Complex source pulsed beams: New test pulses for transient acoustic propagation and diffraction modeling

Abstract

Complex source pulsed beams (CSPB) are transient waveforms generated when the space coordinates and initiation time of a pulsed line source (two dimensional) or point source (three dimensional) are assigned complex values. They generalize to the time domain the time-harmonic, complex-source-point Gaussian beams. A CSPB is described by the analytic signal obtained from analytic continuation of the conventional impulsive time-dependent, free-space Green's function to the domain of the complex source parameters that control the spatial and temporal widths of the pulsed beam. Numerical examples illustrate the CSPB shapes obtained for various choices. Generalized CSPB fields can be constructed by convolving the CSPB with various time functions. The general theory of the CSPB is discussed. It is also shown how to apply the CSPB as the excitation of a propagation or diffraction environment when the complex space-time source coordinate substitution is performed on the conventional space-time Green's function for that environment. This yields new formulations for transient propagation and diffraction. Examples include a two-fluid medium separated by a plane interface, and diffraction by a knife edge. [Work supported by ONR.]