9.6. HIGH-SPEED SOLITON SYSTEMS 457
the Gordon–Haus jitter in the absence of such interactions [197]. The non-Gaussian
corrections can occur even when the interaction is relatively weak (q 0 >5). They af-
fect the bit-error rate of the system and must be included for an accurate estimate of
the system performance. When solitons are packed so tightly that their interaction be-
comes quite important, the probability density function of the timing jitter develops a
five-peak structure [198]. The use of numerical simulations is essential to study the
impact of timing jitter on a bit stream composed of interacting solitons.
In the case of DM solitons, interaction-induced jitter becomes quite important, es-
pecially for strong maps for which the pulse width varies by a large factor within each
map period [199]. It can be reduced by a proper design of the dispersion map. In fact,
local dispersion of each fiber section and the average GVD of the entire link need to
be optimized to reduce both the soliton–soliton interaction and the ASE-induced jitter
simultaneously [161].
Control of Timing Jitter
The increase in the timing jitter brought by the Raman and TOD effects and a shorter
bit slot at higher bit rates make the control of timing jitter essential before high-speed
systems can become practical. As discussed in Section 9.5, both optical filters and syn-
chronous modulators help in reducing the timing jitter. The technique of optical phase
conjugation (OPC), discussed in Section 7.7 in the context of dispersion compensation,
is also quite effective in improving the performance of soliton systems by reducing the
soliton–soliton interaction and the Raman-induced timing jitter [200]–[204].
The implementation of OPC requires either parametric amplifiers [10] in place of
EDFAs or insertion of a nonlinear optical device before each amplifier that changes the
soliton amplitude fromAtoA∗while preserving all other features of the bit stream.
Such a change is equivalent to inverting the soliton spectrum around the wavelength
of the pump laser used for the FWM process. As discussed in Section 7.7, a few-
kilometer-long fiber can be used for spectral inversion. The timing jitter changes con-
siderably because of OPC. The moment method can be used to find the timing jitter in
the presence of parametric amplifiers. The dependence of the Gordon–Haus contribu-
tion on the number of amplifiers changes fromNA^3 toNA. The Raman-induced jitter is
reduced even more dramatically—fromNA^5 toNA[202]. These reductions result from
the OPC-induced spectral inversion, which provides compensation for the effects of
both the GVD and SSFS. However, OPC does not compensate for the effects of TOD.
The effects of TOD on the jitter are shown in Fig. 9.25 by plotting the timing jitter
of 2-ps (FWHM) solitons propagating inside DDFs and amplified using parametric
amplifiers. The Gordon–Haus timing jitter is shown by the thick solid line. Other
curves correspond to different values of the TOD parameter. Forβ 3 = 0 .05 ps^3 /km, a
typical value for dispersion-shifted fibers, the transmission distance is limited by TOD
to below 1500 km. However, considerable improvement occurs whenβ 3 is reduced.
Transmission over 7500 km is possible forβ 3 =0, and the distance can be increased
further for slightly negative values ofβ 3. These results show that the compensation of
bothβ 2 andβ 3 is necessary at high bit rates (see Section 7.9).