"Introduction". In: Fiber-Optic Communication Systems

266 CHAPTER 6. OPTICAL AMPLIFIERS

20 40 60 80 100

Amplifier Spacing (km)

0

5000

10000

15000

System Length (km)

2 mW

1.0

0.5

0.2

Figure 6.22: Maximum ASE-limited system length for a 10-Gb/s channel as a function of am-
plifier spacingLAfor several values of input powers.

of cost considerations. To estimate the optimum value ofLA, Fig. 6.22 shows the total
system lengthLTas a function ofLAfor several values of input powersPinassuming
that an electrical SNR of 20 dB is required for the system to function properly and
usingα= 0 .2 dB/km,nsp= 1 .6 (noise figure 5 dB), and∆f=10 GHz. The main
point to note is that amplifier spacing becomes smaller as the system length increases.
Typically,LAis kept near 50 km for undersea systems but can be increased to 80 km or
so for terrestrial systems with link lengths under 3000 km. Although amplifier spacing
can be improved by increasing the input powerPin, in practice, the maximum power
that can be launched is limited by the onset of various nonlinear effects. We turn to this
issue next.

6.5.3 ASE-Induced Timing Jitter

The amplifier noise can also induce timing jitter in the bit stream by shifting optical
pulses from their original time slot in a random fashion. Such jitter was first studied
in 1986 in the context of solitons and is called the Gordon–Haus jitter [122]. It was
later recognized that timing jitter can occur with any transmission format [NRZ, RZ,
or chirped RZ (CRZ)] and imposes a fundamental limitation on all long-haul systems
designed with a cascaded chain of optical amplifiers [123]–[126].
The physical origin of ASE-induced jitter can be understood by noting that optical
amplifiers affect not only the amplitude but also the phase of the amplified signal as
apparent from Eq. (6.5.32) or Eq. (6.5.34). Time-dependent variations in the optical
phase lead to a change in the signal frequency by a small amount. Since the group
velocity depends on the frequency because of dispersion, the speed at which a soliton
propagates through the fiber is affected by each amplifier in a random fashion. Such