Singularity expansion representations of fields and currents in transient scattering

A unified treatment of the natural mode representations for induced currents and scattered fields is obtained by use of fundamental concepts regarding causality and superposition. The transient scattered field response is shown to have the form of a constant coefficient complex exponential sum only in the 'late-time', after the last driven response is received from the object. Prior to this, the 'early-time' response is found to be due to direct physical optics fields as well as a sum of temporally modulated natural modes produced by the progressive illumination of the incident wavefront. Alternate representations and s-plane behaviors are considered. The implications of these results on natural resonance target identification schemes are discussed.