372 CHAPTER 8. MULTICHANNEL SYSTEMS
pulse spectrum first toward red and then toward blue. In a lossless fiber, collisions of
two pulses are perfectly symmetric, resulting in no net spectral shift at the end of the
collision. In a loss-managed system with optical amplifiers placed periodically along
the link, power variations make collisions between pulses of different channels asym-
metric, resulting in a net frequency shift that depends on the channel spacing. Such
frequency shifts lead to timing jitter (the speed of a channel depends on its frequency
because of GVD) since their magnitude depends on the bit pattern as well as on the
channel wavelengths. The combination of XPM-induced amplitude and timing jitter
degrades the SNR at the receiver, especially for closely spaced channels, and leads to
XPM-induced power penalty that depends on channel spacing and the type of fibers
used for the WDM link. The power penalty increases for fibers with large GVD and
for WDM systems designed with a small channel spacing and can exceed 5 dB even
for 100-GHz spacing.
How can one control the XPM-induced crosstalk in WDM systems? Clearly, the
use of low-GVD fibers will reduce this problem to some extent but is not practical be-
cause of the onset of FWM (see next subsection). In practice, dispersion management
is employed in virtually all WDM systems such that the local dispersion is relatively
large. Careful selection of the dispersion-map parameters may help from the XPM
standpoint but may not be optimum from the SPM point of view [190]. A simple
approach to XPM suppression consists of introducing relative time delays among the
WDM channels after each map period such that the “1” bits in neighboring channels are
unlikely to overlap most of the time [196]. The use of RZ format is quite helpful in this
context because all 1 bits occupy only a fraction of the bit slot. In a 10-channel WDM
experiment, time delays were introduced by using 10 fiber gratings spaced apart by
varying distances chosen to enhance XPM suppression [198]. The BER floor observed
after 500 km of transmission disappeared after the XPM suppressors (consisting of 10
Bragg gratings) were inserted every 100 km. The residual power penalty at a BER of
10 −^10 was below 2 dB for all channels.
8.3.6 Four-Wave Mixing
As discussed in Section 2.6, the nonlinear phenomenon of FWM requires phase match-
ing. It becomes a major source of nonlinear crosstalk whenever the channel spacing
and fiber dispersion are small enough to satisfy the phase-matching condition approxi-
mately [59]. This is the case when a WDM system operates close to the zero-dispersion
wavelength of dispersion-shifted fibers. For this reason, several techniques have been
developed for reducing the impact of FWM in WDM systems [167].
The physical origin of FWM-induced crosstalk and the resulting system degrada-
tion can be understood by noting that FWM generates a new wave at the frequency
ωijk=ωi+ωj−ωk, whenever three waves at frequenciesωi,ωj, andωkcopropagate
inside the fiber. For anN-channel system,i,j, andkcan vary from 1 toN, resulting
in a large combination of new frequencies generated by FWM. In the case of equally
spaced channels, the new frequencies coincide with the existing frequencies, leading to
coherent in-band crosstalk. When channels are not equally spaced, most FWM com-
ponents fall in between the channels and lead to incoherent out-of-band crosstalk. In