Pulsed Beams Expansion Algorithms for Time-Dependent Point-Source Radiation. A Basic Algorithm and a Standard-Pulsed-Beams Algorithm

We introduce two pragmatic pulsed beam (PB) expansion algorithms for radiation from a time-dependant point source, whereby the field is expanded in terms of PB propagators emerging from the source in all directions. The algorithms are based on a rigorous expansion identity involving a continuous angular spectrum of complex source pulsed beams (CSPB). The present algorithms, however, are structured upon a discrete lattice of beam directions, and utilize the iso-diffracting PB propagators (ID-PB) that may readily be tracked in non-uniform media. In the basic algorithm, the PB propagators are determined by the analytic-signal extension of the source and hence have to be re-calculated for any given source. To circumvent this difficulty we introduce a more pragmatic algorithm that utilizes time-samples of the source signal and expresses the radiated field using a set of standard-PB propagators defined by a given filter h(t). The optimal expansion parameters, namely the beam collimation, the angular spectrum discretization, the overall number of PB needed to reconstruct the field, as well as the choice of the filter h(t), are determined analytically as functions of the observation range and the excitation pulse. Guidelines for choosing these parameters are provided and are verified numerically.