Time-dependent multipoles and their application for radiation from volume source distributions

The radiation from a pulsed source distribution is expressed directly in the time-domain using a sum of time-dependent spherical (multipole) wave functions. Two alternative expressions for the time-dependent multipole moments (the excitation pulses) are derived. It is shown how they are related to the time-dependent planewave spectrum of the source (obtained via a Radon transform of the source distribution in the four space-time coordinates). Furthermore, the time-dependent multipole moments, and thereby the total time-dependent field outside the source region, are completely determined by the time-dependent radiation pattern. The series convergence is addressed by showing that the high order multipole moments tend to the quasistatic extension of the static multipole moments. This also puts an upper limit on the spatial resolution that can be achieved by a source distribution with specified size and pulse length. (C) 1995 American Institute of Physics.