Nonlinear Fiber Optics - 4 ed. Agrawal

150 Chapter 5. Optical Solitons
Figure 5.13: (a) Lumped and (b) distributed amplification schemes used for restoring soliton
energy by compensating fiber losses.
the lumped-amplification scheme becomes impractical at high bit rates requiring short
solitons (T 0 < 10 ps) because dispersion length can then become quite short.
The distributed-amplification scheme often employs stimulated Raman scattering
[131]–[134] to provide gain (see Chapter 8). In this approach, a pump beam (upshifted
in frequency from the soliton carrier frequency by nearly 13 THz) is injected
periodically into the fiber. For solitons propagating in the 1.55-μm wavelength region,
one needs a high-power pump laser operating near 1.45 μm. The required pump power
exceeds 100 mW for Raman amplification. Since the optical gain is distributed over the
entire fiber length, solitons can be amplified adiabatically while maintaining N close to
1, a feature that reduces the dispersive part almost entirely [133].
Feasibility of the Raman-amplification scheme was first demonstrated in 1985 in an
experiment in which soliton pulses of 10-ps width were propagated over a 10-km-long
fiber [132]. In the absence of Raman gain, the width of solitons increased by ≈ 50%
because of loss-induced broadening. This is in agreement with Eq. (5.4.11), which
predicts T 1 /T 0 = 1.51 for z = 10 km and α = 0.18 dB/km, the values relevant for the
experiment. The Raman gain was obtained by injecting a CW pump beam at 1.46 μm
from a color-center laser in the direction opposite to that of soliton propagation. The
pump power was adjusted close to 125 mW such that the total fiber loss of 1.8 dB
was exactly balanced by the Raman gain. In a 1988 experiment [134], 55-ps solitons
could be circulated up to 96 times inside a 42-km fiber loop without significant increase
in their width, resulting in an effective transmission distance of >4000 km. The
lumped-amplification scheme was used starting in 1989 [135]. Since erbium-doped
fiber amplifiers became available commercially after 1990, they were used almost exclusively
until 2002 in spite of the lumped nature of amplification provided by them.
After 2002, the use of distributed Raman amplification has become more prevalent for
long-haul lightwave systems.
The main shortcoming of lumped amplifiers is that soliton energy can vary by as
much as a factor of 100 between two neighboring amplifiers. To understand how soli-