PROBLEMS 73
2.9 Show that a chirped Gaussian pulse is compressed initially inside a single-mode
fiber whenβ 2 C<0. Derive expressions for the minimum width and the fiber
length at which the minimum occurs.
2.10Estimate the limiting bit rate for a 60-km single-mode fiber link at 1.3- and 1.55-
μm wavelengths assuming transform-limited, 50-ps (FWHM) input pulses. As-
sume thatβ 2 =0 and−20 ps^2 /km andβ 3 = 0 .1ps^3 /km and 0 at 1.3- and 1.55-μm
wavelengths, respectively. Also assume thatVω 1.
2.11A 0.88-μm communication system transmits data over a 10-km single-mode
fiber by using 10-ns (FWHM) pulses. Determine the maximum bit rate if the
LED has a spectral FWHM of 30 nm. UseD=−80 ps/(km-nm).
2.12Use Eq. (2.4.23) to prove that the bit rate of an optical communication system op-
erating at the zero-dispersion wavelength is limited byBL|S|σλ^2 < 1 /
√
8, where
S=dD/dλandσλis the RMS spectral width of the Gaussian source spectrum.
Assume thatC=0 andVω 1 in the general expression of the output pulse
width.
2.13Repeat Problem 2.12 for the case of a single-mode semiconductor laser for which
Vω 1 and show that the bit rate is limited byB(|β 3 |L)^1 /^3 < 0 .324. What is the
limiting bit rate forL=100 km ifβ 3 = 0 .1ps^3 /km?
2.14An optical communication system is operating with chirped Gaussian input pulses.
Assume thatβ 3 =0 andVω 1 in Eq. (2.4.23) and obtain a condition on the bit
rate in terms of the parametersC,β 2 , andL.
2.15A 1.55-μm optical communication system operating at 5 Gb/s is using Gaus-
sian pulses of width 100 ps (FWHM) chirped such thatC=−6. What is the
dispersion-limited maximum fiber length? How much will it change if the pulses
were unchirped? Neglect laser linewidth and assume thatβ 2 =−20 ps^2 /km.
2.16A 1.3-μm lightwave system uses a 50-km fiber link and requires at least 0.3μW
at the receiver. The fiber loss is 0.5 dB/km. Fiber is spliced every 5 km and has
two connectors of 1-dB loss at both ends. Splice loss is only 0.2 dB. Determine
the minimum power that must be launched into the fiber.
2.17A 1.55-μm continuous-wave signal with 6-dBm power is launched into a fiber
with 50-μm^2 effective mode area. After what fiber length would the nonlinear
phase shift induced by SPM become 2π? Assume ̄n 2 = 2. 6 × 10 −^20 m^2 /W and
neglect fiber losses.
2.18Calculate the threshold power for stimulated Brillouin scattering for a 50-km
fiber link operating at 1.3μm and having a loss of 0.5 dB/km. How much does
the threshold power change if the operating wavelength is changed to 1.55μm,
where the fiber loss is only 0.2 dB/km? Assume thatAeff= 50 μm^2 andgB=
5 × 10 −^11 m/W at both wavelengths.
2.19Calculate the power launched into a 40-km-long single-mode fiber for which
the SPM-induced nonlinear phase shift becomes 180◦. Assumeλ= 1. 55 μm,
Aeff= 40 μm^2 ,α= 0 .2 dB/km, and ̄n 2 = 2. 6 × 10 −^20 m^2 /W.
