366 CHAPTER 8. MULTICHANNEL SYSTEMS
where
r^2 X=〈(∆P)^2 〉/Pm^2 =X(N− 1 ), (8.3.8)
andX=Pn/Pmis the crosstalk level defined as the fraction of power leaking through
the WGR and is taken to be the same for allN−1 sources of coherent in-band crosstalk
by assuming equal powers. An average over the phases was performed by replacing
cos^2 θ=^12. In addition,r^2 Xwas multiplied by another factor of^12 to account for the fact
thatPnis zero on average half of the times (during 0 bits). Experimental measurements
of power penalty for a WGR agree with this simple model [153].
The impact of in-band crosstalk can be estimated from Fig. 4.19, where power
penaltyδXis plotted as a function ofrX. To keep the power penalty below 2 dB,rX<
0 .07 is required, a condition that limitsX(N− 1 )to below−23 dB from Eq. (8.3.8).
Thus, the crosstalk levelXmust be below−38 dB forN=16 and below−43 dB for
N=100, rather stringent requirements.
The calculation of crosstalk penalty in the case of dynamic wavelength routing
through optical cross-connects becomes quite complicated because of a large number
of crosstalk elements that a signal can pass through in such WDM networks [155].
The worst-case analysis predicts a large power penalty (>3 dB) when the number of
crosstalk elements becomes more than 25 even if the crosstalk level of each component
is only−40 dB. Clearly, the linear crosstalk is of primary concern in the design of
WDM networks and should be controlled. A simple technique consists of modulating
or scrambling the laser phase at the transmitter at a frequency much larger than the
laser linewidth [164]. Both theory and experiments show that the acceptable crosstalk
level exceeds 1% (−20 dB) with this technique [162].
8.3.3 Nonlinear Raman Crosstalk
Several nonlinear effects in optical fibers [59] can lead to interchannel and intrachannel
crosstalk that affects the system performance considerably [165]–[171]. Section 2.6
discussed such nonlinear effects and their origin from a physical point of view. This
subsection focuses on the Raman crosstalk.
As discussed in Section 2.6, stimulated Raman scattering (SRS) is generally not
of concern for single-channel systems because of its relatively high threshold (about
500 mW near 1.55μm). The situation is quite different for WDM systems in which
the fiber acts as a Raman amplifier (see Section 6.3) such that the long-wavelength
channels are amplified by the short-wavelength channels as long as the wavelength
difference is within the bandwidth of the Raman gain. The Raman gain spectrum
of silica fibers is so broad that amplification can occur for channels spaced as far
apart as 100 nm. The shortest-wavelength channel is most depleted as it can pump
many channels simultaneously. Such an energy transfer among channels can be detri-
mental for system performance as it depends on the bit pattern—amplification occurs
only when 1 bits are present in both channels simultaneously. The Raman-induced
crosstalk degrades the system performance and is of considerable concern for WDM
systems [172]–[179].
Raman crosstalk can be avoided if channel powers are made so small that SRS-
induced amplification is negligible over the entire fiber length. It is thus important