454 CHAPTER 9. SOLITON SYSTEMS
0 1000 2000 3000 400001234Distance (km)Timing jitter (ps)
GordonHausRamantotalFigure 9.23: Timing jitter as a function of distance for a 160-Gb/s DM system designed with
T 0 = 1 .25 ps. The Raman and Gordon–Haus contributions to timing jitter are also shown.
most of the timing jitter results from the SSFS after 1000 km. Noting that the tolerable
value of the timing jitter is less than 1 ps at 160 Gb/s, it is clear that the total trans-
mission distance of such systems would be limited to below 1000 km in the absence
of any jitter-control mechanism. Longer distances are possible at a lower bit rate of
80 Gb/s. The main conclusion is that the Raman jitter must be included whenever the
width (FWHM) of solitons is shorter than 5 ps.
Acoustic Jitter
A timing-jitter mechanism that limits the total transmission distance at high bit rates has
its origin in the generation of acoustic waves inside optical fibers [190]. Confinement
of the optical mode within the fiber core creates an electric-field gradient in the radial
direction of the fiber. This gradient creates an acoustic wave throughelectrostriction,
a phenomenon that produces density variations in response to changes in the electric
field. As the refractive index of any material depends on its density, the group velocity
also changes with the generation of acoustic waves.
The acoustic-wave-induced index changes produced by a single pulse can last for
more than 100 ns—the damping time associated with acoustic phonons. They can be
measured through the XPM-induced frequency shift∆νimposed on a probe signal and
given by∆ν=−(Leff/λ)d(δna)/dt, whereLeffis the effective length of the fiber [191].
As seen in Fig. 9.24(a), the measured frequency shift is in the form of multiple spikes,
each lasting for about 2 ns, roughly the time required for the acoustic wave to traverse
the fiber core. The 21-ns period between the spikes corresponds to the round-trip time
taken by the acoustic wave to reflect from the fiber cladding. Noting thatLeff≈20 km
for 0.2-dB/km fiber losses, acoustically induced changes are relatively small (∼ 10 −^14 )
but they lead to measurable jitter even at a bit rate of 10 Gb/s [6].
The origin of acoustic jitter can be understood by noting that pulses follow one
another with a time interval that is only 25 ps atB=40 Gb/s and becomes shorter