Electromagnetic scattering theorems for interior dipole excitation of a layered obstacle

A layered scatterer is excited by a time-harmonic spherical electromagnetic wave, generated by a dipole located either in the interior or in the exterior of the scatterer. The scattererʹs core may be perfect conducting, impedance or dielectric. This paper initiates the investigation of scattering theorems corresponding to the excitation of a layered scatterer by a dipole in its interior. We establish reciprocity and general scattering theorems relating the total electric fields with the corresponding far-field patterns. The optical theorem, relating the scattering cross-section with the electric field in the layer containing the dipole, is recovered as a corollary of the general scattering theorem. Furthermore, for a scatterer excited by a spherical and a plane wave, mixed scattering theorems are derived. Besides, all the derived theorems recover known results, concerning the excitation of a homogeneous scatterer by an exterior dipole. We also analyze numerical implementations of the optical theorem in certain concrete scattering applications.