286 CHAPTER 7. DISPERSION MANAGEMENT
external-cavity semiconductor laser, over 70 km of fiber [26]. Figure 7.3 compares the
streak-camera traces of the signal obtained with and without dispersion compensation.
From Eq. (7.1.2), in the absence of amplifier-induced chirp, the transmission distance
at 16 Gb/s is limited by GVD to about 14 km for a fiber withD=15 ps/(km-nm). The
use of the amplifier in the gain-saturation regime increased the transmission distance
fivefold, a feature that makes this approach to dispersion compensation quite attractive.
It has an added benefit that it can compensate for the coupling and insertion losses that
invariably occur in a transmitter by amplifying the signal before it is launched into the
optical fiber. Moreover, this technique can be used for simultaneous compensation of
fiber losses and GVD if SOAs are used as in-line amplifiers [29].
A nonlinear medium can also be used to prechirp the pulse. As discussed in Section
2.6, the intensity-dependent refractive index chirps an optical pulse through the phe-
nomenon of self-phase modulation (SPM). Thus, a simple prechirp technique consists
of passing the transmitter output through a fiber of suitable length before launching it
into the fiber link. Using Eq. (2.6.13), the optical signal at the fiber input is given by
A( 0 ,t)=√
P(t)exp[iγLmP(t)], (7.2.8)whereP(t)is the power of the pulse,Lmis the length of the nonlinear medium, andγis
the nonlinear parameter. In the case of Gaussian pulses for whichP(t)=P 0 exp(−t^2 /T 02 ),
the chirp is nearly linear, and Eq. (7.2.8) can be approximated by
A( 0 ,t)≈√
P 0 exp[
−
1 +iC
2(
t
T 0) 2 ]
exp(−iγLmP 0 ), (7.2.9)where the chirp parameter is given byC= 2 γLmP 0 .Forγ>0, the chirp parameterCis
positive, and is thus suitable for dispersion compensation.
Sinceγ>0 for silica fibers, the transmission fiber itself can be used for chirping the
pulse. This approach was suggested in a 1986 study [30]. It takes advantage of higher-
order solitons which pass through a stage of initial compression (see Chapter 9). Figure
7.4 shows the GVD-limited transmission distance as a function of the average launch
power for 4- and 8-Gb/s lightwave systems. It indicates the possibility of doubling
the transmission distance by optimizing the average power of the input signal to about
3mW.
7.3 Postcompensation Techniques
Electronic techniques can be used for compensation of GVD within the receiver. The
philosophy behind this approach is that even though the optical signal has been de-
graded by GVD, one may be able to equalize the effects of dispersion electronically
if the fiber acts as alinear system. It is relatively easy to compensate for dispersion
if a heterodyne receiver is used for signal detection (see Section 10.1). A heterodyne
receiver first converts the optical signal into a microwave signal at the intermediate fre-
quencyωIFwhile preserving both the amplitude and phase information. A microwave
bandpass filter whose impulse response is governed by the transfer function
H(ω)=exp[−i(ω−ωIF)^2 β 2 L/ 2 ], (7.3.1)