412 CHAPTER 9. SOLITON SYSTEMS
Figure 9.5: Soliton bit stream in RZ format. Each soliton occupies a small fraction of the bit
slot so that neighboring soliton are spaced far apart.
RZ format. Typically, spacing between the solitons exceeds four times their full width
at half maximum (FWHM).
The input pulse characteristics needed to excite the fundamental soliton can be
obtained by settingξ=0 in Eq. (9.1.11). In physical units, the power across the pulse
varies as
P(t)=|A( 0 ,t)|^2 =P 0 sech^2 (t/T 0 ). (9.2.2)
The required peak powerP 0 is obtained from Eq. (9.1.4) by settingN=1 and is related
to the widthT 0 and the fiber parameters as
P 0 =|β 2 |/(γT 02 ). (9.2.3)The width parameterT 0 is related to the FWHM of the soliton as
Ts= 2 T 0 ln( 1 +√
2 ) 1. 763 T 0. (9.2.4)
The pulse energy for the fundamental soliton is obtained using
Es=∫∞−∞P(t)dt= 2 P 0 T 0. (9.2.5)Assuming that 1 and 0 bits are equally likely to occur, the average power of the RZ
signal becomesP ̄s=Es(B/ 2 )=P 0 / 2 q 0. As a simple example,T 0 =10 ps for a 10-Gb/s
soliton system if we chooseq 0 =5. The pulse FWHM is about 17.6 ps forT 0 =10 ps.
The peak power of the input pulse is 5 mW usingβ 2 =−1ps^2 /km andγ=2W−^1 /km
as typical values for dispersion-shifted fibers. This value of peak power corresponds to
a pulse energy of 0.1 pJ and an average power level of only 0.5 mW.
9.2.2 Soliton Interaction
An important design parameter of soliton lightwave systems is the pulse widthTs.As
discussed earlier, each soliton pulse occupies only a fraction of the bit slot. For practical
reasons, one would like to pack solitons as tightly as possible. However, the presence of
pulses in the neighboring bits perturbs the soliton simply because the combined optical
field is not a solution of the NLS equation. This phenomenon, referred to assoliton
interaction, has been studied extensively [29]–[33].