7.9. HIGH-CAPACITY SYSTEMS 315
Figure 7.18: Receiver sensitivities measured in a 160-Gb/s experiment as a function of the
preset dispersion with (squares) and without (circles) a chirped fiber–Bragg grating (CFBG).
The improvement in the eye diagram is shown for 110 ps/nm on the right. (After Ref. [165];
©c2000 IEEE; reprinted with permission.)
7.9.3 Higher-Order Dispersion Management
When the bit rate of a single channel exceeds 40 Gb/s (through the used of time-division
multiplexing, for example), the third- and higher-order dispersive effects begin to in-
fluence the optical signal. For example, the bit slot at a bit rate of 100 Gb/s is only
10 ps wide, and an RZ optical signal would consist of pulses of width<5 ps. Equa-
tion (2.4.34) can be used to estimate the maximum transmission distanceL, limited by
the third-order dispersionβ 3 , when only second-order dispersion is compensated. The
result is
L≤ 0. 034 (|β 3 |B^3 )−^1. (7.9.4)
This limitation is shown in Fig. 2.13 by the dashed line. At a bit rate of 200 Gb/s,Lis
limited to about 50 km and drops to only 3.4 km at 500 Gb/s if we use a typical value
β 3 = 0 .08 ps^3 /km. Clearly, it is essential to use techniques that compensate for both
the second- and third-order dispersion simultaneously when the single-channel bit rate
exceeds 100 Gb/s, and several techniques have been developed for this purpose [168]–
[180].
The simplest solution to third-order dispersion compensation is provided by DCFs
designed to have a negative dispersion slope so that bothβ 2 andβ 3 have opposite signs,
in comparison with the standard fibers. The necessary conditions for designing such
fibers can be obtained by solving Eq. (7.1.3) using the Fourier-transform method. For
a fiber link containing two different fibers of lengthsL 1 andL 2 , the conditions for
dispersion compensation become
β 21 L 1 +β 22 L 2 = 0 and β 31 L 1 +β 32 L 2 = 0 , (7.9.5)whereβ 2 jandβ 3 jare second- and third-order dispersion parameters for the fiber of
lengthLj. The first condition is the same as Eq. (7.4.2). By using Eq. (7.4.3), the
second condition can be used to find the third-order dispersion parameter for the DCF:
β 32 =(β 22 /β 21 )β 31 =−(L 1 /L 2 )β 31. (7.9.6)