442 CHAPTER 9. SOLITON SYSTEMS
For DM solitons the energy enhancement factorfLMis replaced byfLMfDM/3. The tol-
erable value ofbjdepends on the acceptable BER and on details of the receiver design;
typically,bj< 0 .1. To see how amplifier noise limits the total transmission distance,
consider a standard soliton system operating close to the zero-dispersion wavelength
with parameter valuesq 0 =5,α= 0 .2 dB/km,γ=2W−^1 /km,β ̄ 2 =−1 ps/(km-nm),
nsp= 1 .5,LA=80 km, andbj= 0 .1. UsingG=16 dB, we findfLM= 3 .78 and
Ssp= 6. 46 × 10 −^6 pJ. With these values,BLTmust be below 132 (Tb/s)-km. For a
40-Gb/s system, the transmission distance is limited to below 3300 km. This value can
be increased to above 10,000 km for DM solitons.
9.5.4 Control of Timing Jitter
As the timing jitter ultimately limits the performance of soliton systems, it is essential
to find a solution to the timing-jitter problem before the use of solitons can become
practical. Several techniques were developed during the 1990s for controlling the tim-
ing jitter [126]–[146]. This section is devoted to a brief discussion of them.
The use of optical filters for controlling the timing jitter of solitons was proposed
as early as 1991 [126]–[128]. This approach makes use of the fact that the ASE oc-
curs over the entire amplifier bandwidth but the soliton spectrum occupies only a small
fraction of it. The bandwidth of optical filters is chosen such that the soliton bit stream
passes through the filter but most of the ASE is blocked. If an optical filter is placed
after each amplifier, it improves the SNR because of the reduced ASE and also re-
duces the timing jitter simultaneously. This was indeed found to be the case in a 1991
experiment [127] but the reduction in timing jitter was less than 50%.
The filter technique can be improved dramatically by allowing the center frequency
of the successive optical filters to slide slowly along the link. Suchsliding-frequency
filters avoid the accumulation of ASE within the filter bandwidth and, at the same time,
reduce the growth of timing jitter [129]. The physical mechanism behind the operation
of such filters can be understood as follows. As the filter passband shifts, solitons
shift their spectrum as well to minimize filter-induced losses. In contrast, the spectrum
of ASE cannot change. The net result is that the ASE noise accumulated over a few
amplifiers is filtered out later when the soliton spectrum has shifted by more than its
own bandwidth.
The moment method can be extended to include the effects of optical filters by
noting that each filter modifies the soliton field such that
Bf(zf,t)=1
2 π∫∞−∞Hf(ω−ωf)B ̃(zf,ω)e−iωtdω, (9.5.36)whereB ̃(zf,ω)is the pulse spectrum andHfis the transfer function of the optical filter
located atξf. The filter passband is shifted byωffrom the soliton carrier frequency.
If we approximate the filter spectrum by a parabola over the soliton spectrum and use
Hf(ω−ωf)= 1 −b(ω−ωf)^2 , it is easy to see that the filter introduces an additional
loss for the soliton that should be compensated by increasing the gain of optical am-
plifiers. The analysis of timing jitter shows that sliding-frequency filters reduce jitter
considerably for both the standard and DM solitons [142].