Preface
The first generation of fiber-optic communication systems debuting in 1980 operated at a meager bit rate of 45 Mb/s and required signal regeneration every 10 km or so. However, by 1990 further advances in lightwave technology not only increased the bit rate to 10 Gb/s (by a factor of 200) but also allowed signal regeneration after 80 km or more. The pace of innovation in all fields of lightwave technology only quickened during the 1990s, as evident from the development and commercialization of erbium-doped fiber amplifiers, fiber Bragg gratings, and wavelength-division-multiplexed lightwave systems. By 2001, the capacity of commercial terrestrial systems exceeded 1.6 Tb/s. At the same time, the capacity of transoceanic lightwave systems installed worldwide exploded. A single transpacific system could transmit information at a bit rate of more than 1 Tb/s over a distance of 10,000 km without any signal regeneration. Such a tremendous improvement was possible only because of multiple advances in all areas of lightwave technology. Although commercial development slowed down during the economic downturn that began in 2001, it was showing some signs of recovery by the end of 2004, and lightwave technology itself has continued to grow. The primary objective of this two-volume book is to provide a comprehensive and up-to-date account of all major aspects of lightwave technology. The first volume, subtitled Components and Devices, is devoted to a multitude of silica- and semiconductor-based optical devices. The second volume, subtitled Telecommunication Systems, deals with the design of modern lightwave systems; the acronym LT1 is used to refer to the material in the first volume. The first two introductory chapters cover topics such as modulation formats and multiplexing techniques employed to form an optical bit stream. Chapters 3 through 5 consider the degradation of such an optical signal through loss, dispersion, and nonlinear effects during its transmission through optical fibers and how they affect the system performance. Chapters 6 through 8 focus on the management of the degradation caused by noise, dispersion, and fiber nonlinearity. Chapters 9 and 10 cover the engineering issues related to the design of WDM systems and optical networks. This text is intended to serve both as a textbook and a reference monograph. For this reason, the emphasis is on physical understanding, but engineering aspects are also discussed throughout the text. Each chapter also includes selected problems that can be assigned to students. The book's primary readership is likely to be graduate students, research scientists, and professional engineers working in fields related to lightwave technology. An attempt is made to include as much recent material as possible so that students are exposed to the recent advances in this exciting field. The reference section at the end of each chapter is more extensive than what is common for a typical textbook. The listing of recent research papers should be helpful to researchers using this book as a reference. At the same time, students can benefit from this feature if they are assigned problems requiring reading of the original research papers. This book may be useful in an upper-level graduate course devoted to optical communications. It can also be used in a two-semester course on optoelectronics or lightwave technology. A large number of persons have contributed to this book either directly or indirectly. It is impossible to mention all of them by name. I thank my graduate students and the students who took my course on optical communication systems and helped improve my class notes through their questions and comments. I am grateful to my colleagues at the Institute of Optics for numerous discussions and for providing a cordial and productive atmosphere. I thank, in particular, Renè Essiambre and Qiang Lin for reading several chapters and providing constructive feedback. Last, but not least, I thank my wife Anne and my daughters, Sipra, Caroline, and Claire, for their patience and encouragement. Govind P. Agrawal Rochester, NY |
Chapter 9 - Problems
Problems9.1 Dry fibers have acceptable losses over a spectral region extending from 1.3 to 1.6 µm. Estimate the capacity of a WDM system covering this entire region using 40-Gb/s channels spaced apart by 50 GHz. 9.2 The C and L spectral bands cover a wavelength range from 1.53 to 1.61 µm. How many channels can be transmitted through WDM when the channel spacing is 25 GHz? What is the effective bit rate-distance product when a WDM signal covering the two bands using 10-Gb/s channels is transmitted over 2,000 km? 9.3 What is meant by the in-band linear crosstalk? Derive an expression for the power penalty induced by a waveguide-grating router through this phenomenon. 9.4 Explain why the cascading of identical optical filters can produce signal distortion even when filter bandwidth is wider than the signal bandwidth. Calculate the effective bandwidth of 20 cascaded filters with a Gaussian-shape transfer function of 50-GHz bandwidth. 9.5 Explain how stimulated Raman scattering can cause crosstalk in multichannel lightwave systems. Derive Eq. (9.3.3) after approximating the Raman gain spectrum by a triangular profile. 9.6 Derive Eq. (9.3.12) by extending the four-wave mixing theory of Section 4.3.1 to a fiber link with a two-section dispersion map. 9.7 Explain in physical terms the origin of FWM resonances in WDM systems. How do they affect such systems? 9.8 How does XPM lead to both amplitude fluctuations and timing jitter in WDM systems? How are such fluctuations affected by group-velocity mismatch? Use diagrams as necessary to support your arguments. 9.9 Explain what is meant by an interchannel collision. How is the collision length defined and how does it depend on the channel spacing? 9.10 Derive the set of Eqs. (9.4.6) through (9.4.9) by considering a collision of two Gaussian pulses in two channels spaced apart by Ωch. 9.11 Use Eqs. (9.4.6) through (9.4.9) with p = 1 and prove that the maximum frequency shift occurring during a collision is given by Eq. (9.4.11). 9.12 Describe how the technique of polarization interleaving is implemented for WDM systems. Why does it help in practice? 9.13 Explain why the use of the RZ-DPSK format is beneficial for WDM systems. 9.14 Start the OptSim software tool and load Example 9.A. Plot the channel spectra at the end of fiber link by changing the dispersion of fiber to D = 0, 2, and 4 ps/(km-nm) and interpret your results in terms of FWM. 9.15 Start the OptSim software tool and load Example 9.C. Run this example for link lengths of 250, 375, and 500 km and compare the eye diagrams for different channels. |
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