290 TRANSMISSION SYSTEM ENGINEERING today to increase the available bandwidth, and hence the number of wavelengths, in a single fiber. Amplifiers are used in three different configurations, as shown in Figure 5.2. An optical preamplifier is used just in front of a receiver to improve its sensitivity. A power amplifier is used after a transmitter to increase the output power. A line amplifier is used typically in the middle of the link to compensate for link losses. The design of the amplifier depends on the configuration. A power amplifier is designed to provide the maximum possible output power. A preamplifier is designed to provide high gain and the highest possible sensitivity, that is, the least amount of additional noise. A line amplifier is designed to provide a combination of all of these. Unfortunately, the amplifier is not a perfect device. There are several major imperfections that system designers need to worry about when using amplifiers in a system. First, an amplifier introduces noise, in addition to providing gain. Second, the gain of the amplifier depends on the total input power. For high input powers, the EDFA tends to saturate and the gain drops. This can cause undesirable power transients in networks. Finally, although EDFAs are a particularly attractive choice for WDM systems, their gain is not flat over the entire passband. Thus some channels see more gain than others. This problem gets worse when a number of amplifiers are cascaded. We have studied optically preamplified receivers in Section 4.4.5. In this sec- tion, we will study the effect of gain saturation, gain nonflatness, noise, and power transients in systems with cascades of optical amplifiers. 5.5.1 Gain Saturation in EDFAs An important consideration in designing amplified systems is the saturation of the EDFA. Depending on the pump power and the amplifier design itself, the output power of the amplifier is limited. As a result, when the input signal power is increased, I Figure 5.2 Power amplifiers, line amplifiers, and preamplifiers. 5.5 Optical Amplifiers 291 40- 35 30 ~ 25 ~ 2O < 15 | | | | -40 -30 -20 - 10 0 Input power (dBm) Figure 5.3 Gain saturation in an optical amplifier. Unsaturated gain Gmax = 30 dB and saturation power psat = 10 dBm. the amplifier gain drops. This behavior can be captured approximately by the fol- lowing equation: psat Gmax G- 1 q-~ ln~. (5.5) Pin G Here, Gmax is the unsaturated gain, and G the saturated gain of the amplifier, psat is the amplifier's internal saturation power, and Pin is the input signal power. Figure 5.3 plots the amplifier gain as a function of the input signal power for a typical EDFA. For low input powers, the amplifier gain is at its unsaturated value, and at very high input powers, G , 1 and the output power Pout = Pin. The output saturation power PoSua~ is defined to be the output power at which the amplifier gain has dropped by 3 dB. Using (5.5) and the fact that Pout = GPin, and assuming that G >> 1, the output saturation power is given by PoSat ~ psat In 2 ut The saturation power is a function of the pump power and other amplifier param- eters. It is quite common to have output saturation powers on the order of 10 to 100 mW (10 to 20 dBm). There is no fundamental problem in operating an EDFA in saturation, and power amplifiers uslaally do operate in saturation. The only thing to keep in mind is that the saturated gain will be less than the unsaturated gain. 292 TRANSMISSION SYSTEM ENGINEERING 5.5.2 Gain Equalization in EDFAs The flatness of the EDFA passband becomes a critical issue in WDM systems with cascaded amplifiers. The amplifier gain is not exactly the same at each wavelength. Small variations in gain between channels in a stage can cause large variations in the power difference between channels at the output of the chain. For example, if the gain variation between the worst channel and the best channel is 1 dB at each stage, after 10 stages it will be 10 dB, and the worst channel will have a much poorer signal-to-noise ratio than the best channel. This effect is shown in Figure 5.4(a). Building amplifiers with flat gain spectra is therefore very important (see Section 3.4.3) and is the best way to solve this problem. In practice, it is possible to design EDFAs to be inherently flat in the 1545-1560 nm wavelength region, and this is where many early WDM systems operate. However, systems with a larger number of channels will need to use the 1530-1545 nm wavelength range, where the gain of the EDFA is not flat. The gain spectrum of L-band EDFAs is relatively flat over the L-band from about 1565 nm to about 1625 nm so that gain flattening over this band is not a significant issue. At the system level, a few approaches have been proposed to overcome this lack of gain flatness. The first approach is to use preequalization, or preemphasis, as shown in Figure 5.4(b). Based on the overall gain shape of the cascade, the transmitted power per channel can be set such that the channels that see low gain are launched with higher powers. The goal of preequalization is to ensure that all channels are received with approximately the same signal-to-noise ratios at the receiver and fall within the receiver's dynamic range. However, the amount of equalization that can be done is limited, and other techniques may be needed to provide further equalization. Also this technique is difficult to implement in a network, as opposed to a point-to-point link. The