Diffractive effects in pulse propagation through a resonant medium

The propagation of a weak optical pulse through a resonant two-level atomic medium is discussed in the paraxial approximation. Transverse propagation effects within that approximation are treated exactly by development of the method of Fresnel transforms. In particular, for a temporally short pulse with an amplitude of arbitrary transverse spatial dependence it is shown that longitudinal propagation is not affected by diffractive spreading. Thus diffraction does not attenuate the characteristic ringing of one-dimensional pulse propagation in resonant media.