9.6. HIGH-SPEED SOLITON SYSTEMS 455
(a) (b)Figure 9.24: (a) Temporal changes in the XPM-induced frequency shift produced by acoustic
waves in a 30-km-long fiber; (b) Increase in timing jitter produced by acoustic waves. (After
Ref. [191];©c2001 Academic; reprinted with permission.)
at higher bit rates. As a result, the acoustic wave generated by a single pulse affects
hundreds of the following pulses. Physically, time-dependent changes in the refractive
index induced by acoustic waves modulate the optical phase and manifest as a shift in
the frequency (chirping) by a small amount (∼1 GHz in Fig. 9.24). Similar to the case
of SSFS and amplifier-induced noise, a frequency shift manifests as a shift in the pulse
position because of GVD. The main difference is that acoustic jitter has a deterministic
origin in contrast with the amplifier-induced jitter. In fact, if a pulse were to occupy
each bit slot, all pulses would be shifted in time by the same amount through acoustic
waves, resulting in a uniform shift of the pulse train but no timing jitter. However, any
information-coded bit stream consists of a random string of 1 and 0 bits. As the change
in the group velocity of each pulse depends on the presence or absence of pulses in
the preceding hundreds of bit slots, different solitons arrive at slightly different times,
resulting in timing jitter. The deterministic nature of acoustic jitter makes it possible to
reduce its impact in practice by moving the detection window at the receiver through
an automatic tracking circuit [192] or by using a coding scheme [193].
Acoustic jitter has been studied for both the standard and DM solitons [191]. In
the case of standard solitons propagating inside a constant-GVD fiber of lengthL, the
jitter scales asσacou=Ca|D|L^2 , where the parameterCadepends on the index change
δnaamong other things. Figure 9.24(b) shows how the timing jitter is enhanced by the
acoustic effect for a 10-Gb/s system designed withD= 0 .45 ps/(km-nm),T 0 =10 ps,
nsp= 1 .6, andLA=25 km. Sliding-frequency filters reduce both the ASE-induced
and acoustically induced timing jitters. The acoustic jitter then dominates because it
increases linearly with the system lengthLwhile the ASE-induced jitter scales as
√
L.
PMD-Induced Jitter
PMD is another mechanism that can generate timing jitter through random fluctuations
in the fiber birefringence [194]. As discussed in Section 2.3.5, the PMD effects are
quantified through the PMD parameterDp. In a practical lightwave system, all solitons
are launched with the same state of polarization at the input end of a fiber link. How-