## Effects of FWM and XPM on Long-Haul Design

FWM is a third-order nonlinearity in optical links that can be compared to
the intermodulation distortion in standard electrical systems. FWM is worse for
equally spaced WDM systems and at high powers. When three optical channels at
frequencies ω_{i}, ω_{j}, and ω_{k
}travel such that they are close to the zero dispersion wavelength, they
intermingle to produce a fourth signal whose frequency is shown in Equation
4-24.

#### Equation 4-24

This ω_{ijk} can mix with another WDM channel, causing severe
cross-talk. For W wavelengths in a fiber, the number of FWM channels (N)
produced is shown in Equation 4-25.

#### Equation 4-25

Figure 4-12 shows the effects of FWM in equally spaced systems and power considerations, and Figure 4-13 shows the same considerations for unequally spaced systems.

**Figure 4-12 Equal
Channel Spacing (Three Equally Spaced Channels Generated Nine FWM Signals, Out
of Which Three Fall on Top of the Signals)**

**Figure 4-13 Three
Unequal Spaced Channels Generating Nine FWM Signals; None of the Generated Signals
Falls on Top of the Original Signals**

The solution for minimizing FWM is to use unequal channel spacing in such a way that the generated wavelength does not interfere with the signal channel(s). Use of NZDSF minimizes the effect of FWM.

In multichannel WDM systems, XPM causes intensity-based modulation to adjacent frequency channels. XPM causes fluctuations in pulse propagation due to the effect of other channels. Furthermore, if adjacent channels are traveling at the same bit rate, XPM effects are more pronounced. One way to avoid XPM is by carefully selecting bit rates for adjacent channels that are not equal to the present channel bit rate. When designing WDM links, we typically keep a 0.5 dB power penalty margin for both FWM and XPM. XPM has more impact on certain types of modulation formats. Typically, FSK and PSK have a more pronounced impact than pure NRZ and RZ coding.