9.5. IMPACT OF AMPLIFIER NOISE 443
Figure 9.18: Timing jitter with (dotted curves) and without (solid curves) sliding-frequency fil-
ters at several bit rates as a function of distance. The inset shows a Gaussian fit to the numerically
simulated jitter at 10,000 km for a 10-Gb/s system. (After Ref. [129];©c1992 OSA; reprinted
with permission.)
Figure 9.18 shows the predicted reduction in the timing jitter for standard solitons.
The bit-rate dependence is due to the acoustic jitter (discussed later); theB=0 curves
show the contribution of the Gordon–Haus jitter alone. Optical filters help in reducing
both types of timing jitter and permit transmission of 10-Gb/s solitons over more than
20 Mm. In the absence of filters, timing jitter becomes so large that a 10-Gb/s soliton
system cannot be operated beyond 8000 km. The inset in Fig. 9.18 shows a Gaussian
fit to the timing jitter of 10-Gb/s solitons at a distance of 10 Mm calculated by solving
the NLS equation numerically after including the effects of both the ASE and sliding-
frequency filters [129]. The timing-jitter distribution is approximately Gaussian with a
standard deviation of about 1.76 ps. In the absence of filters, the jitter exceeds 10 ps
under the same conditions.
Optical filters benefit a soliton system in many other ways. Their use reduces in-
teraction between neighboring solitons [130]. The physical mechanism behind the
reduced interaction is related to the change in the soliton phase at each filter. A rapid
variation of the relative phase between neighboring solitons, occurring as a result of
filtering, averages out the soliton interaction by alternating the nature of the interaction
force from attractive to repulsive. Optical filters also help in reducing the accumulation
of dispersive waves [131]. The reason is easy to understand. As the soliton spectrum
shifts with the filters, dispersive waves produced at earlier stages are blocked by filters
together with the ASE.
Solitons can also be controlled in the time domain using the technique ofsyn-
chronousamplitude modulation, implemented in practice using a LiNbO 3 modula-
tor [132]. The technique works by introducing additional losses for those solitons that
have shifted from their original position (center of the bit slot). The modulator forces
solitons to move toward its transmission peak where the loss is minimum. Mathemati-