Self-similar parabolic pulses in optical fiber amplifiers with gain dispersion and gain saturation

The generation and propagation of an asymptotic parabolic pulse in an optical fiber amplifier with the gain dispersion effect and gain saturation effect is studied. It is found that initial input pulses with small amplitudes and widths can evolve into self-similar pulses at the asymptotic limit. The central region of the self-similar pulse is described by the invert parabola, and its width and power increase linearly, but with its peak amplitude and the width of its spectrum, remain constant. The parameter region for the existence of the parabolic pulse is given.