second approach is to introduce equalization at each amplifier stage, as shown in Figure 5.4(c). After each stage, the channel powers are equalized. This equalization can be done in many ways. One way is to demultiplex the channels, attenuate each channel differently, and then multiplex them back together. This approach involves using a considerable amount of hardware. It adds wavelength tolerance penalties due to the added muxes and demuxes (see Section 5.6.6). For these reasons, such an approach is impractical. Another approach is to use a multichannel filter, such as an acousto-optic tunable filter (AOTF). In an AOTF, each channel can be attenuated differently by applying a set of RF signals with different frequencies. Each RF signal controls the attenuation of a particular center wavelength, and by controlling the RF powers of each signal, it is possible to equalize the channel powers. However, an AOTF requires a large amount of RF drive power (on the order of i W) 5.5 Optical Amplifiers 293 Figure 5.4 Effect of unequal amplifier gains at different wavelengths. (a) A set of chan- nels with equal powers at the input to a cascaded system of amplifiers will have vastly different powers and signal-to-noise ratios at the output. (b) This effect can be reduced by preequalizing the channel powers. (c) Another way to reduce this effect is to introduce equalization at each amplifier stage. The equalization can be done using a filter inside the amplifier as well. to equalize more than a few (2-4) channels. Both approaches introduce several decibels of additional loss and some power penalties due to crosstalk. The preferred solution today is to add an optical filter within the amplifier with a carefully designed passband to compensate for the gain spectrum of the amplifier so as to obtain a flat spectrum at its output. Both dielectric thin-film filters (Section 3.3.6) and long-period fiber gratings (Section 3.3.4) are good candidates for this purpose. 5.5.3 Amplifier Cascades Consider a system of total length L with amplifiers spaced I km apart (see Figure 5.5). The loss between two stages is e -~l, where c~ is the fiber attenuation. Each amplifier adds some spontaneous emission noise. Thus the optical signal-to-noise ratio, OSNR (see Section 4.4.6 for the definition), gradually degrades along the chain. The amplifier gain must be at least large enough to compensate for the loss between amplifier stages; otherwise, the signal (and hence the OSNR) will degrade rapidly with the number of stages. Consider what happens when we choose the unsaturated amplifier gain to be larger than the loss between stages. For the first few 294 TRANSMISSION SYSTEM ENGINEERING 5.5.4 stages, the total input power (signal plus noise from the previous stages) to a stage increases with the number of stages. Consequently, the amplifiers begin to saturate and their gains drop. Farther along the chain, a spatial steady-state condition is reached where the amplifier output power and gain remains the same from stage to stage. These values, Pout and G, respectively, can be computed by observing that (Poute-~/)G + 2PnBo(-G- 1) - Pout- (5.6) Here Poute -~/ is the total input power to the amplifier stage, and the second term, from (4.5), is the spontaneous emission noise added at this stage. Also from (5.5) we must have psat Gmax G-l+_ In _ . (5.7) P oute -~ G Equations (5.6) and (5.7) can be solved simultaneously to compute the values of Pout and G (Problem 5.11). Observe from (5.6) that Ge -~l < 1; that is, the steady-state gain will be slightly smaller than the loss between stages, due to the added noise at each stage. Thus in designing a cascade, we must try to choose the saturated gain G to be as close to the loss between stages as possible. Let us consider a simplified model of an amplifier cascade where we assume the saturated gain G = e at. With L/l amplifiers in the system, the total noise power at the output, using (4.5), is tot Pnoise = 2PnBo(G- 1)L/l 2PnBo(e ~l - 1)L/1. (5.8) Given a desired OSNR, the launched power P must satisfy P > (OSNR) tot Pnoise - (OSNR)2PnBo( e~t - 1)L/ l. Figure 5.6 plots the required power P versus amplifier spacing I. If we don't worry about nonlinearities, we would try to maximize I subject to limitations on transmit power and amplifier output power. The story changes in the presence of nonlineari- ties, as we will see in Section 5.8. Amplifier Spacing Penalty In the preceding section, we saw that in an amplifier cascade the gain of each amplifier must approximately compensate for the span loss (the loss between two amplifier stages in the cascade). For a given span length, say, 80 km, this determines the gain of the amplifiers in the cascade. For example, for a span length of I = 80 km and a fiber loss of ot(dB) = 0.25 dB/km, we get an amplifier gain G = 20 dB. If the amplifier gain is smaller, we must choose a smaller span length. In this section, we will study 5.5 Optical Amplifiers 295 Figure 5.5 A system with cascaded optical amplifiers. 