REFERENCES 273
6.8 Explain why semiconductor optical amplifiers impose a chirp on the pulse during
amplification. Derive an expression for the imposed chirp when a Gaussian pulse
is incident on the amplifier. Use Eq. (6.2.21) withm=1 for the input pulse.
6.9 Discuss the origin of gain saturation in fiber Raman amplifiers. Solve Eqs. (6.3.2)
and (6.3.3) withαs=αpand derive Eq. (6.3.8) for the saturated gain.
6.10A Raman amplifier is pumped in the backward direction using 1 W of power.
Find the output power when a 1-μW signal is injected into the 5-km-long ampli-
fier. Assume losses of 0.2 and 0.25 dB/km at the signal and pump wavelengths,
respectively,Aeff= 50 μm^2 , andgR= 6 × 10 −^14 m/W. Neglect gain saturation.
6.11Explain the gain mechanism in EDFAs. Use Eqs. (6.4.2) and (6.4.3) to derive an
expression for the small-signal gain in the steady state.
6.12Discuss how EDFAs can be used to provide gain in the L band. How can you
use them to provide amplification over the both C and L bands?
6.13Starting from Eq. (6.5.11), derive Eq. (6.5.16) for the sensitivity of a direct-
detection receiver when an EDFA is used as a preamplifier.
6.14Calculate the receiver sensitivity at a BER of 10−^9 and 10−^12 by using Eq.
(6.5.16). Assume that the receiver operates at 1.55μm with 3-GHz bandwidth.
The preamplifier has a noise figure of 4 dB, and a 1-nm optical filter is installed
between the preamplifier and the detector.
6.15Calculate the optical SNR at the output end of a 4000-km lightwave system de-
signed using 50 EDFAs with 4.5-dB noise figure. Assume a fiber-cable loss of
0.25 dB/km at 1.55μm. A 2-nm-bandwidth optical filter is inserted after every
amplifier to reduce the noise.
6.16Find the electrical SNR for the system of the preceding problem for a receiver of
8-GHz bandwidth.
6.17Why does ASE induce timing jitter in lightwave systems? How would you de-
sign the system to reduce the jitter?
6.18Use the moment method to find an expression for the timing jitter for a lightwave
system employing the CRZ format.
References
[1] A. E. Siegman,Lasers, University Science Books, Mill Valley, CA, 1986.
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(1964).
[3] T. Saitoh and T. Mukai,IEEE J. Quantum Electron. 23 , 1010 (1987).
[4] M. J. O’Mahony,J. Lightwave Technol. 6 , 531 (1988).
[5] N. A. Olsson,J. Lightwave Technol. 7 , 1071 (1989).
[6] T. Saitoh and T. Mukai, inCoherence, Amplification, and Quantum Effects in Semicon-
ductor Lasers, Y. Yamamoto, Ed., Wiley, New York, 1991, Chap. 7.
[7] G. P. Agrawal,Semiconductor Lasers, Van Nostrand Reinhold, New York, 1993.
