| Recently, a variety of methods for sending
optical solitons over long distances have been developed
with the use of erbium-doped fiber amplifiers (Hasegawa
and Kodama, 1990; Kubota and Nakazawa, 1990; Mollenauer
et al., 1991; Nakazawa et al., 1991; Mollenauer et al.,
1992; and Nakazawa and Kubota, 1995). For example, synchronous
modulation with optical filters allows for unlimited-distance
soliton transmission because evolution of noise is suppressed
(Nakazawa et al., 1991). The sliding frequency filter technique
can also reduce the noise, and stable soliton transmission
has been achieved for over 10,000 km (Mollenauer et al.,
1992). As long as the average Group Velocity Dispersion
(GVD) is anomalous, a soliton can propagate even in fibers
with normal GVD (Nakazawa and Kubota, 1995). Dispersion
allocation can be used to construct transmission lines with
a suitable average GVD from many fibers which have different
GVDs. This technique made it possible to undertake a soliton
communication field trial very easily using the conventional
fiber cable already installed for commercial systems, and
10-20 Gb/s soliton signals have been successfully transmitted
over 2,000 km in the Tokyo metropolitan optical network
(Nakazawa et al., 1995). Suzuki et al. (1995) recently reported
an allocation technique in a `soliton' system where the
average dispersion is zero. They succeeded in stable pulse
transmission over 10,000 km at 20 Gbps. However, it is not
clear as to what kind of non-linear pulse is propagating
because, in principle, no solitons can exist for zero-average
GVD. Further, the transmission improvement in ultra-long
dispersion managed soliton Wave length Divisional Multiplexing
(WDM) systems, by using pulses with different widths, has
been reported in Lakoba (1995). The proposed method was
suitable for the transmission distances beyond 3,000 km;
however, there is a stipulation of input pulses with different
widths.
In this paper, we have investigated that relatively stable
pulses can propagate over a long-haul dispersion-managed
soliton regime in a fiber link with loss and periodic amplification
by keeping the average dispersion small but non-zero.
Figure 1 demonstrates the layout of a dispersion-managed
soliton regime in a long-haul optical fiber link. It represents
the circulating loop setup, where each loop consists of
six regular fiber spans, one Dispersion-Compensating Fiber
(DCF) span, optical filter and seven optical amplifiers
(EDFAs), with total loop length of 180 km. Soliton pulses
travel through total 100 loops or transmission length up
to 18,000 km. Fibers in a loop are 30 km long with a dispersion
coefficient of 0.2 ps/km/nm at 1550 nm and a dispersion
slope of 0.07 ps/km/nm2. For six spans, total accumulated
dispersion is 36 ps/nm. DCF has a dispersion of 72 ps/km/nm
and a length of 0.5 km, i.e., total dispersion is 36 ps/nm
that fully compensates the cumulative dispersion in the
loop to zero. DCF is inserted non-symmetrically after two
spans of 30 km each. Fiber loss is 0.22 dB/km and EDFAs
are set to a gain of 6.6 dB after every fiber span so as
to compensate signal attenuation. The optical filter is
placed at the end of the loop and has a width of 2.7 nm.
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