Timing jitter in dispersion-managed soliton systems with distributed, lumped, and hybrid amplification

We analyze the role of distributed amplification in controlling timing jitter in dispersion-managed soliton systems and discuss, using analytical and numerical techniques, how timing jitter is reduced by up to a factor of two when lumped amplification is replaced by complete or partial distributed amplification. We derive an analytical expression for the timing jitter at any position within the fiber link in the case of ideal distributed amplification for which losses are exactly compensated by gain at every point. We show that the timing jitter is well approximated by this formula in the case of erbium-based amplification. We derive a similar expression for the timing jitter for lumped amplifiers and compare it with the case of distributed amplification. We find that with erbium-based distributed amplification, timing jitter depends on the density of dopants and is smaller for lower densities. In the case of hybrid Raman amplification, the transmission distance of a 40-Gb/s system can be increased by up to 30% depending on the amount of Raman gain. Finally, we show that timing jitter decreases for stronger maps at a given bit rate (constant minimum pulsewidth).