Complex source pulsed beam representation of transient radiation

A new exact representation of transient radiation is presented, wherein the time-dependent point source field is modeled by an equivalent distribution of impulsive complex sources located on a spherical surface that encloses the source, and which may therefore be interpreted as a time-dependent complex Huygens' principle. Physically, each one of the equivalent sources launches a pulsed beam field in the radial direction. A new spectral representation for transient radiation is thereby obtained in terms of a continuum of pulsed beam fields emanating radially from the source in all directions. The convergence of the representation, and in particular the conditions under which a given source field may be represented only by paraxial contributions from neighboring pulsed beams are explored. In this latter approximation, our representation is the time-domain analogue of the Gaussian beam summation method which has recently been introduced as an efficient tool for computing time-harmonic fields in a complicated environment.