STRONG PERIODIC AMPLIFICATION OF SOLITONS IN A LOSSY OPTICAL-FIBER - ANALYTICAL RESULTS

Transmission of a femtosecond soliton is analyzed in a model of a loss y fiber with periodically installed pointlike amplifiers. The model in corporates dispersion of the losses, the Raman frequency downshift, an d a finite amplification bandwidth. The analysis is focused on the cas e in which spacing between amplifying pulses is large, so that the pul se must be strong enough to reshape the attenuated soliton. It is demo nstrated that evolution of the soliton in this model is governed by a two-dimensional map that defines the soliton's peak power and central frequency after a given amplification pulse as functions of their valu es after a previous pulse. The map is considered analytically for the limiting case in which the frequency shift between the spectral maximu m of the amplifying gain and the minimum of the dissipative absorption is large enough to permit reduction to a one-dimensional map in terms of the soliton's peak power only. It is demonstrated that the one-dim ensional map has a nontrivial stable fixed point, providing stable tra nsmission of the soliton. An important generic feature of the reshapin g regime with large spacing between amplifiers is that the strong ampl ification pulses inevitably produce additional parasitic (secondary) s olitons. In terms of the same one-dimensional map, a regime of operati on is found in which only transmission of the primary soliton is suppo rted while all the parasites are completely destroyed by the losses. T his regime is based on a sufficiently narrow gain bandwidth.