212 CHAPTER 5. LIGHTWAVE SYSTEMS
Figure 5.12: Power penalty as a function of the extinction ratio. (After Ref. [105];©c 1987
IEEE; reprinted with permission.)
as is the case for 1.55-μm lightwave systems. TheC=0 curve corresponds to the
case of a chirp-free pulse. The power penalty is negligible (<0.1 dB) in this ideal
case as long as|β 2 |B^2 L< 0 .05. However, the penalty can exceed 5 dB if the pulses
transmitted are chirped such thatC=−6. To keep the penalty below 0.1 dB, the system
should be designed with|β 2 |B^2 L< 0 .002. For|β 2 |=20 ps^2 /km,B^2 Lis limited to 100
(Gb/s)^2 -km. Interestingly, system performance is improved for positive values ofC
since the optical pulse then goes through an initial compression phase (see Section
2.4). Unfortunately,Cis negative for semiconductor lasers; it can be approximated by
−βc, whereβcis the linewidth enhancement factor with positive values of 2–6.
It is important to stress that the analytic results shown in Figs. 5.10 and 5.11 pro-
vide only a rough estimate of the power penalty. In practice, the chirp-induced power
penalty depends on many system parameters. For instance, several system experiments
have shown that the effect of chirp can be reduced by biasing the semiconductor laser
above threshold [103]. However, above-threshold biasing increases that extinction ratio
rex, defined in Eq. (4.6.1) asrex=P 0 /P 1 , whereP 0 andP 1 are the powers received for bit
0 and bit 1, respectively. As discussed in Section 4.6.1, an increase inrexdecreases the
receiver sensitivity and leads to its own power penalty. Clearly,rexcannot be increased
indefinitely in an attempt to reduce the chirp penalty. The total system performance
can be optimized by designing the system so that it operates with an optimum value
ofrexthat takes into account the trade-off between the chirp and the extinction ratio.
Numerical simulations are often used to understand such trade-offs in actual lightwave
systems [110]–[113]. Figure 5.12 shows the power penalty as a function of the extinc-
tion ratiorexby simulating numerically the performance of a 1.55-μm lightwave sys-
tem transmitting at 4 Gb/s over a 100-km-long fiber. The total penalty can be reduced