We report on the theoretical and numerical analysis of the nonlinear Schrödinger equation describing the dynamical evolution of frequency-modulated (FM) optical signals propagating through the fiber configuration comprising active fibers with the anomalous dispersion nonuniformly distributed over the fiber length. In our consideration, a single active fiber section including segments with initially increasing and then decreasing dispersion is used for amplification and compression of an external FM pulse resulting in an increase of ~6 orders of magnitude in the pulse peak power and a 100-fold narrowing of the pulse duration down to a few picoseconds. Moreover, we demonstrate that, with a ~1 mW weakly modulated continuous wave input signal, the fiber configuration comprising two active fiber sections with different dispersion profiles is able to generate a strongly periodic pulse train, resulting in a pulse repetition rate >100 GHz, a pulse duration ~0.5 ps, and peak power up to ~1 kW. An evolution of optical signals governed by modulation instability in both fiber configurations is explored.
