7.9. HIGH-CAPACITY SYSTEMS 319
(a) (b)Figure 7.21: Tunable PMD compensation provided by a birefringent chirped fiber grating. (a)
The origin of differential group delay; (b) stop-band shift induced by stretching the grating.
(After Ref. [160];©c1999 IEEE; reprinted with permission.)
the ratioL/LPMDfor a fiber of lengthL, whereLPMD=(T 0 /Dp)^2 is the PMD length
for pulses of widthT 0 [202]. Considerable improvement is expected as long as this
ratio does not exceed 4. BecauseLPMDis close to 10,000 km forDp≈ 0 .1 ps/
√
km
andT 0 =10 ps, such a PMD compensator can work over transoceanic distances for
10-Gb/s systems.
Several other all-optical techniques can be used for PMD compensation [205]. For
example, a LiNbO 3 -based Soleil–Babinet compensator can provide endless polariza-
tion control. Other devices include ferroelectric liquid crystals, twisted polarization-
maintaining fibers, optical all-pass filters [209], and birefringent chirped fiber grat-
ings [204]. Figure 7.21 shows how a grating-based PMD compensator works. Because
of a large birefringence, the two field components polarized along the slow and fast axis
have different Bragg wavelengths and see slightly shifted stop bands. As a result, they
are reflected at different places within the grating and experience a differential group
delay that can compensate for the PMD-induced group delay. The delay is wavelength
dependent because of the chirped nature of the grating. Moreover, it can be tuned over
several nanometers by stretching the grating [160]. Such a device can provide tunable
PMD compensation and is suited for WDM systems.
It should be stressed that optical PMD compensators shown in Figs. 7.20 and 7.21
remove only the first-order PMD effects. At high bit rates, optical pulses are short
enough and their spectrum becomes wide enough that the PSPs cannot be assumed
to remain constant over the whole pulse spectrum. Higher-order PMD effects have
become of concern with the advent of 40-Gb/s lightwave systems, and techniques for
compensating them have been proposed [207].
The effectiveness of first-order PMD compensation can be judged by considering
how much PMD-induced pulse broadening is reduced by such a compensator. An
analytical theory of PMD compensation shows that the average or expected value of
the broadening factor, defined asb^2 =σ^2 /σ 02 , is given by the following expression for
an unchirped Gaussian pulse of widthT 0 [206]:
b^2 c=b^2 u+ 2 x/ 3 − 4 [( 1 + 2 x/ 3 )^1 /^2 − 1 ], (7.9.9)