452 CHAPTER 9. SOLITON SYSTEMS
pulse remains unchirped throughout the link. Moreover, the SSFS will depend on the
map strength and will be lower for stronger maps [182].
The effects of TOD on DM solitons is apparent from Eq. (9.6.5). The second term
in this equation shows that the TOD produces a shift in the soliton position even in
the absence of the Raman term (TR=0). The shift increases linearly with distance
as(β 3 / 18 T 02 )zand is negligible untilT 0 becomes much shorter than 10 ps. As an
example, the temporal shift is 5 fs/km forT 0 =1psandβ 3 = 0 .09 ps^3 /km and becomes
comparable to the pulse width after 200 km of propagation. The shift increases in the
presence of SSFS as apparent from the last term in Eq. (9.6.5). This shift is relatively
small as it requires the presence of both the SSFS and TOD and can be neglected in
most cases of practical interest. The TOD also distorts the DM soliton and generates
dispersive waves [184]. Under certain conditions, a DM soliton can propagate over
long distances after some energy has been shed in the form of dispersive waves [183].
Numerical simulations based on Eq. (9.6.1) show that 80-Gb/s solitons can prop-
agate stably over 9000 km in the presence of higher-order effects if (i) TOD is com-
pensated within the map, (ii) optical filters are used to reduce soliton interaction, tim-
ing jitter, and the Raman-induced frequency shift, and (iii) the map periodLmapis
reduced to a fraction of amplifier spacing [153]. The bit rate can even be increased to
160 Gb/s by controlling the GVD slope and PMD, but the distance is limited to about
2000 km [155]. These results show that soliton systems operating at 160 Gb/s are
possible if their performance is not limited by timing jitter. We turn to this issue next.
9.6.4 Timing Jitter
Timing jitter discussed earlier in Section 9.5.4 increases considerably at higher bit rates
because of the use of shorter optical pulses. Both the Raman effect and TOD lead to
additional jitter that increases rapidly with the bit rate [186]–[189]. Moreover, several
other mechanisms begin to contribute to the timing jitter. In this section we consider
these additional sources of timing jitter.
Raman Jitter
The Raman jitter is a new source of timing jitter that dominates at high bit rates re-
quiring short optical pulses (T 0 <5 ps). Its origin can be understood as follows [187].
The Raman-induced frequency shift depends on the pulse energy as seen in Eq. (9.6.4).
This frequency shift by itself does not introduce jitter because of its deterministic na-
ture. However, fluctuations in the pulse energy introduced by amplifier noise can be
converted into fluctuations in the soliton frequency through the Raman effect, which
are in turn translated into position fluctuations by the GVD. The Raman jitter occurs
for both the standard and DM solitons. In the case of standard solitons, the use of DDFs
is often necessary but the analysis is simplified because the solitons are unchirped and
maintain their width during propagation [187].
In the case of DM solitons, the pulse energy, width, and chirp oscillate in a periodic
manner. To keep the discussion simple, the effects of TOD are ignored although they
can be easily included. Using Eqs. (9.6.2) and (9.6.3) and following the method used
in Section 9.5.4, the frequency shift and position of the soliton at the end of thenth