9.6.3 PMD and PolarizationDependent LossesAs discussed in Section 3.4, fluctuations in the residual birefringence of optical fibers change the state of polarization (SOP) of all channels in a random fashion and also distort optical pulses because of random changes in the speeds of the orthogonally polarized components of the same pulse (PMD). In a realistic WDM system, one should also consider the effects of polarizationdependent loss (PDL) associated with various optical components (see Section 3.5). Moreover, when optical amplifiers are used periodically for loss compensation, the polarizationdependent gain (PDG) of such amplifiers can also degrade a WDM system. For this reason, considerable attention has been paid to understanding the impact of PMD, PDL, and PDG on the performance of WDM systems [157][163]. The main problem from the standpoint of system performance is that fiber birefringence can change with time in a random fashion owing to variations in temperature and stress along the fiber link. As a result, both PMD and PDL can lead to channel outage – a phenomenon in which the BER of a channel increases so much that it is effectively out of use. Such an outage can occur at random times for random durations. The only solution to this problem is to design the WDM system such that the outage probability remains below a certain value. Acceptable values of the outage probability are below 10^{5}, a value that corresponds to an outage of less than 5 min/year. As seen in Section 3.4, the impact of PMD depends on the differential group delay (DGD) that leads to distortion and broadening of optical pulses. The outage probability depends on the average value of DGD and can be reduced by controlling it below a certain value. The origin of PDLinduced outage is quite different and is related to how PDL affects the optical SNR as the signal traverses the fiber link. To understand why PDL changes the SNR, one should consider what happens to the signal and noise as they pass through an optical element with different losses along its principle axes. Since noise is unpolarized, on average half of the noise is polarized along the signal and the other half is orthogonal to it. Because of this feature, a part of the orthogonal noise component is transferred to the signal, and it affects the SNR by an amount that depends on the SOP of the signal before it enters the lossy element. Since signal SOP is random for different PDL elements, the SNR at the end of the fiber link fluctuates in a random fashion. When the number of PDL elements is relatively large, optical SNR as well as the Q factor follow a Gaussian distribution [162]. Because of PDL, the Q factor may increase or decrease, and channel outage occurs when the reduction in Q exceeds a certain value. One can introduce the concept of the PDLinduced penalty as the maximum change in the Q factor for a given amount of PDL. However, since a Gaussian distribution has long tails, the penalty can be arbitrarily large albeit with a lower and lower probability. In one set of numerical simulations, the penalty was defined with 99% confidence, that is, the probability was at most 1% that the actual penalty may exceed the predicted value [162]. Figure 9.33 shows how the Qfactor penalty increases with the average value of accumulated PDL for several values of rootmeansquare DGD. The simulations were performed for a 10Gb/s channel carrying an RZ bit stream with 33% dutycycle Gaussian pulses and operating over 4,000 km with 40 fiber spans. Each span had three PDL elements whose principle axes were oriented randomly. The dotted lines show the improvement that can be realized by employing a PMD compensation scheme. Such a scheme is beneficial but it does not affect the PDLinduced penalty. As seen in Figure 9.33, PDL can degrade the system even in the absence of PMD, and PMD compensation cannot reduce this penalty. Moreover, PDG can lead to additional penalties [158].
Figure 9.33: Qfactor penalty as a function of the average value of PDL along the fiber link for several values of DGD. Dotted lines show the improvement realized with PMD compensation. (After Ref. [162]; ©2003 IEEE.)
Many WDM systems employ a dynamic gain equalizer (DGE) at the location of amplifiers in an attempt to equalize channel powers. It has been noted that PDLinduced fluctuations of the SNR are reduced when such devices are employed [163]. The reason behind the SNR improvement can be understood by considering the noise components that are copolarized or orthogonally polarized with respect to the signal. DGEs reduce the effect of the copolarized noise component but leave the orthogonal part nearly unchanged. An analytic approach has been used to quantify the effects of PDL in the presence of DGEs. The results show that the magnitude of SNR improvement depends on the number of DGEs but as few as four DGEs placed along a longhaul fiber link can improve the SNR by more than 2 dB for accumulated PDL values in the range of 3 to 6 dB.
