9.3. LOSS-MANAGED SOLITONS 425
where the TOD parameterδ 3 and the Raman parameterτRare defined as
δ=β 3 /( 6 |β 2 |T 0 ), τR=TR/T 0. (9.3.17)The quantityTRis related to the slope of the Raman gain spectrum and has a value of
about 3 fs for silica fibers [10].
Numerical simulations based on Eq. (9.3.16) show that the distributed-amplification
scheme benefits considerably high-capacity soliton communication systems [69]. For
example, whenLD=50 km but amplifiers are placed 100 km apart, fundamental soli-
tons withT 0 =5 ps are destroyed after 500 km in the case of lumped amplifiers but can
propagate over a distance of more than 5000 km when distributed amplification is used.
For soliton widths below 5 ps, the Raman-induced spectral shift leads to considerable
changes in the evolution of solitons as it modifies the gain and dispersion experienced
by solitons. Fortunately, the finite gain bandwidth of amplifiers reduces the amount of
spectral shift and stabilizes the soliton carrier frequency close to the gain peak [63].
Under certain conditions, the spectral shift can become so large that it cannot be com-
pensated, and the soliton moves out of the gain window, loosing all its energy.
9.3.4 Experimental Progress
Early experiments on loss-managed solitons concentrated on the Raman-amplification
scheme. An experiment in 1985 demonstrated that fiber losses can be compensated
over 10 km by the Raman gain while maintaining the soliton width [59]. Two color-
center lasers were used in this experiment. One laser produced 10-ps pulses at 1.56μm,
which were launched as fundamental solitons. The other laser operated continuously
at 1.46μm and acted as a pump for amplifying 1.56-μm solitons. In the absence of the
Raman gain, the soliton broadened by about 50% because of loss-induced broadening.
This amount of broadening was in agreement with Eq. (9.3.3), which predictsT 1 /T 0 =
1.51 forz=10 km andα= 0 .18 dB/km, the values used in the experiment. When the
pump power was about 125 mW, the 1.8-dB Raman gain compensated the fiber losses
and the output pulse was nearly identical with the input pulse.
A 1988 experiment transmitted solitons over 4000 km using the Raman-amplifica-
tion scheme [4]. This experiment used a 42-km fiber loop whose loss was exactly
compensated by injecting the CW pump light from a 1.46-μm color-center laser. The
solitons were allowed to circulate many times along the fiber loop and their width
was monitored after each round trip. The 55-ps solitons could be circulated along
the loop up to 96 times without a significant increase in their pulse width, indicating
soliton recovery over 4000 km. The distance could be increased to 6000 km with
further optimization. This experiment was the first to demonstrate that solitons could
be transmitted over transoceanic distances in principle. The main drawback was that
Raman amplification required pump lasers emitting more than 500 mW of CW power
near 1.46μm. It was not possible to obtain such high powers from semiconductor
lasers in 1988, and the color-center lasers used in the experiment were too bulky to be
useful for practical lightwave systems.
The situation changed with the advent of EDFAs around 1989 when several exper-
iments used them for loss-managed soliton systems [38]–[40]. These experiments can