394 CHAPTER 8. MULTICHANNEL SYSTEMS
κ=8cm−^1 and ̄n= 1.45, and a Bragg wavelength of 1.55μm forL=3,5,and
8 mm. Estimate the grating bandwidth in GHz in the three cases.
8.10You have been given ten 3-dB fiber couplers. Design a 4×4 demultiplexer with
as few couplers as possible.
8.11Explain how an array of planar waveguides can be used for demultiplexing
WDM channels. Use diagrams as necessary.
8.12Use a single fiber coupler and two fiber gratings to design an add–drop filter.
Explain how such a device functions.
8.13Use a waveguide-grating router to design an integrated WDM transmitter. How
would the design change for a WDM receiver?
8.14What is meant by the in-band linear crosstalk? Derive an expression for the
power penalty induced by such crosstalk for a waveguide-grating router.
8.15Explain how stimulated Raman scattering can cause crosstalk in multichannel
lightwave systems. Derive Eq. (8.3.10) after approximating the Raman gain
spectrum by a triangular profile.
8.16Solve the set ofMequations in Eq. (8.3.11) and show that the channel powers
are given by Eq. (8.3.12).
8.17Derive Eq. (8.3.14) by considering the nonlinear phase change induced by both
self- and cross-phase modulation.
8.18Solve Eq. (8.3.16) and show that the FWM efficiency is given by Eq. (8.3.18).
Estimate its value for a 50-km fiber withα= 0 .2 dB/km andβ 2 =−1ps^2 /km.
8.19Derive an expression for the CNR of analog SCM lightwave systems by includ-
ing thermal noise, shot noise, and intensity noise. Show that the CNR saturates
to a constant value at high power levels.
8.20Consider an analog SCM lightwave system operating at 1.55μm. It uses a re-
ceiver of 90% quantum efficiency, 10 nA dark current, and thermal-noise RMS
current of 0.1 mA over a 50-MHz bandwidth. The RIN of the transmitter laser
is−150 dB/Hz. Calculate the average received power necessary to obtain 50-dB
CNR for an AM–VSB system with a modulation index of 0.2.
References
[1] H. Ishio, J. Minowa, and K. Nosu,J. Lightwave Technol. 2 , 448 (1984).
[2] G. Winzer,J. Lightwave Technol. 2 , 369 (1984).
[3] N. A. Olsson, J. Hegarty, R. A. Logan, L. F. Johnson, K. L. Walker, L. G. Cohen, B. L.
Kasper, and J. C. Campbell,Electron. Lett. 21 , 105 (1985).
[4] C. A. Brackett,IEEE J. Sel. Areas Commun. 8 , 948 (1990).
[5] P. E. Green, Jr.,Fiber-Optic Networks, Prentice-Hall, Upper Saddle River, NJ, 1993.
[6] B. Mukherjee,Optical Communication Networks, McGraw-Hill, New York, 1997.
[7] A. Borella, G. Cancellieri, and F. Chiaraluce,WDMA Optical Networks, Artec House,
Norwood, MA, 1998.
