PROBLEMS 321
Problems
7.1 What is the dispersion-limited transmission distance for a 1.55-μm lightwave
system making use of direct modulation at 10 Gb/s? Assume that frequency
chirping broadens the Gaussian-shape pulse spectrum by a factor of 6 from its
transform-limited width. UseD=17 ps/(km-nm) for fiber dispersion.
7.2 How much improvement in the dispersion-limited transmission distance is ex-
pected if an external modulator is used in place of direct modulation for the
lightwave system of Problem 7.1?
7.3 Solve Eq. (7.1.3) by using the Fourier transform method. Use the solution to
find an analytic expression for the pulse shape after a Gaussian input pulse has
propagated toz=Lin a fiber withβ 2 =0.
7.4 Use the result obtained in Problem 7.3 to plot the pulse shape after a Gaussian
pulse with a full-width at half-maximum (FWHM) of 1 ps is transmitted over
20 km of dispersion-shifted fiber withβ 2 =0 andβ 3 = 0 .08 ps^3 /km. How would
the pulse shape change if the sign ofβ 3 is inverted?
7.5 Use Eqs. (7.1.4) and (7.2.2) to plot the pulse shapes forC=− 1 ,0, and 1 when
50-ps (FWHM) chirped Gaussian pulses are transmitted over 100 km of standard
fiber withD=16 ps/(km-nm). Compare the three cases and comment on their
relative merits.
7.6 The prechirp technique is used for dispersion compensation in a 10-Gb/s light-
wave system operating at 1.55μm and transmitting the 1 bits as chirped Gaussian
pulses of 40 ps width (FWHM). Pulse broadening by up to 50% can be tolerated.
What is the optimum value of the chirp parameterC, and how far can the signal
be transmitted for this optimum value? UseD=17 ps/(km-nm).
7.7 The prechirp technique in Problem 7.6 is implemented through frequency modu-
lation of the optical carrier. Determine the modulation frequency for a maximum
change of 10% from the average value.
7.8 Repeat Problem 7.7 for the case in which the prechirp technique is implemented
through sinusoidal modulation of the carrier phase.
7.9 The transfer function of an optical filter is given by
H(ω)=exp[−( 1 +ib)ω^2 /ω^2 f].
What is the impulse response of this filter? Use Eq. (7.5.1) to find the pulse
shape at the filter output when a Gaussian pulse is launched at the fiber input.
How would you optimize the filter to minimize the effect of fiber dispersion?
7.10Use the result obtained in Problem 7.9 to compare the pulse shapes before and
after the filter when 30-ps (FWHM) Gaussian pulses are propagated over 100 km
of fiber withβ 2 =−20 ps^2 /km. Assume that the filter bandwidth is the same as
the pulse spectral width and that the filter parameterbis optimized. What is the
optimum value ofb?
7.11Derive Eq. (7.5.3) by considering multiple round trips inside a FP filter whose
back mirror is 100% reflecting.
