434 CHAPTER 9. SOLITON SYSTEMS
considerably larger in the anomalous-GVD section compared with the normal-GVD
section. Noting that the phase shift imposed on each spectral component varies as
β 2 ω^2 locally, one can define an effective value of the average GVD as [101]
β ̄ 2 eff=〈β 2 Ω^2 〉/〈Ω^2 〉, (9.4.13)whereΩis the local value of the spectral width and the angle brackets indicate average
over the map period. Ifβ ̄ 2 effis negative, the DM soliton can exist even ifβ ̄ 2 is positive.
For map strengths below a critical value (about 3.9 numerically), the average GVD
is anomalous for DM solitons. In that case, one is tempted to compare them with
standard solitons forming in a uniform-GVD fiber link withβ 2 =β ̄ 2. For relatively
small values ofSm, variations in the pulse width and chirp are small enough that one
can ignore them. The main difference between the average-GVD and DM solitons
then stems from the higher peak power required to sustain DM solitons. The energy
enhancement factor for DM solitons is defined as [85]
fDM=E 0 DM/Eav 0 (9.4.14)and can exceed 10 depending on the system design. The larger energy of DM solitons
benefits a soliton system in several ways. Among other things, it improves the SNR
and decreases the timing jitter; these issues are discussed in Section 9.5.
Dispersion-management schemes were used for solitons as early as 1992 although
they were referred to by names such as partial soliton communication and dispersion
allocation [103]. In the simplest form of dispersion management, a relatively short seg-
ment of dispersion-compensating fiber (DCF) is added periodically to the transmission
fiber, resulting in dispersion maps similar to those used for nonsoliton systems. It was
found in a 1995 experiment that the use of DCFs reduced the timing jitter consider-
ably [104]. In fact, in this 20-Gb/s experiment, the timing jitter became low enough
when the average dispersion was reduced to a value near− 0 .025 ps^2 /km that the 20-
Gb/s signal could be transmitted over transoceanic distances.
Since 1996, a large number of experiments have shown the benefits of DM solitons
for lightwave systems [105]–[114]. In one experiment, the use of a periodic dispersion
map enabled transmission of a 20-Gb/s soliton bit stream over 5520 km of a fiber link
containing amplifiers at 40-km intervals [105]. In another 20-Gb/s experiment [106],
solitons could be transmitted over 9000 km without using any in-line optical filters
since the periodic use of DCFs reduced timing jitter by more than a factor of 3. A 1997
experiment focused on transmission of DM solitons using dispersion maps such that
solitons propagated most of the time in the normal-GVD regime [107]. This 10-Gb/s
experiment transmitted signals over 28 Mm using a recirculating fiber loop consist-
ing of 100 km of normal-GVD fiber and 8-km of anomalous-GVD fiber such that the
average GVD was anomalous (about− 0 .1ps^2 /km). Periodic variations in the pulse
width were also observed in such a fiber loop [108]. In a later experiment, the loop
was modified to yield the average-GVD value of zero or slightly positive [109]. Stable
transmission of 10-Gb/s solitons over 28 Mm was still observed. In all cases, experi-
mental results were in excellent agreement with numerical simulations [110].
An important application of dispersion management consists for upgrading the ex-
isting terrestrial networks designed with standard fibers [111]–[114]. A 1997 exper-
iment used fiber gratings for dispersion compensation and realized 10-Gb/s soliton