458 CHAPTER 9. SOLITON SYSTEMS
Figure 9.25: Effect of third-order dispersion on timing jitter in a periodically amplified DDF-
based soliton system designed using parametric amplifiers.
9.7 WDM Soliton Systems
As discussed in Chapter 8, the capacity of a lightwave system can be increased consid-
erably by using the WDM technique. A WDM soliton system transmits several soliton
bit streams over the same fiber using different carrier frequencies. This section focuses
on the issues relevant for designing WDM soliton systems [205].
9.7.1 Interchannel Collisions.....................
A new feature that becomes important for WDM systems is the possibility of collisions
among solitons belonging to different channels and traveling different group velocities.
To understand the importance of such collisions as simply as possible, we first focus on
standard solitons propagating in DDFs and use Eq. (9.4.3) as it includes the effects of
both loss and dispersion variations. Dropping prime overξfor notational convenience,
this equation can be written as
i
∂v
∂ξ+
1
2
∂^2 v
∂τ^2+b(ξ)|v|^2 v= 0 , (9.7.1)whereb(ξ)=p(ξ)/d(ξ). The functional form ofb(ξ)depends on the details of the
loss- and dispersion-management schemes.
The effects of interchannel collisions on the performance of WDM systems can
be best understood by considering the simplest case of two WDM channels separated
byfch. In normalized units, solitons are separated in frequency byΩch= 2 πfchT 0.
Replacingvbyu 1 +u 2 in Eq. (9.7.1) and neglecting the FWM terms, solitons in each
channel evolve according to the following two coupled equations [206]:
i
∂u 1
∂ξ+
1
2
∂^2 u 1
∂τ^2+b(ξ)(|u 1 |^2 + 2 |u 2 |^2 )u 1 = 0 , (9.7.2)i∂u 2
∂ξ+
1
2
∂^2 u 2
∂τ^2+b(ξ)(|u 2 |^2 + 2 |u 1 |^2 )u 2 = 0. (9.7.3)