Nonlinear Fiber Optics - 4 ed. Agrawal

5.2. Fiber Solitons 129
Figure 5.5: Predicted gain spectrum (a) for a 1000-km-long fiber link when 95% of dispersion is
compensated after each 100-km-long span such that the average dispersion D = 0.8 ps/(km-nm).
The curve (b) shows the gain spectrum for a constant-dispersion fiber link with the same net
dispersion. (After Ref. [61]; c○1999 IEEE.)
standard fiber with a loss of 0.22 dB/km, dispersion D = 16 ps/(km-nm), and γ = 1.7
W −1 /km. An amplifier at the end of each span compensates total losses incurred in that
span [61]. When dispersion is not compensated, the spectrum exhibits many sidebands.
These sidebands are suppressed and the peak gain is reduced considerably when 95%
of dispersion is compensated after each span (curve a) such that the average dispersion
is 0.8 ps/(km-nm). As shown by curve (b), the gain is much higher if the lightwave
system is designed using a uniform-dispersion fiber with D = 0.8 ps/(km-nm).
Modulation instability affects WDM systems in several other ways. It has been
shown that WDM systems suffer from a resonant enhancement of four-wave mixing
that degrades the system performance considerably when channel spacing is close to
the frequency at which the modulation-instability gain is strongest [60]. On the positive
side, this enhancement can be used for low-power, high-efficiency, wavelength
conversion [64]. Modulation instability has been used for measuring the distribution
of zero-dispersion wavelength along a fiber by noting that the instability gain becomes
quite small in the vicinity of |β 2 | = 0 [65]. As discussed in Section 11.1.4, it can also
be used to deduce the value of the nonlinear parameter γ [66].
5.2 Fiber Solitons
The occurrence of modulation instability in the anomalous-GVD regime of optical
fibers is an indication of a fundamentally different character of Eq. (5.1.1) when β 2 < 0.
It turns out that this equation has specific pulselike solutions that either do not change
along fiber length or follow a periodic evolution pattern—such solutions are known
as optical solitons. The history of solitons, in fact, dates back to 1834, the year in
which Scott Russell observed a heap of water in a canal that propagated undistorted
over several kilometers. Here is a quote from his report published in 1844 [67]: