ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A new and conceptually simple derivation is presented of the time-dependent multipole expansion of the electromagnetic field radiated by a time-varying, localized, volume charge-current distribution. The analysis is based on a new time-dependent plane wave representation of the electromagnetic field (i.e., an "angular spectrum expansion" in the time domain), also derived in the paper. Expressions are given for the time-dependent plane wave spectra in terms of a fourfold Radon transform representation of the transverse current distribution. Two alternative 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 second gives them in terms of a weighted radial-temporal average of the current distribution. Thus the analysis also sheds light on the relationship between the time-dependent plane wave and multipole expansions in their common domains of validity. © 1998 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.532457
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