Calculation of pulse shaping in saturable media with consideration of phase memory

Starting from the complete set of Maxwell equations and density matrix equations, we derive approximate expressions for the change of pulse envelope and phase in passing samples composed of homogeneously broadened two level systems. The influence of saturation and phase memory on chirped and chirp-free pulses are discussed with respect to characteristic pulse parameters. The phase memory is found to be responsible for the dispersion of the small signal absorption (amplification), the dispersion of the saturation and the inertia of the atomic systems.