A note on the representation of scattered fields as a singularity expansion

The representation of the electromagnetic field scattered by a perfectly conducting finite-extent scatterer immersed in a lossless medium as a singularity expansion is considered. While the analytic properties of the temporal Laplace transform of the surface currents residing on such an object have received a great deal of attention, the properties of the scattered fields have not. It is shown that the representation of the transform of the scattered field must include an exponential entire function except for observation points in the forward-scattered direction. Explicit time domain representations that are counterpart to the Laplace domain representation are constructed and are shown to embody, in the early time, temporal variation besides that of the damped sinusoidal factors intrinsic to the singularity expansion. An important practical consequence of this more complicated time variation arises in connection with the application of the singularity expansion for target classification purposes and is commented upon herein.