  We present a method for imaging the polarization vector of an electric dipole
distribution in a homogeneous medium from measurements of the electric field
made at a passive array. We study an electromagnetic version of Kirchhoff
imaging and prove, in the Fraunhofer asymptotic regime, that range and
cross-range resolution estimates are identical to those in acoustics. Our
asymptotic analysis provides error estimates for the cross-range dipole
orientation reconstruction and shows that the range component of the dipole
orientation is lost in this regime. A naive generalization of the Kirchhoff
imaging function is afflicted by oscillatory artifacts in range, that we
characterize and correct. We also consider the active imaging problem which
consists in imaging both the position and polarizability tensors of small
scatterers in the medium using an array of collocated sources and receivers. As
in the passive array case, we provide resolution estimates that are consistent
with the acoustic case and give error estimates for the cross-range entries of
the polarizability tensor. Our theoretical results are illustrated by numerical
experiments.
