  Slow light of an amplitude modulated Gaussian (AMG) pulse in cesium vapor is
demonstrated and studied, as an appropriate amplitude modulation to a single
pulse can expand its spectrum and thus increase the utilization efficiency of
the bandwidth of a slow light system. In a single-$\Lambda$ type
electromagnetically induced transparency (EIT) system, the slowed AMG pulse
experiences severe distortion, mainly owing to the frequency dependent
transmission of medium. Additionally, due to its spectral distribution, the
frequency dependent dispersion of the medium causes simultaneous slow and fast
light of different spectral components and thus a certain dispersive distortion
of the AMG pulse. Further, a post-processing method is proposed to recover the
slowed (distorted) pulse, which indicates that by introducing a linear optical
system with a desired gain spectrum we can recover the pulse in an
"all-optical" way. Finally, we discuss the limitations during this compensation
procedure in detail. Although it is demonstrated in the cesium vapor using EIT,
this method should be applicable to a wide range of slow light systems.
