The perturbation of electromagnetic fields at distances

We rigorously derive the leading order terms in asymptotic expansions for the scattered electric and magnetic fields in the presence of a small object at distances that are large compared to its size. Our expansions hold for fixed wavenumber when the scatterer is a (lossy) homogeneous dielectric object with constant material parameters or a perfect conductor. We also derive the corresponding leading order terms in expansions for the fields for a low frequency problem when the scatterer is a non–lossy homogeneous dielectric object with constant material parameters or a perfect conductor. In each case we express our results in terms of polarisation tensors.