230 COMPONENTS Figure 3.82 A four-channel add/drop multiplexer architecture. 3.24 9 AOTF: Can an AOTF be used to achieve the same level of crosstalk suppression? This problem compares different simple add/drop multiplexer architectures. (a) First consider the fiber Bragg grating-based add/drop element shown in Fig- ure 3.14(b). Suppose a 5% tap is used to couple the added signal into the output, and the grating induces a loss of 0.5 dB for the transmitted signals and no loss for the reflected signal. Assume that the circulator has a loss of 1 dB per pass. Carefully compute the loss seen by a channel that is dropped, a channel that is added, and a channel that is passed through the device. Suppose the input power per channel is -15 dBm. At what power should the add channel be transmitted so that the powers on all the channels at the output are the same? (b) Suppose you had to realize an add/drop multiplexer that drops and adds four wavelengths. One possible way to do this is to cascade four add/drop elements of the type shown in Figure 3.14 in series. In this case, compute the best-case and worst-case loss seen by a channel that is dropped, a channel that is added, and a channel that is passed through the device. (c) Another way to realize a four-channel add/drop multiplexer is shown in Figure 3.82. Repeat the preceding exercise for this architecture. Assume that the losses are as shown in the figure. Which of the two would you prefer from a loss perspective? Problems 231 3.25 3.26 3.27 3.28 (d) Assume that fiber gratings cost $500 each, circulators $3000 each, filters $1000 each, and splitters, combiners, and couplers $100 each. Which of the two preceding architectures would you prefer from a cost point of view? In a photodetector, why don't the conduction band electrons absorb the incident photons? Consider an EDFA that is required to amplify wavelengths between 1532 nm and 1550 nm within the C-band (separated by 100 GHz). (a) Draw a schematic of this basic EDFA, and assume the pump laser is selected to minimize ASE. Also, be sure to prevent backward reflections at the EDFA input/output. (b) Draw the relevant energy bands and associated energy transitions between these bands. (c) How many wavelengths could be amplified within this range (and spacing)? (d) Compute the required range in energy transitions to support the entire range of wavelengths. (e) Suppose we wanted to (1) add and drop a subset of these wavelengths at the EDFA and (2) add a second stage that would be best suited for maximum output powers. Please draw this new two-stage EDFA, with the add/drop multiplexing function drawn as a "black box" labeled "ADM." (f) Now focusing on the "ADM," assume that two fiber Bragg gratings (along with associated circulator, splitters, and filters) are used to provide static drop capability of the lowest two contiguous wavelengths in the spectral range. In addition, a combiner is used to subsequently add these same wavelengths (of course, carrying different embedded signals). Sketch the architecture for this ADM (that is, the inside of the black box). (g) If the effective refractive index of the ADM fiber segment is 1.5, calculate the associated fiber Bragg grating periods. Consider the 4 x 4 switch shown in Figure 3.66 made up of 2 x 2 switches. Suppose each 2 x 2 switch has crosstalk suppression of 50 dB. What is the overall crosstalk suppression of the 4 x 4 switch? Assume for now that powers can be added and that we do not have to worry about individual electric fields adding in phase. If we wanted an overall crosstalk suppression of 40 dB, what should the crosstalk suppression of each switch be? This problem looks at the Vernier effect, which is used to obtain a filter with a large periodicity given individual filters with smaller periodicities. Consider two periodic filters, one with period fl and the other with period f2, both assumed to be integers. In other words, the first filter selects frequencies f = mr1, where m is an integer, and the second filter selects wavelengths f = mr2. If the two filters are cascaded, 232 COMVONENTS 3.29 show that the resulting filtering function is periodic, with a period given by the least common multiple of fl and f2. For example, if periods of the two filters are 500 GHz and 600 GHz, then the cascaded structure will be periodic with a period of 3000 GHz. Now suppose the period of each filter can be tuned by 10%. For the numbers given above, the first filter's period can be tuned to 500 + 25 GHz and the sec- ond filter's to 600 + 30 GHz. Note that the two combs overlap at a frequency of 193,000 GHz. To get an idea of the tuning range of the cascaded structure, determine the nearest frequency to this initial frequency at which the two combs overlap when periods ofthe individual filters are tuned to (1) 525 GHz and 630 GHz, (2) 475 GHz and 630 GHz, (3) 475 GHz and 570 GHz, and (4) 525 GHz and 570 GHz. To get an idea of how complex it is to tune this structure, also determine the periods of each filter to obtain an overlap at 193,100 GHz. Consider the Clos switch architecture described in Section 3.7.1. Show that if p > 2m - 1, the switch is strictly nonblocking. References [AB98] M C. Amann and J. Buus. Tunable Laser Diodes. Artech House, Boston, 1998. [AD93] G.P. Agrawal and N. K. Dutta. Semiconductor Lasers. Kluwer Academic Press, Boston, 1993. [Agr95] G.P. Agrawal. Nonlinear Fiber Optics, 2nd edition. Academic Press, San Diego, CA, 1995. [AI93] M C. Amann and S. Illek. Tunable laser diodes utilising transverse tuning scheme. 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In Proceedings of European Conference on Optical Communication, pages 1019-1022, 1995. [Zah92] C.E. Zah et al. Monolithic integration of multiwavelength compressive strained multiquantum-well distributed-feedback laser array with star coupler and optical amplifiers. Electronics Letters, 28:2361-2362, 1992. [Zir96] M. Zirngibl et al. An 18-channel multifrequency laser. IEEE Photonics Technology Letters, 8:870-872, 1996. [zJ94] M. Zirngibl and C. H. Joyner. A 12-frequency WDM laser source based on a transmissive waveguide grating router. Electronics Letters, 30:700-701, 1994. Modulation and Demodulation O UR GOAL IN THIS CHAPTER is to understand the processes of modulation and demodulation of digital signals. We start by discussing modulation, which is the process of converting digital data in electronic form to an optical signal that can be transmitted over the fiber. We then study the demodulation process, which is the process of converting the optical signal back into electronic form and extracting the data that was transmitted. Mainly due to various kinds of noise that get added to the signal in the trans- mission process, decisions about the transmitted bit (0 or 1) based on the received signal are subject to error. We will derive expressions for the bit error rate introduced by the whole transmission process. Subsequently, we discuss how the bit error rate can be reduced, for the same level of noise (more precisely, signal-to-noise ratio) by the use of forward error-correcting codes. We also discuss clock recovery or syn- chronization, which is the process of recovering the exact transmission rate at the receiver. With this background, in the next chapter, we will tackle transmission system engineering, which requires careful attention to a variety of impairments that affect system performance. 4.1 Modulation The most commonly used modulation scheme in optical communication is on-off keying (OOK), which is illustrated in Figure 4.1. In this modulation scheme, a 1 bit is 239 . this case, compute the best-case and worst-case loss seen by a channel that is dropped, a channel that is added, and a channel that is passed through the device. (c) Another way to realize a four-channel. [Ven9 6a] A. M. Vengsarkar et al. Long-period fiber-grating-based gain equalizers. Optics Letters, 21(5):33 6-3 38, 1996. [Ven96b] A. M. Vengsarkar et al. Long-period gratings as band-rejection. pages FF-1-FF-2, 2000. [NE01] S. Namiki and Y. Emori. Ultra-broadband Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes. IEEE Journal of Selected