8.3. SYSTEM PERFORMANCE ISSUES 371
Figure 8.25: XPM-induced power fluctuations on a CW probe for a 130-km link (middle) and
a 320-km link (top) with dispersion management. An NRZ bit stream in the pump channel is
shown at the bottom. (After Ref. [191],©c1999 IEEE; reprinted with permission.)
where the first term is due to SPM andLeffhas been replaced with 1/αassuming
αL1. The parameterγis in the range 1–10 W−^1 km−^1 depending on the type of
fiber used, larger values occurring for dispersion-compensating fibers. The nonlinear
phase shift depends on the bit pattern of various channels and can vary from zero to its
maximum valueφmax=(γ/α)( 2 N− 1 )PjforNchannels, if we assume equal channel
powers.
Strictly speaking, the XPM-induced phase shift should not affect system perfor-
mance if the GVD effects were negligible. However, any dispersion in fiber converts
pattern-dependent phase shifts to power fluctuations, reducing the SNR at the receiver.
This conversion can be understood by noting that time-dependent phase changes lead
to frequency chirping that affects dispersion-induced broadening of the signal. Figure
8.25 shows XPM-induced fluctuations for a CW probe launched with a 10-Gb/s pump
channel modulated using the NRZ format. The probe power fluctuates by as much as
6% after 320 km of dispersive fiber. The root-mean-square (RMS) value of fluctuations
depends on the channel power and can be reduced by lowering it. As a rough estimate,
if we use the conditionφmax<1, the channel power is restricted to
Pch<α/[γ( 2 N− 1 )]. (8.3.15)For typical values ofαandγ,Pchshould be below 10 mW even for five channels and
reduces to below 1 mW for more than 50 channels.
The preceding analysis provides only a rough estimate as it ignores the fact that
pulses belonging to different channels travel at different speeds and walk through each
other at a rate that depends on their wavelength difference. Since XPM can occur only
when pulses overlap in the time domain, its impact is reduced considerably by the
walk-off effects. As a faster-moving pulse belonging to one channel collides with and
passes through a specific pulse in another channel, the XPM-induced chirp shifts the