100 80 g ~ ~ 6o o 40 ~ ~ 2o | | | 50 100 150 200 250 300 Amplifier spacing (km) Figure 5.6 Power versus amplifier spacing. Required OSNR = 50, nsp = 2, Bo = 20 GHz, ~ = 0.22 dB/km, and the total link length L = 1000 km. the effect of the span length, or, equivalently, the amplifier gain G, on the noise at the output of an amplifier cascade. This will enable us to then discuss quantitatively the penalty reduction we can obtain by the use of distributed amplifiers, in particular, distributed Raman amplifiers. The ASE noise power at the output of a cascade of L/1 amplifiers is given by (5.8). Rewriting this in terms of G, using l = (In G)/o~, we get Pn t~ 2LPnBoot(G - 1)/In G olse (5.9) Ideally, the minimum noise power is achieved in an amplifier cascade with perfectly distributed gain, that is, G - 1 (and N - ~ but N In G -otL). The "power penalty" for using lumped amplifiers with gain G > 1, instead of an ideal distributed amplifier, 296 TRANSMISSION SYSTEM ENGINEERING is given by the factor G-1 P Plumped = In G ' which is unity for G = 1. For G = 20 dB, PPlumped 13.3 dB, while for G = 10 dB, P Plumped 5.9 dB. Thus, assuming a = 0.25 dB/km, the total ASE noise in an amplifier cascade can be reduced by more than 7 dB by reducing the amplifier spacing to 40 km from 80 kin. The reduction in ASE must be balanced against the increased system cost re- sulting from reducing the amplifier spacing, since twice the number of amplifier locations (huts) will be required when the amplifier spacing is halved from 80 km to 40 km. However, distributed amplification can reduce the ASE significantly without increasing the number of amplifier locations. When a distributed amplifier is used, the amplification occurs continuously as the signal propagates in the fiber. The primary example of such an amplifier is the Raman amplifier we studied in Section 3.4.4. Since system design engineers are accustomed to assuming lumped amplifiers, the increased ASE due to lumped amplification compared to distributed amplification is not viewed as a power penalty. Rather, the distributed amplifier is considered to have an equivalent (lower) noise figure, relative to a lumped amplifier, with the same total gain. For even moderate gains, this equivalent noise figure for the distributed amplifier can be negative! In our example above, we saw that the power penalty for using lumped amplifiers with gain G = 20 dB was 13.3 dB. A distributed amplifier with an actual noise figure (2nsp) of 3.3 dB that provides the same total gain can also be viewed as having an effective noise figure of 3.3 - 13.3 = -10 dB. This is because the accumulated ASE due to the use of such a distributed amplifier is the same as that of a lumped amplifier with a noise figure of -10 dB. 5.5.5 Power Transients and Automatic Gain Control Power transients are an important effect to consider in WDM links and networks with a number of EDFAs in cascade. If some of the channels fail, the gain of each amplifier will increase because of the reduction in input power to the amplifier. In the worst case, W - 1 out of the W channels could fail, as shown in Figure 5.7. The surviving channels will then see more gain and will then arrive at their receivers with higher power. Likewise, the gain seen by existing channels will depend on what other channels are present. Thus setting up or taking down a new channel may affect the power levels in other channels. These factors drive the need for providing automatic gain control (AGC) in the system to keep the output power per channel at each amplifier constant, regardless of the input power. 5.5 Optical Amplifiers 297 Figure 5.7 Illustrating the impact of failures in a network with optical amplifiers. In this example, )~8, which is the only wavelength being added at the node, sees all the gain of the amplifier upon failure of the link preceding the node. With only one EDFA in the cascade, the increase in power due to channel outages occurs rather slowly, in about 100 #s. However, with multiple amplifiers in the chain, the increase in power is much more rapid, with a rise-time of a few to tens of microseconds, and can result in temporary outages in the surviving channels. To prevent this, the AGC system must work very fast, within a few microseconds, to prevent these power transients from occurring. Several types of AGC systems have been proposed. A simple AGC circuit mon- itors the signal power into the amplifier and adjusts the pump power to vary the gain if the input signal power changes. The response time of this method is limited ultimately by the lifetime of the electrons from the third energy level to the second energy level in erbium (see Section 3.4.3), which is around 1 #s. Another interesting AGC circuit uses an optical feedback loop, as shown in Figure 5.8. A portion of the amplifier output is tapped off, filtered by a bandpass filter, and fed back into the amplifier. The gain of the loop is controlled carefully by using an attenuator in the loop. This feedback loop causes the amplifier to lase at the wavelength passed by the filter in the loop. This has the effect of clamping the amplifier gain seen by other wavelengths to a fixed value, irrespective of the input signal power. Moreover, it is usually sufficient to have this loop in the first amplifier in the cascade. This is because the output lasing power at the loop wavelength becomes higher as the input signal power decreases, and acts as a compensating signal to amplifiers farther down the cascade. Therefore, amplifiers farther down the cascade do not see a significant variation in the input power. Because of the additional couplers required for the AGC at the input and output, the amplifier noise figure is slightly increased and its output power is reduced. Yet another approach is to introduce an additional wavelength on the link to act as a compensating wavelength. This wavelength is introduced at the beginning of the link and tapped off at the end of the link. The power on this wavelength is increased to compensate for any decrease in power seen at the input to the link. This 298 TRANSMISSION SYSTEM ENGINEERING Figure 5.8 Optical automatic gain control circuit for an optical amplifier. method requires an additional laser and is not as cost-effective as the other ones. It can compensate for only a few channels. 