622-628). Our approach is based on the study of the scattering operator, or scattering matrix, the unitarity property of which plays a central role. The spectral decomposition of this operator leads to a particular characteristic far fields (or eigenfar-fields), from which a set of characteristic currents can be derived. These currents are those of Garbacz, Harrington and Mautz. They satisfy a generalized eigenequation involving usual integral operators split according to the regular/singular decomposition of the free space Green kernel. We provide proof of existence, denseness and orthogonality for these sets of characteristic modes (both currents and far fields). In addition to its theoretical interest, our analysis is motivated by its application to radar cross-section (RCS) analysis, where this particular decomposition turns out to be a powerful tool, especially for objects of small dimensions compared with the wavelength of the incident wave. Numerical computations are presented for a general three-dimensional object and the electrical field integral equation, including the first characteristic currents and their analyses in terms of their impact on the monostatic RCS.

The time-harmonic electromagnetic scattering or radiation problem is considered. The singular value decomposition (SVD) is applied to the radiation operator that maps the set of electric and magnetic currents defined on the surface of an inhomogeneous object onto the set of the far-fields scattered (or radiated) from this object. The SVD yields orthonormal bases for both sets. Because the radiation operator is compact and regularizing, it is demonstrated that the far-field calculated from the series expansions of the currents on these bases converges exponentially fast to the exact one if a sufficient number of terms is considered in these series. This number is closely related to the degrees of freedom that characterize the far-field. The latter can be computed from a reduced number of unknowns in the discretized integral equation that links electric and magnetic surface currents by writing it in the new currents bases. Also, it allows the reduction of the far-field in a given angular sector. The numerical complexity of this technique is addressed, and 2D numerical examples are presented that illustrate its potentialities.

In this Note, we return to the theory of characteristic modes which was introduced 30 years ago for electromagnetic scattering problems. A simple mathematical framework is proposed and complete definitions are given. The potential interest of this theory in terms of Radar Cross Section (RCS) analysis is then discussed, especially in the low frequency case. Finally, a 3-D example is presented to illustrate the efficiency of this decomposition. (C) 2004 Academie des sciences. Publie par Elsevier SAS. Tons droits reserves.