"Introduction". In: Fiber-Optic Communication Systems

420 CHAPTER 9. SOLITON SYSTEMS

Figure 9.10: (a) Lumped and (b) distributed amplification schemes for compensation of fiber
losses in soliton communication systems.

9.3.2 Lumped Amplification.....................

The lumped amplification scheme shown in Fig. 9.10 is the same as that used for non-
soliton systems. In both cases, optical amplifiers are placed periodically along the fiber
link such that fiber losses between two amplifiers are exactly compensated by the am-
plifier gain. An important design parameter is the spacingLAbetween amplifiers—it
should be as large as possible to minimize the overall cost. For nonsoliton systems,LA
is typically 80–100 km. For soliton systems,LAis restricted to much smaller values
because of the soliton nature of signal propagation [57].
The physical reason behind smaller values ofLAis that optical amplifiers boost soli-
ton energy to the input level over a length of few meters without allowing for gradual
recovery of the fundamental soliton. The amplified soliton adjusts its width dynami-
cally in the fiber section following the amplifier. However, it also sheds a part of its
energy as dispersive waves during this adjustment phase. The dispersive part can ac-
cumulate to significant levels over a large number of amplification stages and must be
avoided. One way to reduce the dispersive part is to reduce the amplifier spacingLA
such that the soliton is not perturbed much over this short length. Numerical simula-
tions show [57] that this is the case whenLAis a small fraction of the dispersion length
(LALD). The dispersion lengthLDdepends on both the pulse widthT 0 and the GVD
parameterβ 2 and can vary from 10 to 1000 km depending on their values.
Periodic amplification of solitons can be treated mathematically by adding a gain
term to Eq. (9.3.1) and writing it as [61]

i

∂u

∂ξ

+

1

2

∂^2 u

∂τ^2

+|u|^2 u=−

i

2

Γu+

i

2

g(ξ)LDu, (9.3.4)

whereg(ξ)=∑NmA= 1 gmδ(ξ−ξm),NAis the total number of amplifiers, andgmis the
gain of the lumped amplifier located atξm. If we assume that amplifiers are spaced
uniformly,ξm=mξA, whereξA=LA/LDis the normalized amplifier spacing.