5,5.6 Lasing Loops In systems with amplifiers, if we are not careful, we may end up with closed fiber loops that may lase. In our designs so far, we have tried to make the amplifier gain almost exactly compensate for the span losses encountered. If for some reason a closed fiber loop is encountered with amplifiers in the loop, and the total gain in the loop is comparable to the total loss in the loop, the loop may begin to lase. The effect here is similar to the optical automatic gain control circuit that we discussed in Section 5.5.5, but in this case lasing loops can cause power to be taken away from live channels and distributed to the channel that is lasingma highly undesirable attribute. Note that this phenomenon may occur even if the loop is closed only for a single wavelength and not closed for the other wavelengths. Lasing loops are particularly significant problems in ring networks (which are inherently closed loops!) with optical add/drop multiplexers. In this case, even the amplified spontaneous emission traveling around the ring may be sufficient to cause the ring to lase. We can deal with lasing loops in a few different ways. The preferred safe method is to ensure that the amplifier gain is always slightly lower than the loss being compensated for. The trade-off is that this would result in a small degradation of the signal-to-noise ratio. Another possibility is to ensure that closed loops never occur during operation of the system. For example, we could break a ring at a certain point and terminate all the wavelengths. Note, however, that it may not be sufficient to ensure loop freedom just under normal operation. We would not want a service person making a wrong fiber connection in the field to take down the entire network. 5.6 Crosstalk 299 Therefore we need to make sure that loops aren't created even in the presence of human errorsmnot an easy problem to solve. 5.6 Crosstalk Crosstalk is the general term given to the effect of other signals on the desired sig- nal. Almost every component in a WDM system introduces crosstalk of some form or another. The components include filters, wavelength multiplexers/demultiplexers, switches, semiconductor optical amplifiers, and the fiber itself (by way of nonlin- earities). Two forms of crosstalk arise in WDM systems: interchannel crosstalk and intrachannel crosstalk. The first case is when the crosstalk signal is at a wave- length sufficiently different from the desired signal's wavelength that the difference is larger than the receiver's electrical bandwidth. This form of crosstalk is called interchannel crosstalk. Interchannel crosstalk can also occur through more indirect interactions, for example, if one channel affects the gain seen by another channel, as with nonlinearities (Section 5.8). The second case is when the crosstalk signal is at the same wavelength as that of the desired signal or sufficiently close to it that the difference in wavelengths is within the receiver's electrical bandwidth. This form of crosstalk is called intrachannel crosstalk or, sometimes, coherent crosstalk. Intra- channel crosstalk effects can be much more severe than interchannel crosstalk, as we will see. In both cases, crosstalk results in a power penalty. 5.6.1 Intrachannel Crosstalk Intrachannel crosstalk arises in transmission links due to reflections. This is usually not a major problem in such links since these reflections can be controlled. However, intrachannel crosstalk can be a major problem in networks. One source of this arises from cascading a wavelength demultiplexer (demux) with a wavelength multiplexer (mux), as shown in Figure 5.9(a). The demux ideally separates the incoming wave- lengths to different output fibers. In reality, however, a portion of the signal at one wavelength, say, )~i, leaks into the adjacent channel ~i+1 because of nonideal sup- pression within the demux. When the wavelengths are combined again into a single fiber by the mux, a small portion of the )~i that leaked into the )~i+1 channel will also leak back into the common fiber at the output. Although both signals contain the same data, they are not in phase with each other, due to different delays encountered by them. This causes intrachannel crosstalk. Another source of this type of crosstalk arises from optical switches, as shown in Figure 5.9(b), due to the nonideal isolation of one switch port from the other. In this case, the signals contain different data. . | | | | -4 0 -3 0 -2 0 - 10 0 Input power (dBm) Figure 5.3 Gain saturation in an optical amplifier. Unsaturated gain Gmax = 30 dB and saturation power psat = 10 dBm. the amplifier gain drops behavior can be captured approximately by the fol- lowing equation: psat Gmax G- 1 q-~ ln~. (5.5) Pin G Here, Gmax is the unsaturated gain, and G the saturated gain of the amplifier, psat. in operating an EDFA in saturation, and power amplifiers uslaally do operate in saturation. The only thing to keep in mind is that the saturated gain will be less than the unsaturated gain. 292