9.2. SOLITON-BASED COMMUNICATIONS 411
fiber was used to generate a train of dark solitons [22]. A 100-GHz train of 1.6-ps dark
solitons was generated with this technique and propagated over 2.2 km of (two soliton
periods) of a dispersion-shifted fiber. Optical switching using a fiber-loop mirror, in
which a phase modulator is placed asymmetrically, can also produce dark solitons [23].
In another variation, a fiber with comb-like dispersion profile was used to generate dark
soliton pulses with a width of 3.8 ps at the 48-GHz repetition rate [24].
An interesting scheme uses electronic circuitry to generate a coded train of dark
solitons directly from the nonreturn-to-zero (NRZ) data in electric form [25]. First,
the NRZ data and its clock at the bit rate are passed through an AND gate. The re-
sulting signal is then sent to a flip-flop circuit in which all rising slopes flip the signal.
The resulting electrical signal drives a Mach–Zehnder LiNbO 3 modulator and converts
the CW output from a semiconductor laser into a coded train of dark solitons. This
technique was used for data transmission, and a 10-Gb/s signal was transmitted over
1200 km by using dark solitons. Another relatively simple method uses spectral filter-
ing of a mode-locked pulse train through a fiber grating [26]. This scheme has also
been used to generate a 6.1-GHz train and propagate it over a 7-km-long fiber [27].
Numerical simulations show that dark solitons are more stable in the presence of noise
and spread more slowly in the presence of fiber losses compared with bright solitons.
Although these properties point to potential application of dark solitons for optical
communications, only bright solitons were being pursued in 2002 for commercial ap-
plications.
9.2 Soliton-Based Communications
Solitons are attractive for optical communications because they are able to maintain
their width even in the presence of fiber dispersion. However, their use requires sub-
stantial changes in system design compared with conventional nonsoliton systems. In
this section we focus on several such issues.
9.2.1 Information Transmission with Solitons
As discussed in Section 1.2.3, two distinct modulation formats can be used to generate
a digital bit stream. The NRZ format is commonly used because the signal bandwidth
is about 50% smaller for it compared with that of the RZ format. However, the NRZ
format cannot be used when solitons are used as information bits. The reason is easily
understood by noting that the pulse width must be a small fraction of the bit slot to
ensure that the neighboring solitons are well separated. Mathematically, the soliton
solution in Eq. (9.1.11) is valid only when it occupies the entire time window (−∞<
τ<∞). It remains approximately valid for a train of solitons only when individual
solitons are well isolated. This requirement can be used to relate the soliton widthT 0
to the bit rateBas
B=1
TB
=
1
2 q 0 T 0, (9.2.1)
whereTBis the duration of the bit slot and 2q 0 =TB/T 0 is the separation between
neighboring solitons in normalized units. Figure 9.5 shows a soliton bit stream in the