On the distortion of a wave packet propagating in an amplifying medium

The propagation of a narrow-band signal (wave packet) in a medium with population inversion is considered. It is shown that in an optically thick medium layer the signal decomposes into the initial and amplified signals propagating at different velocities and having different durations. The initial signal propagates without distortions at the velocity c/n₀ (n₀ is the refractive index of the medium away from the resonance frequency) and plays the role of a precursor of the amplified signal. The amplified signal moves at a lower velocity. It lags behind the initial signal during propagation and acquires a universal Gaussian shape (irrespective of the shape of the initial signal and the spectral line profile). The appearance of the amplified signal, which substantially differs from the initial signal in all the parameters, as well as the interference between the amplified and initial signals looks like a 'extra-distortion' of the initial signal.