Space-time dynamics of ultrashort pulses in vacuum

An analytical study is made of the evolution of spatially bounded pulses wh ose length amounts to several periods of the field oscillations. An equatio n is analyzed that describes unidirectional (reflectionless) propagation of light pulses in vacuum. The method of moments is used to find the variatio ns in length, effective width of the wave field, and other characteristic a veraged parameters of a pulse along its propagation path. A broad class of self-similar solutions describing the focusing of the light pulses is found . Finally, by direct integration of the starting equation it is shown that a horseshoe-shaped precursor forms near the leading edge of the pulse. (C) 1999 American Institute of Physics. [S1063-7761(99)00407-2].