Ultrashort pulsed Gaussian light beams

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Abstract
We find a family of solutions of the paraxial wave equation that represents ultrashort pulsed light beams propagating in free space. These pulsed beams have an arbitrary temporal form and a nearly Gaussian cross section, while modeling for the pulses emitted by mode-locked lasers with stable two-mirror resonators. We also study the effects arising from their spatiotemporal coupled behavior, such as pulse time delay, distortion, and a frequency shift toward the beam periphery. Time-varying diffraction (with diffraction reduction at the first instants of arrival of the pulsed beam at a given distance) and the dependence of the spatial distribution of energy on the pulse form are also described. These effects become important for pulsed beams with a few optical oscillations within the pulse envelope.