Optical Networks - _3_5 Transmitters_39

This expression is plotted in figure 349 for n 10 for

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This expression is plotted in Figure 3.49 for N = 10 , for different sets of values of the φ i . In Figure 3.49(a), the φ i are chosen at random, and in Figure 3.49(b), they
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182 Components are chosen to be equal to each other. All the a i are chosen to be equal in both cases, and the frequency f 0 has been diminished from its typical value for the purpose of illustration. From Figure 3.49(a), we observe that the output amplitude of an MLM laser varies rapidly with time when it is not mode locked. We have also seen in Fig- ure 3.43(a) that the frequency spacing between adjacent longitudinal modes is c/ 2 nl . If n = 3 and l = 200 μ m, which are typical values for semiconductor lasers, this frequency spacing is 250 GHz. Thus these amplitude fluctuations occur extremely rapidly (at a time scale on the order of a few picoseconds) and pose no problems for on-off modulation even at bit rates of a few tens of gigabits per second. We see from Figure 3.49(b) that when the φ i are chosen to be equal to each other, the output oscillation of the laser takes the form of a periodic train of narrow pulses. A laser operating in this manner is called a mode-locked laser and is the most common means of generating narrow optical pulses. The time interval between two pulses of a mode-locked laser is 2 nl/c , as indicated in Figure 3.49(b). For a typical semiconductor laser, as we have seen earlier, this corresponds to a few picoseconds. For modulation in the 1–10 GHz range, the interpulse interval should be in the 0.1–1 ns range. Cavity lengths, l , of the order of 1–10 cm (assuming n = 1 . 5 ) are required in order to realize mode-locked lasers with interpulse intervals in this range. These large cavity lengths are easily obtained using fiber lasers, which require the length anyway to obtain sufficient gain to induce lasing. The most common means of achieving mode lock is by modulating the gain of the laser cavity. Either amplitude or frequency modulation can be used. Mode locking using amplitude modulation is illustrated in Figure 3.50. The gain of the cavity is modulated with a period equal to the interpulse interval, namely, 2 nl/c . The amplitude of this modulation is chosen such that the average gain is insufficient for any single mode to oscillate. However, if a large number of modes are in phase, there can be a sufficient buildup in the energy inside the cavity for laser oscillation to occur at the instants of high gain, as illustrated in Figure 3.50. Gain modulation of the fiber laser can be achieved by introducing an external modulator inside the cavity. 3.5.2 Light-Emitting Diodes Lasers are expensive devices and are not affordable for many applications where the data rates are low and distances are short. This is the case in many data communi- cations applications (see Chapter 6) and in some access networks (Chapter 11). In such cases, light-emitting diodes (LEDs) provide a cheaper alternative.
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3.5 Transmitters 183 Figure 3.50 Illustration of mode locking by amplitude modulation of the cavity gain.
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