440 CHAPTER 9. SOLITON SYSTEMS
0 2000 4000 6000 8000
02468Distance (km)DM SolitonStandard SolitonTiming jitter (ps)Figure 9.17: (a) ASE-induced timing jitter as a function of length for a 40-Gb/s system designed
with DM (solid curve) and standard (dashed line) solitons.
Using Eqs. (9.5.13)–(9.5.15) in this equation and performing the sums, the timing jitter
of DM solitons is given by [124]
σt^2 =SspTm^2
E 0[NA( 1 +C 02 )+NA(NA− 1 )C 0 d+^16 NA(NA− 1 )( 2 NA− 1 )d^2 ], (9.5.29)where the normalized parameterdis related to the accumulated dispersion over one
amplifier spacing as
d=1
Tm^2∫LA0β 2 (z)dz=
β ̄ 2 LA
Tm^2. (9.5.30)
The three terms in Eq. (9.5.29) have the following origins. The first term inside
the square brackets results from direct position fluctuations of a soliton within each
amplifier. The second term is related to the cross-correlation between frequency and
position fluctuations because both are produced by the same ASE noise. The third
term is solely due to frequency fluctuations. For a long chain of cascaded amplifiers
(NA1), the jitter is dominated by the last term in Eq. (9.5.30) because of itsN^3 A
dependence and is approximately given by
σt^2
Tm^2≈
Ssp
3 E 0NA^3 d^2 =SspL^3 T
3 E 0 L^2 DLA, (9.5.31)
where Eq. (9.5.30) was used together withLD=Tm^2 /|β ̄ 2 |andNA=LT/LAfor a light-
wave system with the total transmission distanceLT.
Because of the cubic dependence ofσt^2 on the system lengthLT, the timing jitter
can become an appreciable fraction of the bit slot for long-haul systems, especially at
bit rates exceeding 10 Gb/s for which the bit slot is shorter than 100 ps. Such jitter
would lead to large power penalties if left uncontrolled. As discussed in Section 6.5.2,
jitter should be less than 10% of the bit slot in practice. Figure 9.17 shows how timing
jitter increases withLTfor a 40-Gb/s DM soliton system designed using a dispersion
map consisting of 10.5 km of anomalous-GVD fiber and 9.7 km of normal-GVD fiber