Nonlinear Fiber Optics - 4 ed. Agrawal

152 Chapter 5. Optical Solitons
Figure 5.14: Evolution of loss-managed solitons over 10,000 km for L D = 200 (left) and L D =
25 km (right) when L A = 50 km, α = 0.22 dB/km, and β 2 = 0.5ps 2 /km.
The condition ξ A ≪ 1orL A ≪ L D , required to operate within the average-soliton
regime, can be related to the width T 0 by using L D = T0 2/|β
2|. The resulting condition
is
T 0 ≫ √ |β 2 |L A . (5.4.19)
The bit rate B of a soliton communication system is related to T 0 through T B = 1/B =
2q 0 T 0 , where T B is the bit slot and q 0 represents the factor by which it is larger than
the soliton width. Thus, the condition (5.4.19) can be written in the form of a simple
design criterion:
B 2 L A ≪ (4q 2 0|β 2 |) −1 . (5.4.20)
By choosing typical values β 2 = −0.5 ps 2 /km, L A = 50 km, and q 0 = 5, we obtain
T 0 ≫ 5psandB ≪ 20 GHz. Clearly, the use of amplifiers for soliton amplification
imposes a severe limitation on both the bit rate and the amplifier spacing in practice.
Optical amplifiers, needed to restore the soliton energy, also add noise originating
from spontaneous emission. The effect of spontaneous emission is to change randomly
the four soliton parameters, η,δ,q, and φ in Eq. (5.4.2), at the output of each amplifier
[141]. Amplitude fluctuations, as one might expect, degrade the signal-to-noise ratio
(SNR). However, for applications of solitons in optical communications, frequency
fluctuations are of much more concern. The reason can be understood from Eq. (5.4.2),
and noting that a change in the soliton frequency by δ affects the speed at which the
soliton propagates through the fiber. If δ fluctuates because of amplifier noise, soliton
transit time through the fiber also becomes random. Fluctuations in the arrival time
of a soliton are referred to as the Gordon–Haus timing jitter [153]. Such timing jitter
often limits the performance of soliton-based systems but it can be reduced in practice
by using a variety of techniques [93]–[95].
5.4.4 Soliton Interaction
The time interval T B between two neighboring bits or pulses determines the bit rate of
a communication system as B = 1/T B . It is thus important to determine how close two
solitons can come without affecting each other. Interaction between two solitons has