Propagation of single-cycle pulsed light beams in dispersive media

We describe a family of solutions of the three-dimensional envelope equation in dispersive media beyond the slowly varying envelope approximation [T. Brabec et al., Phys. Rev. Lett. 78, 3282 (1997)] that represents few-cycle pulsed light beams evolving due to gain (losses), phase and gain dispersion, diffraction, and space-time focusing. We then show that group velocity dispersion tends to bend the propagating pulse front, in the same sense as diffraction in anomalous dispersion, and in the opposite sense in normal dispersion. In the latter case, the diffraction-induced pulse front curvature and the associated pulse broadening can be eliminated along the whole propagation by setting the diffraction length equal to the dispersion length. Simple analytic expressions for these dispersion-diffraction coupled effects are given.