Page 511 - Fiber Optic Communications Fund

492 Fiber Optic Communications

2
10.2 A Kerr medium has a cross-sectional area of 500 μm . Calculate the optical power required to change
−8
2
the refractive index by 10 . Assume n = 3 × 10 −20 m /W.
2
(Ans: 166.66 W.)
−1
10.3 The nonlinear coefficient of a single-mode fiber is 1.2 W −1 km . Calculate the effective area. Assume
2
n = 2.5 × 10 −20 m /W and wavelength = 1530 nm.
2
2
(Ans: 85 μm .)
10.4 A fiber-optic system has the following parameters: span length = 75 km, number of spans = 20,
2
fiber loss = 0.21 dB/km, Kerr coefficient n = 2.6 × 10 −20 m /W, wavelength = 1540 nm, effec-
0
2
2
tive area = 50 μm . Find the upper limit on the transmitter output power so that the nonlinear phase
shift accumulated over 20 spans is less than 0.5 rad.
(Ans: 0.585 mW.)
10.5 The effective length of a fiber L eff is 18 km and fiber loss = 0.17 dB/km. Find the fiber length.
(Ans: 31.15 km.)

10.6 A single Gaussian pulse of width (FWHM) 20 ps and a peak power of 10 mW is transmitted in a
dispersion-free fiber over 80 km. Find the nonlinear phase shift at the center of the pulse at the fiber
output. Assume = 2.2W −1 km −1 and fiber loss = 0.2 dB/km.
(Ans: 0.465 rad.)

10.7 Solve the previous exercise numerically using the split-step Fourier scheme (see Chapter 11) and
verify the analytical calculations.

2
2
10.8 Repeat Exercise 10.7 if =−2ps /km (instead of 0 ps /km). Is the nonlinear phase shift at the center
2
of the pulse smaller? Explain.
10.9 Explain the differences between the instantaneous frequency of a pulse due to (i) SPM, (ii) anomalous
dispersion, and (iii) normal dispersion.
10.10 Discuss the properties of a soliton in single-mode fibers.

10.11 A modulated pump with a modulating frequency of 8 GHz co-propagated with a weak CW signal.
Fiber loss = 0.18 dB/km, length L = 80 km, walk-off parameter d = 13.2 ps/km, signal wavelength
= 1530 nm, and pump wavelength = 1530.78 nm. Calculate the XPM efficiency.
−4
(Ans: 9.72 × 10 .)
10.12 Explain the differences between XPM and FWM.
10.13 A WDM system consists of three channels centered at Δf,2Δf, and 3Δf with Δf = 100 GHz. Fiber
−1
2
loss coefficient = 0.0461 km , fiber length L = 60 km, and =−4ps /km. Calculate the effi-
2
ciency of non-degenerate as well as degenerate FWM tones at 4Δf. Ignore .
3
−4
−4
(Ans: Non-degenerate, 2.27 × 10 ; degenerate, 8.66 × 10 .)