Propagation of ultrashort optical pulses and computation of pulse evolution in free space by numerical simulations

Pulse propagation in a vacuum is described as being the superposition of elementary pulses given by the time derivative of the initial pulse and weighted by local inclination factors attached to the pulse wave front. Optical pulses with any wave-front profile and propagating in near-field and far-field regions are considered. The analytical expressions thus obtained demonstrate the possibility to compute the pulse structure as a function of time and its evolution through numerical simulations.