Page 464 - Fiber Optic Communications Fund

Nonlinear Effects in Fibers 445

= = 1550 × 10 −9 m, (10.179)
s
8
c = 3 × 10 m∕s, (10.180)
s ∕m,
= 1.33 × 10 −40 3 (10.181)
3
=−2.166 × 10 −26 2 (10.182)
s ∕m.
2
Using Eq. (10.147), the walk-off parameter is given by
Ω 2 p
3
d = Ω + , (10.183)
p
2
p
2
Ω = 2(c∕ − c∕ )
p p s
11
= 3.14 × 10 rad/s, (10.184)
d =−6.8 × 10 −15 s∕m. (10.185)
p
The XPM efficiency is given by Eq. (10.173),
[ 2 ( ) −L ]
2 4sin Ωd L e
p
= 1 + . (10.186)
XPM −L 2
2 2
2
+ 4Ω d (1 − e )
p
10
10
Modulating frequency = 10 Hz. So, Ω= 2 × 10 rad/s. Using this value in Eq. (10.186), we find
−3
= 3.34 × 10 . (10.187)
XPM
10.7.1.3 XPM Impact on System Performance
For intensity-modulated direct detection (IMDD) systems, the phase shift due to XPM does not degrade
the system performance if dispersion is absent. In a dispersive fiber, the frequency components generated
due to XPM travel at different speeds and arrive at different times at the fiber output, leading to amplitude
distortion. In other words, dispersion translates phase modulation (PM) into amplitude modulation (AM).
This is known as PM-to-AM conversion. The degradation due to XPM is one of the dominant impairments in
WDM systems and, hence, it has drawn significant attention [15–21]. The amplitude fluctuations due to XPM
can not be calculated analytically without approximations. In this section, we make a few approximations to
find a closed-form approximation for the amplitude distortion due to XPM. As before, we assume that the
pump is much stronger than the signal, so that the SPM of the probe can be ignored. Distortion of the pump due
to dispersion and nonlinearity is also ignored. While calculating the phase shift due to XPM, fiber dispersion
is ignored but its effect will be included later while converting PM to AM. Let the signal be CW,
√
q (T, 0)= P . (10.188)
s s0
Let the pump be the modulated signal,
√
∑
q (T, 0)= P p0 a f(t − nT ), (10.189)
b
p
n
n