Lightwave Technology

Chapter 9 - Problems

Problems

9.1  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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