Exact complex source representations of transient radiation

Exact expansions are presented for frequency-domain and time-domain fields generated by sources in a finite region of space. These expansions determine the field outside the minimum sphere from the values of the field on any sphere outside the source region, e.g., the far-field sphere. The basis functions are directionally localized monopole or multipole point sources located on a sphere in complex space. The frequency-domain expansions are first presented and then used along with the analytic Fourier transform to obtain the corresponding time-domain expansions.