422 CHAPTER 9. SOLITON SYSTEMS
(a) (b)Figure 9.11: Evolution of loss-managed solitons over 10,000 km for (a)LD=200 km and (b)
25 km withLA=50 km,α= 0 .22 dB/km, andβ 2 =− 0 .5ps^2 /km.
10 Mm because the conditionξA1 is reasonably well satisfied. However, if the
dispersion length is reduced to 25 km (ξA=2), the soliton is unable to sustain itself
because of excessive emission of dispersive waves. The conditionξA1orLALD,
required to operate within the average-soliton regime, can be related to the widthT 0 by
usingLD=T 02 /|β 2 |. The resulting condition is
T 0 √
|β 2 |LA. (9.3.9)Since the bit rateBis related toT 0 through Eq. (9.2.1), the condition (9.3.9) can be
written in the form of the following design criterion:
B^2 LA( 4 q^20 |β 2 |)−^1. (9.3.10)Choosing typical valuesβ 2 =− 0 .5ps^2 /km,LA=50 km, andq 0 =5, we obtainT 0
5psandB20 GHz. Clearly, the use of path-averaged solitons imposes a severe
limitation on both the bit rate and the amplifier spacing for soliton communication
systems.
9.3.3 Distributed Amplification
The conditionLALD, imposed on loss-managed solitons when lumped amplifiers are
used, becomes increasingly difficult to satisfy in practice as bit rates exceed 10 Gb/s.
This condition can be relaxed considerably when distributed amplification is used. The
distributed-amplification scheme is inherently superior to lumped amplification since
its use provides a nearly lossless fiber by compensating losses locally at every point
along the fiber link. In fact, this scheme was used as early as 1985 using the distributed
gain provided by Raman amplification when the fiber carrying the signal was pumped
at a wavelength of about 1.46μm using a color-center laser [59]. Alternatively, the
transmission fiber can be doped lightly with erbium ions and pumped periodically to
provide distributed gain. Several experiments have demonstrated that solitons can be
propagated in such active fibers over relatively long distances [62]–[66].