Time-dependent self-action of periodically modulated laser beams in resonant media

We study the self-action of an amplitude-modulated beam in a two-level saturable absorbing medium. We also consider the radial quadratic dependence of the linear refraction index to apply the results to doped waveguides. As the modulation period approaches the relaxation times, the medium response is no more instantaneous, so that one should solve the full set of Maxwell-Bloch equations. We propose a second-order scheme with the Gauss-Laguerre transformation of the transverse field pattern. A simplified approach based on the synchronous interaction approximation is used for thin layers. We analyze the transient behavior of the medium response and its manifestation in the modulation of the beam diffracting after a thin saturable absorber. Nonlinear distortions of the modulation signal passed through a doped waveguide appear to be unexpectedly small compared with those of the local polarization and population difference.