. Notice that the channel of the shortest Wavelength Wavelength wavelength is most depleted. Increases Increases bandwidth, the power loss by the channel with the shortest wavelength, say channel 0, is given by (5.67) The penalty for channel 0 is now given by Penaltylo -10Log[1-Po] (5.68) If a penalty equal to or less than 0.5 dB is desired, then Po0.1 and after some changes in the units of parameters, totalXBtotalXLeff<40x103 mWxnmxkm (5.69) This equation is conservative because it ignores chromatic dispersion; with chromatic dis- persion in the system the right side of equation 5.69 is nearly doubled. Using a channel spacing of 0.8 nm (10 GHz), an amplifier spacing of 80 km, and an Leff of 20 km, the limita- tions imposed on channel power by SRS are shown in Figure 5.28. It is clear that for a small number of channels SRS does not impose a strong upper bound on power per channel, but for a large number of channels care should be taken to control the impact of SRS. 8 Wavelengths 16 Wavelengths 32 Wavelengths Fig. 5.28 Maximum power limitations imposed by SRS in a WDM system. Source: Based on Ramaswami 10,000 and Sivarajan (2002). Link Length (km) Chapter 5 Optical Fibers [2c] Four-Wave Mixing The origin of four-wave mixing is the dependency of refractive index on optical power. This dependency not only gives rise to SPM but also induces new frequencies to appear. This effect is called Four-Wave Mixing (FWM) and it is independent of the bitrate but dependent on channel spacing and the chromatic dispersion present in the propagation path. It is a complex effect to analyze, but FWM efficiency is reduced by increasing the channel spacing and the chromatic dispersion between channels. New frequencies are generated by the process Wijk=Wi+wj-Wkwithi,jk (5.70) where the indices i, j, and k refer to the frequencies present. Assuming that N frequencies are present, the number of new frequencies is given by Number of new frequencies = N(N-1)2 (5.71) As an example, consider a three-channel system. The number of new frequenc