8.3. SYSTEM PERFORMANCE ISSUES 363
discuss both the linear and nonlinear crosstalk mechanisms and also consider other
performance issues relevant for WDM systems.
8.3.1 Heterowavelength Linear Crosstalk
Linear crosstalk can be classified into two categories depending on its origin [148]–
[163]. Optical filters and demultiplexers often let leak a fraction of the signal power
from neighboring channels that interferes with the detection process. Such crosstalk
is calledheterowavelengthorout-of-bandcrosstalk and is less of a problem because
of its incoherent nature than thehomowavelengthorin-bandcrosstalk that occurs dur-
ing routing of the WDM signal from multiple nodes. This subsection focuses on the
heterowavelength crosstalk.
Consider the case in which a tunable optical filter is used to select a single channel
among theNchannels incident on it. If the optical filter is set to pass themth channel,
the optical power reaching the photodetector can be written asP=Pm+∑Nn =mTmnPn
wherePmis the power in themth channel andTmnis the filter transmittivity for channel
nwhen channelmis selected. Crosstalk occurs ifTmn =0 forn =m. It is called out-
of-band crosstalk because it belongs to the channels lying outside the spectral band
occupied by the channel detected. Its incoherent nature is also apparent from the fact
that it depends only on the power of the neighboring channels.
To evaluate the impact of such crosstalk on system performance, one should con-
sider the power penalty, defined as the additional power required at the receiver to
counteract the effect of crosstalk. The photocurrent generated in response to the inci-
dent optical power is given by
I=RmPm+N∑
n =mRnTmnPn≡Ich+IX, (8.3.1)whereRm=ηmq/hνmis the photodetector responsivity for channelmat the optical fre-
quencyνmandηmis the quantum efficiency. The second termIXin Eq. (8.3.1) denotes
the crosstalk contribution to the receiver currentI. Its value depends on the bit pattern
and becomes maximum when all interfering channels carry 1 bits simultaneously (the
worst case).
A simple approach to calculating the crosstalk power penalty is based on the eye
closure (see Section 4.3.3) occurring as a result of the crosstalk [148]. The eye closes
most in the worst case for whichIXis maximum. In practice,Ichis increased to main-
tain the system performance. IfIchneeds to be increased by a factorδX, the peak
current corresponding to the top of the eye isI 1 =δXIch+IX. The decision threshold
is set atID=I 1 /2. Theeye openingfromIDto the top level would be maintained at its
original valueIch/2if
(δXIch+IX)−IX−^12 (δXIch+IX)=^12 Ich, (8.3.2)or whenδX= 1 +IX/Ich. The quantityδXis just the power penalty for themth channel.
By usingIXandIchfrom Eq. (8.3.1),δXcan be written (in dB) as
δX=10 log 10(
1 +
∑Nn =mRnTmnPn
RmPm