368 CHAPTER 8. MULTICHANNEL SYSTEMS
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Number of Channels0.01.02.03.04.05.0Power Penalty10 mW
521Figure 8.23: Raman-induced power penalty as a function of channel number for several values
ofPch. Channels are 100 GHz apart and launched with equal powers.
In the limitM^2 CRPchLeff1, this complicated expression reduces to the simple result
in Eq. (8.3.10). In general, Eq. (8.3.10) overestimates the Raman crosstalk.
The Raman-induced power penalty is obtained usingδR=−10 log( 1 −DR)be-
cause the input channel power must be increased by a factor of( 1 −DR)−^1 to maintain
the same system performance. Figure 8.23 shows how the power penalty increases
with an increase in the channel power and the number of channels. The channel spac-
ing is assumed to be 100 GHz. The slope of the Raman gain is estimated from the gain
spectrum to beSR= 4. 9 × 10 −^18 m/(W-GHz) whileAeff= 50 μm^2 andLeff≈ 1 /α=
21.74 km. As seen from Fig. 8.23, the power penalty becomes quite large for WDM
systems with a large number of channels. If a value of at most 1 dB is considered ac-
ceptable, the limiting channel powerPchexceeds 10 mW for 20 channels, but its value
is reduced to below 1 mW when the number of WDM channels is larger than 70.
The foregoing analysis provides only a rough estimate of the Raman crosstalk as
it neglects the fact that signals in each channel consist of a random sequence of 0 and
1 bits. A statistical analysis shows that the Raman crosstalk is lower by about a factor
of 2 when signal modulation is taken into account [167]. The GVD effects that were
neglected in the above analysis also reduce the Raman crosstalk since pulses in differ-
ent channels travel at different speeds because of the group-velocity mismatch [173].
On the other hand, periodic amplification of the WDM signal can magnify the impact
of SRS-induced degradation. The reason is that in-line amplifiers add noise which ex-
periences less Raman loss than the signal itself, resulting in degradation of the SNR.
The Raman crosstalk under realistic operating conditions was calculated in a 2001
study [179]. Numerical simulations showed that it can be reduced by inserting opti-
cal filters along the fiber link that block the low-frequency noise below the longest-
wavelength channel [178]. Raman crosstalk can also be reduced using the technique of
midway spectral inversion [174].