Beam Frame Representation for Ultrawideband Radiation From Volume Source Distributions: Frequency-Domain and Time-Domain Formulations

We present two novel beam-summation schemes for radiation from time-harmonic or time-dependent volume source distributions, where the field is expanded using a discrete phase-space set of beam-wave propagators. The generic term “beams” is used here for both the frequency-domain and the time-domain formulations where the propagators are isodiffracting Gaussian beam or isodiffracting pulsed beams, respectively. The formulations are structured upon the recently formulated “beam-frame” theorem that establishes these phase-space beam sets as frame sets everywhere in the propagation domain and not only over the aperture plane as in previous formulations. The expansion coefficients are obtained by projecting the source distributions over the dual beam-frame sets that have essentially the same structure as the basic sets. As such, these formulations constitute local generalization to the conventional plane waves or Green’s function formulations, and also reduce the overall degrees of freedom needed to describe the radiated field. As demonstrated by the numerical examples, they resolve the local features of the source distributions in space time, and hence provide a basis for a new local inverse scattering theory to be presented subsequently.