Complex source pulsed beams - New wave functions for local description of time-dependent propagation and diffraction

Complex source pulsed beams (CSPB) are exact solutions of the wave equation which can be modeled by a time-dependent source located at a complex coordinate point. With a proper choice of parameters, these wavefields are confined in beam-like fashion in transverse planes perpendicular to the propagation axis while confinement along the axis is due to temporal windowing. Because they have these properties, CSPB are useful wave objects for generating and synthesizing highly focused transient fields and for local probing of a medium. Furthermore, as has been shown recently, CSPBs form a new set of basis functions for an exact angular spectrum expansion of source-excited, time-dependent fields. In this paper, the time-dependent complex source point method is reviewed. Starting with the time-harmonic complex source field, we derive the CSPB field in free space and explore its properties, discuss how to analyze scattering and diffraction of CSPB and finally show how CSPB can be utilized as basis functions for spectral expansion of time-dependent fields.