The main issue from a system standpoint is how FWM affects the performance of a WDM system. When all channels are spaced equally in the frequency domain, it follows from the FWM condition (ü)m = a), + (Oj - cok) that the frequencies of most FWM components will coincide with the channel frequencies. Under such conditions, FWM effects are not apparent in the spectral domain, as seen in Figure 4.9(c), except for uneven channel powers. However, their presence leads to an enhanced noise level in the time domain.
The origin of noise enhancement can be understood physically by noting that one or more FWM components interfere with the signal in a specific channel in a coherent fashion if they have the same carrier frequency. If channel powers were constant with time, this interference will not be a major problem since each channel that loses power through FWM also receives some power from neighboring channels, thereby roughly balancing the power transfer. However, the situation is much more complicated for channels containing optical bit streams that are neither synchronized in time nor have identical bit patterns. Moreover, these bit streams travel though the fiber at slightly different speeds because of the group-velocity mismatch. FWM can only occur when optical pulses are present simultaneously in the same time slot in at least two channels. Since near coincidence of bits in different channels occurs in a random fashion, FWM manifests as fluctuations in the power level of each channel, and the level of such fluctuations increases for low-dispersion fibers because FWM efficiency is enhanced for them.
A simple scheme for reducing the FWM-induced degradation consists of designing WDM systems with unequal channel spacings . Figures 4.9(b) and 4.9(d) show the input and output optical spectra for an eight-channel WDM system when channel wavelengths are adjusted to ensure that none of the FWM components falls within the channel bandwidths. Similar to the case of equal channel spacings, new FWM components are generated but they do not interfere with the signal in a coherent fashion and thus do not degrade the SNR significantly. The average power of each channel is reduced because of FWM, but the reduction is nearly the same for all channels. In a 1999 experiment, this technique was used to transmit 22 channels, each operating at 10 Gb/s, over 320 km of dispersion-shifted fiber with 80-km amplifier spacing . Channel spacings ranged from 125 to 275 GHz in the wavelength range of 1,532 to 1,562 nm and were determined using a periodic allocation scheme . The zero-dispersion wavelength of the fiber was close to 1,548 nm, resulting in near phase matching of many FWM components. Nonetheless, the system performed quite well, because of unequal channel spacings, resulting in less than 1.5-dB power penalty for all channels.
The use of a nonuniform channel spacing is not always practical since many WDM components, such as Fabry-Perot filters and arrayed waveguide gratings (see Chapter 8 of LT1), operate on the assumption that channels are spaced apart equally. Also, such a scheme is spectrally inefficient, as the bandwidth of the resulting WDM signal is considerably larger compared with the case of equally spaced channels .
A practical solution is offered by the dispersion-management technique discussed in Section 3.3.4. In this scheme, fibers with normal and anomalous GVD are combined to form a periodic dispersion map such that GVD is locally high all along the fiber link, even though its average value is relatively low and can even be zero. As a result, the FWM efficiency r]p is negligible in each fiber section. As early as 1993, eight channels at 10 Gb/s could be transmitted over 280 km through dispersion management . By 1996, the use of dispersion management had become quite common for FWM suppres sion in WDM systems because of its practical simplicity. FWM can also be suppressed by using fibers whose GVD varies along the fiber length .
Modulation instability can enhance the effects of FWM for certain specific values of channel spacing even when dispersion management is used and local GVD is relatively high . The reason can be understood by noting that SPM and XPM, ignored in deriving Eq. (4.3.5), can produce phase matching even when ft ^ 0. It is possible to extend the preceding analysis and include the phase shifts induced by SPM and XPM . It turns out that Eq. (4.3.5) can still be used but the phase-mismatch factor Ak in Eq. (4.3.7) is replaced with 
Ak « ft(03i - (Ok)((Oj - cok) + r(ñ + Pj ~ Pk)[ 1 " exp(—aLeff)]/(aLeff)- (4.3.8)
Clearly, Ak may become close to zero for some FWM terms, depending on the channel powers and spacings, when ft is in the anomalous-GVD regime of the fiber. The corresponding FWM process will then become phase-matched, resulting in significant FWM efficiency.
One can understand such a FWM enhancement as follows. If the frequency at which the gain of modulation instability peaks nearly coincides with the channel spacing in a WDM system, modulation-instability sidebands will overlap with the neighboring channels. As a result, the FWM process will become enhanced resonantly in spite of the large value of the GVD parameter. We can estimate the channel spacing 5vch for which such resonant FWM is expected to occur using Eq. (4.1.28). Settimg the channel spacing equal to the gain-peak frequency, we obtain ils = 2^5vch - (2rPch/|ft|)1/2. (4.3.9)
As a rough estimate, <5vch « 10 GHz when Pch = 5 mW, ft = -5 ps2/km, and y = 2 W '/km. Since channel spacing in modern WDM systems is typically 50 GHz or more, resonance enhancement of FWM can easily be avoided. However, it may become of concern for dense WDM systems designed with a channel spacing close to 10 GHz.
As discussed in Chapters 9 and 10 of LT1, FWM can be quite beneficial for certain applications related to lightwave systems. It is often used for demultiplexing individual channels when time-division multiplexing is used in the optical domain. It can also be employed for applications such as wavelength conversion and fast optical switching. FWM is sometimes used for generating a spectrally inverted signal through the process of optical phase conjugation. As discussed in Chapter 7, the phase-conjugation technique can be used for dispersion compensation. Fiber-optic parametric amplifiers (see Section 3.3 of LT1) constitute another application of FWM. In all such applications of FWM, the fiber-based device is pumped using one or two lasers whose wavelengths are chosen judiciously in the vicinity of the zero-dispersion wavelength of the fiber to enhance FWM efficiency.
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