320 CHAPTER 7. DISPERSION MANAGEMENT
Average DGD/Pulse widthFigure 7.22: Pulse broadening factor as a function of average DGD in four cases. The dotted
curve shows the improvement realized using a first-order PMD compensator. Filled and empty
circles show the results of numerical simulations (After Ref. [206];©c2000 IEEE; reprinted with
permission.)
wherex=〈(∆T)^2 〉/ 4 T 02 ,∆Tis the differential group delay along the PSPs, andb^2 uis
the value before PMD compensation:
b^2 u= 1 +x−^12 [( 1 + 4 x/ 3 )^1 /^2 − 1 ]. (7.9.10)Figure 7.22 shows the broadening factorsbu(solid line) andbc(dotted line) as a func-
tion of〈∆T〉/T 0. For comparison, the worst and best cases corresponding to the two
specific choices of the input state of polarization (SOP) are also shown.
Figure 7.22 can be used to estimate the improvement realized by a first-order PMD
compensator. As discussed earlier, the average DGD should not exceed about 10%
of the bit slot in uncompensated systems for keeping the outage probability below
10 −^5. Thus, the tolerable value of PMD-induced pulse broadening is close tob= 1 .02.
From Eqs. (7.9.9) and (7.9.10) it is easy to show that this value can be maintained
in PMD-compensated systems even whenσTexceeds 30%. Thus, a first-order PMD
compensator can increase the tolerable value of DGD by more than a factor of 3. The
net result is a huge increase in the transmission distance of PMD-compensated systems.
One should note that a single PMD compensator cannot be used for all WDM channels.
Rather, a separate PMD compensator is required for each channel. This fact makes
PMD compensation along the fiber link a costly proposition for WDM systems. An
optical compensator just before the receiver or an electrical PMD equalizer built into
the receiver provides the most practical solution; both were being pursued in 2001 for
commercial applications.