Direct and inverse dipole electromagnetic scattering by a piecewise homogeneous sphere

Abstract

AbstractThis paper deals with the investigation of the direct and the inverse electromagnetic scattering problem by a piecewise homogeneous sphere, excited by an interior or exterior dipole. The research is motivated by important physical, biomedical, and technological applications detailed in the introduction. First, we utilize Sommerfeld's and T‐matrix method to determine the exact electromagnetic Green's function, that is the solution of the direct scattering problem. Then, we use the low‐frequency assumption to derive asymptotic far‐field expansions of the Green's function of an electrically small piecewise homogeneous sphere. These low‐frequency expansions contribute essentially to the development of far‐field inverse scattering algorithms for the determination of the sphere's geometrical and physical characteristics. It is shown that for these algorithms interior dipoles offer additional information, which may be utilized effectively for the localization and reconstruction of the sphere. Several numerical results exhibit the variations of the far‐field quantities with respect to the dipole's and the sphere's characteristics. Reductions to plane wave scattering by a layered sphere and exterior dipole scattering by a homogeneous sphere are pointed out.