9.6. HIGH-SPEED SOLITON SYSTEMS 451
Figure 9.22: Pulse envelopes at distancesξ=z/LD=0, 5, and 10 showing the delay of a soliton
because of the Raman-induced-frequency shift.
where Eq. (9.5.33) was used for the input soliton energy. The frequency shift grows
linearly withzin the case of perfect distributed amplification (p=1) but follows energy
variations in the case of lumped amplification. In both cases, its magnitude scales with
pulse width asT 0 −^4. It is this feature that makes the SSFS increasingly more important
as the bit rate increases. The soliton positionqis affected by both the Raman-induced
frequency shift and the TOD parameterβ 3. This shift is deterministic in nature, in
contrast with the position shift induced by amplifier-induced frequency fluctuations.
The dominant contribution toqin Eq. (9.6.5) comes from theβ 2 term.
One can understand the origin of changes in the soliton position by noting that
the Raman-induced frequency shift in the carrier frequency toward longer wavelengths
slows down a pulse propagating in the anomalous-GVD regime of the fiber. Figure
9.22 shows such a slowing down of a standard soliton (N=1) by solving Eq. (9.6.1)
numerically withβ 3 =0 andTR/T 0 = 0 .05. By the time the soliton has propagated over
10 dispersion lengths, it has been delayed by a significant fraction of its own width. A
delay in the arrival time of a soliton is not of much concern when all bits are delayed
by the same amount. However, the pulse energy and width fluctuate from bit to bit
because of fluctuations induced by the amplifier noise. Such fluctuations are converted
into timing jitter by the SSFS. The Raman-induced timing jitter is discussed later in
this section.
How is the Raman-induced frequency shift affected by dispersion management?
The width of DM solitons is not constant but oscillates in a periodic manner. Since the
SSFS depends on the pulse width, it is clear that it will also vary significantly within
each map period. The highest frequency shift occurs in the central region of each sec-
tion where the pulse is nearly unchirped and the width is shortest. The total frequency
shift will be less for DM solitons compared with the standard solitons for which the