7.8. LONG-HAUL LIGHTWAVE SYSTEMS 309
nonlinear systems. This observation has led to the adoption of the CRZ (chirped RZ)
format for dispersion-managed fiber links. If the dispersion map is made such that the
pulse broadens in the first section and compresses in the second section, the impact of
the nonlinear effects can be reduced significantly. The reason is as follows: The pulse
peak power is reduced considerably in the first section because of rapid broadening of
chirped pulses, while in the second section it is lower because of the accumulated fiber
losses. Such dispersion-managed links are calledquasi-lineartransmission links [127].
The solution given in Eq. (7.8.9) applies reasonably well for such links. As optical
pulses spread considerably outside their assigned bit slot over a considerable fraction
of each map period, their overlapping can degrade the system performance when the
nonlinear effects are not negligible. These effects are considered in the next section.
If the input peak power is so large that a quasi-linear situation cannot be realized,
one must solve Eqs. (7.8.7) and (7.8.8) with the nonlinear term included. No analytic
solution is possible in this case. However, one can find periodic solutions of these
equations numerically by imposing the periodic boundary conditions
T(Lm)=T 0 , C(Lm)=C 0 , (7.8.11)which ensure that the pulse recovers its initial shape at the end of each map period.
Such pulses propagate through the dispersion-managed link in a periodic fashion and
are called dispersion-managed solitons because they exhibit soliton-like features. This
case is discussed in Chapter 9.
7.8.3 Intrachannel Nonlinear Effects.................
The nonlinear effects play an important role in dispersion-managed systems, especially
because they are enhanced within the DCF because of its reduced effective core area.
Placement of the amplifier after the DCF helps since the signal is then weak enough
that the nonlinear effects are less important in spite of the small effective area of DCFs.
The optimization of system performance using different dispersion maps has been a
subject of intense study. In a 1994 experiment, a 1000-km-long fiber loop contain-
ing 31 fiber amplifiers was used to study three different dispersion maps [112]. The
maximum transmission distance of 12,000 km was realized for the case in which short
sections of normal GVD fibers were used to compensate for the anomalous GVD of
long sections. In a 1995 experiment, a 80-Gb/s signal, obtained by multiplexing eight
10-Gb/s channels with 0.8-nm channel spacing, was propagated inside a recirculating
fiber loop [114]. The total transmission distance was limited to 1171 km because of
various nonlinear effects.
Perfect compensation of GVD in each map period is not the best solution in the
presence of nonlinear effects. A numerical approach is often used to optimize the
design of dispersion-managed systems [115]–[124]. In general, local GVD should be
kept relatively large to suppress the nonlinear effects, while minimizing the average
dispersion for all channels. In a 1998 experiment, a 40-Gb/s signal was transmitted
over 2000 km of standard fiber using a novel dispersion map [125]. The distance could
be increased to 16,500 km at a lower bit rate of 10 Gb/s by placing an optical amplifier
right after the DCF within the recirculating fiber loop [126]. Since the nonlinear effects