9.7. WDM SOLITON SYSTEMS 465
Distance (Mm)Frequency shift (GHz)Time shift (ps)Figure 9.28: Collision-induced frequency and temporal shifts for a soliton surrounded by four
channels on each side (75 GHz spacing). Curves 1 and 2 represent the case copolarized and
orthogonally polarized solitons in neighboring channels, respectively. Curves 3 and 4 show the
improvement realized with sliding-frequency filters. The dotted line shows the prediction of an
analytical model. (After Ref. [238]);©c1999 OSA; reprinted with permission.)
much slower relative motion governed by the average value of GVD. Since the effec-
tive collision length is much larger than the map period (and the amplifier spacing),
the conditionLcoll> 2 LAis satisfied even when soliton wavelengths differ by 20 nm
or more. This feature makes it possible to design WDM soliton systems with a large
number of high-bit-rate channels.
The residual frequency shift introduced during such a process depends on a large
number of parameters including the map period, map strength, and amplifier spacing
[236]–[240]. Physically speaking, residual frequency shifts occurring during complete
collisions average out to zero. However, not all collisions are complete. For example,
if solitons overlap initially, the incomplete nature of the collision will produce some
residual frequency shift. The zigzag motion of solitons can also produce frequency
shifts if the solitons approach each other near the junction of opposite-GVD fibers
since they will reverse direction before crossing each other. Such partial collisions can
result in large frequency shifts, which can shift solitons by a large amount within their
bit slots. This behavior is unacceptable from a system standpoint.
A simple solution to this problem is provided by sliding-frequency filters [238].
Such filters reduce the frequency and temporal shifts to manageable levels in the same
way they mitigate the effects of ASE-induced frequency shifts. Curve 1 in Figure 9.28
shows the frequency and temporal shifts (calculated numerically) for the middle chan-
nel surrounded by four channels on each side (channel spacing 75 GHz). The soliton
shifts by 100 ps (one bit slot) over 10,000 km because its frequency shifts by more than
10 GHz. The use of orthogonally polarized solitons (curve 2) improves the situation