TIME-DEPENDENT PLANE-WAVE AND MULTIPOLE EXPANSIONS OF THE ELECTROMAGNETIC-FIELD

A new and conceptually simple derivation is presented of the time-depe ndent multipole expansion of the electromagnetic field radiated by a t ime-varying, localized, volume charge-current distribution. The analys is is based on a new time-dependent plane wave representation of the e lectromagnetic field (i.e., an ''angular spectrum expansion'' in the t ime domain), also derived in the paper. Expressions are given for the time-dependent plane wave spectra in terms of a fourfold Radon transfo rm representation of the transverse current distribution. Two alternat ive expressions for the time-dependent multipole moments are derived; the first gives them in terms of the spectral amplitude vectors of the corresponding time-dependent plane wave representation while the seco nd gives them in terms of a weighted radial-temporal average of the cu rrent distribution. Thus the analysis also sheds light on the relation ship between the time-dependent plane wave and multipole expansions in their common domains of validity. (C) 1998 American Institute of Phys ics. [S0022-2488(98)01007-X].