On the scattering of point-generated electromagnetic waves by a perfectly conducting sphere, and related near-field inverse problems

A spherical electromagnetic wave is scattered by a bounded perfectly conducting obstacle. A generalization of the plane‐wave optical theorem is established. For a spherical scatterer, low frequency results are obtained by approximating the known exact solution (separation of variables). In particular, a closed‐form approximation of the scattered wavefield at the source of the incident spherical wave is obtained. This leads to the solution of a near‐field inverse problem, where both the source and coincident receiver are located at several points in the vicinity of a small sphere. The same inverse problem is also treated from the knowledge of the leading order term in the low‐frequency asymptotic expansion of the scattering cross‐section.