Page 463 - Fiber Optic Communications Fund

444 Fiber Optic Communications

1

0.8

XPM efficiency 0.6

0.4

0.2

0
0 2 4 6 8
Walk-off parameter, |d p | (ps/km)

−1
Figure 10.13 XPM efficiency versus absolute of the walk-off parameter. Parameters: = 0.046 km , fiber length =
80 km, modulating frequency Ω∕2 = 5 GHz.

pump and the probe decreases and the XPM efficiency decreases. Fig. 10.13 shows the FWM efficiency as a
function of the absolute walk-off parameter. From Eq. (10.147), we see that as the channel spacing increases,
the walk-off increases and the XPM efficiency decreases. In other words, in a WDM system, the impact of the
XPM due to the nearest-neighbor channels is the greatest. An arbitrary pump may be written as a superposition
of sinusoids of the form given by Eq. (10.168), and the total XPM-induced phase shift can be calculated by
adding terms of the form given by Eq. (10.172) due to each frequency component.

Example 10.4
A pump is sinusoidally modulated with modulating frequency 10 GHz. The fiber-optic system has the follow-
−1
ing parameters: loss coefficient = 0.046 km , length L = 50 km, dispersion coefficient D = 17 ps/nm⋅km,
2
and dispersion slope S = 0.06 ps/nm /km. The signal wavelength is 1550 nm and the pump wavelength is
1549.6 nm. Calculate the XPM efficiency.
Solution:
From Eqs. (2.216) and (2.202), we have
( 2 ) 2 3

= S + D , (10.175)
3
2 2
2c 2 c
2
=−D , (10.176)
2
2c
2
D = 17 × 10 −6 s∕m , (10.177)
3
3
S = 0.06 × 10 s∕m , (10.178)