8.3. SYSTEM PERFORMANCE ISSUES 365
distribution ofIXhas been calculated for a FP filter and is generally far from being
Gaussian. The crosstalk power penaltyδXcan be calculated by finding the increase
inIchneeded to maintain a certain value of BER. Figure 8.22 shows the calculated
penalty for several values of BER plotted as a function ofN/F[149] with the choice
F=100. The solid curve corresponds to the error-free case (BER=0). The power
penalty can be kept below 0.2 dB to maintain a BER of 10−^9 for values ofN/Fas large
as 0.33. From Eq. (8.2.2) the channel spacing can be as little as three times the bit rate
for such FP filters.
8.3.2 Homowavelength Linear Crosstalk
Homowavelength or in-band crosstalk results from WDM components used for rout-
ing and switching along an optical network and has been of concern since the advent
of WDM systems [150]–[163]. Its origin can be understood by considering a static
wavelength router such as a WGR (see Fig. 8.16). For anN×Nrouter, there existN^2
combinations through whichN-wavelength WDM signals can be split. Consider the
output at one wavelength, sayλm. Among theN^2 −1 interfering signals that can ac-
company the desired signal,N−1 signals have the same carrier wavelengthλm, while
the remainingN(N− 1 )belong to different carrier wavelengths and are likely to be
eliminated as they pass through other WDM components. TheN−1 crosstalk signals
at the same wavelength (in-band crosstalk) originate from incomplete filtering through
a WGR because of its partially overlapping transmission peaks [153]. The total optical
field, including only the in-band crosstalk, can be written as
Em(t)=(
Em+N∑
n =mEn)
exp(−iωmt), (8.3.5)whereEmis the desired signal andωm= 2 πc/λm. The coherent nature of the in-band
crosstalk is obvious from Eq. (8.3.5).
To see the impact of in-band crosstalk on system performance, we should again
consider the power penalty. The receiver currentI=R|Em(t)|^2 in this case contains
interference or beat terms similar to the case of optical amplifiers (see Section 6.5).
One can identify two types of beat terms; signal–crosstalk beating with terms like
EmEnand crosstalk–crosstalk beating with terms likeEkEn, wherek =mandn =m.
The latter terms are negligible in practice and can be ignored. The receiver current is
then given approximately as
I(t)≈RPm(t)+ 2 RN∑
n =m√
Pm(t)Pn(t)cos[φm(t)−φn(t)], (8.3.6)wherePn=|En|^2 is the power andφn(t)is the phase. In practice,Pn<<Pmforn =m
because a WGR is built to reduce the crosstalk. Since phases are likely to fluctuate
randomly, we can write Eq. (8.3.6) asI(t)=R(Pm+∆P), treat the crosstalk as intensity
noise, and use the approach of Section 4.6.2 for calculating the power penalty. In fact,
the result is the same as in Eq. (4.6.11) and can be written as
δX=−10 log 10 ( 1 −rX^2 Q^2 ), (8.3.7)