312 CHAPTER 7. DISPERSION MANAGEMENT
Figure 7.16: Cascaded gratings used for dispersion compensation in a WDM system. (After
Ref. [143];©c1999 IEEE; reprinted with permission.)
channel WDM system [147]. As the number of channels increases, it becomes more
and more difficult to compensate the GVD of all channels at the same time.
The use ofnegative-slopeDCFs offers the simplest solution to dispersion manage-
ment in high-capacity WDM systems with a large number of channels. Indeed, such
DCFs were developed and commercialized during the 1990s and are employed in virtu-
ally all dense WDM systems [148]–[159]. The need of a negative dispersion slope can
be understood from the condition (7.4.2) obtained in Section 7.4 for a single channel.
This condition should be satisfied for all channels, i.e.,
D 1 (λn)L 1 +D 2 (λn)L 2 = 0 , (7.9.1)whereλnis the wavelength of thenth channel. Because of a finite positive value of the
dispersion slopeS, or the third-order dispersionβ 3 (see Section 2.3.4),D 1 increases
with wavelength for both the standard and dispersion-shifted fibers (see Fig. 2.11). As
a result the accumulated dispersionD 1 L 1 is different for each channel. If the same
DCF has to work for all channels, its dispersion slope should be negative and has a
value such that Eq. (7.9.1) is approximately satisfied for all channels.
WritingDj(λn)=Dj+Sj(λn−λc)in Eq. (7.9.1), whereDj(j= 1 , 2 )is the value
at the wavelengthλcof the central channel, the dispersion slope of the DCF should be
S 2 =−S 1 (L 1 /L 2 )=S 1 (D 2 /D 1 ), (7.9.2)where we used the condition (7.4.2) for the central channel. This equation shows that
the ratioS/D, called therelative dispersion slope, should be the same for both fibers
used to form the dispersion map [44]. For standard fibers withD≈16 ps/(km-nm)
andS≈ 0 .05 ps/(km-nm^2 ), this ratio is about 0.003 nm−^1. Thus, for a DCF with
D≈−100 ps/(km-nm), the dispersion slope should be about−0.3 ps/(km-nm^2 ). Such
DCFs have been made and are available commercially. In the case of dispersion-shifted
fibers, the ratioS/Dcan exceed 0.02 nm−^1. It is hard to manufacture DCFs with such
large values of the relative dispersion slope, although two-mode DCFs can provide
values as large as 0.01 nm−^1 (see Fig. 7.5). In their place,reverse-dispersionfibers