Tài liệu Fibre optic communication systems P7 ppt

Chapter 7 Dispersion Management It should be clear from Chapter 6 that with the advent of optical amplifiers, fiber losses are no longer a major limiting factor for optical communication systems. Indeed, mod- ern lightwave systems are often limited by the dispersive and nonlinear effects rather than fiber losses. In some sense, optical amplifiers solve the loss problem but, at the same time, worsen the dispersion problem since, in contrast with electronic regener- ators, an optical amplifier does not restore the amplified signal to its original state. As a result, dispersion-induced degradation of the transmitted signal accumulates over multiple amplifiers. For this reason, several dispersion-management schemes were de- veloped during the 1990s to address the dispersion problem [1]. In this chapter we review these techniques with emphasis on the underlying physics and the improve- ment realized in practice. In Section 7.1 we explain why dispersion management is needed. Sections 7.2 and 7.3 are devoted to the methods used at the transmitter or re- ceiver for managing the dispersion. In Sections 7.4–7.6 we consider the use of several high-dispersion optical elements along the fiber link. The technique of optical phase conjugation, also known as midspan spectral inversion, is discussed in Section 7.7. Section 7.8 is devoted to dispersion management in long-haul systems. Section 7.9 focuses on high-capacity systems by considering broadband, tunable, and higher-order compensation techniques. Polarization-mode dispersion (PMD) compensation is also discussed in this section. 7.1 Need for Dispersion Management In Section 2.4 we have discussed the limitations imposed on the system performance by dispersion-induced pulse broadening. As shown by the dashed line in Fig. 2.13, the group-velocity dispersion (GVD) effects can be minimized using a narrow-linewidth laser and operating close to the zero-dispersion wavelength λ ZD of the fiber. How- ever, it is not always practical to match the operating wavelength λ with λ ZD .An example is provided by the third-generation terrestrial systems operating near 1.55 µ m and using optical transmitters containing a distributed feedback (DFB) laser. Such systems generally use the existing fiber-cable network installed during the 1980s and 279 Fiber-Optic Communications Systems, Third Edition. Govind P. Agrawal Copyright  2002 John Wiley & Sons, Inc. ISBNs: 0-471-21571-6 (Hardback); 0-471-22114-7 (Electronic) 280 CHAPTER 7. DISPERSION MANAGEMENT consisting of more than 50 million kilometers of the “standard” single-mode fiber with λ ZD ≈1.31 µ m. Since the dispersion parameter D ≈16 ps/(km-nm) in the 1.55- µ m re- gion of such fibers, the GVD severely limits the performance when the bit rate exceeds 2 Gb/s (see Fig. 2.13). For a directly modulated DFB laser, we can use Eq. (2.4.26) for estimating the maximum transmission distance so that L < (4B|D|s λ ) −1 , (7.1.1) where s λ is the root-mean-square (RMS) width of the pulse spectrum broadened con- siderably by frequency chirping (see Section 3.5.3). Using D = 16 ps/(km-nm) and s λ = 0.15 nm in Eq. (7.1.1), lightwave systems operating at 2.5 Gb/s are limited to L ≈ 42 km. Indeed, such systems use electronic regenerators, spaced apart by about 40 km, and cannot benefit from the availability of optical amplifiers. Furthermore, their bit rate cannot be increased beyond 2.5 Gb/s because the regenerator spacing becomes too small to be feasible economically. System performance can be improved considerably by using an external modulator and thus avoiding spectral broadening induced by frequency chirping. This option has become practical with the commercialization of transmitters containing DFB lasers with a monolithically integrated modulator. The s λ = 0 line in Fig. 2.13 provides the dispersion limit when such transmitters are used with the standard fibers. The limiting transmission distance is then obtained from Eq. (2.4.31) and is given by L < (16| β 2 |B 2 ) −1 , (7.1.2) where β 2 is the GVD coefficient related to D by Eq. (2.3.5). If we use a typical value β 2 = −20 ps 2 /km at 1.55 µ m, L < 500 km at 2.5 Gb/s. Although improved consid- erably compared with the case of directly modulated DFB lasers, this dispersion limit becomes of concern when in-line amplifiers are used for loss compensation. Moreover, if the bit rate is increased to 10 Gb/s, the GVD-limited transmission distance drops to 30 km, a value so low that optical amplifiers cannot be used in designing such light- wave systems. It is evident from Eq. (7.1.2) that the relatively large GVD of standard single-mode fibers severely limits the performance of 1.55- µ m systems designed to use the existing telecommunication network at a bit rate of 10 Gb/s or more. A dispersion-management scheme attempts to solve this practical problem. The basic idea behind all such schemes is quite simple and can be understood by using the pulse-propagation equation derived in Section 2.4.1 and written as ∂ A ∂ z + i β 2 2 ∂ 2 A ∂ t 2 − β 3 6 ∂ 3 A ∂ t 3 = 0, (7.1.3) where A is the pulse-envelope amplitude. The effects of third-order dispersion are included by the β 3 term. In practice, this term can be neglected when | β 2 | exceeds 0.1 ps 2 /km. Equation (7.1.3) has been solved in Section 2.4.2, and the solution is given by Eq. (2.4.15). In the specific case of β 3 = 0 the solution becomes A(z,t)= 1 2 π  ∞ −∞ ˜ A(0, ω )exp  i 2 β 2 z ω 2 −i ω t  d ω , (7.1.4) 7.2. PRECOMPENSATION SCHEMES 281 where ˜ A(0, ω ) is the Fourier transform of A(0,t). Dispersion-induced degradation of the optical signal is caused by the phase factor exp(i β 2 z ω 2 /2), acquired by spectral components of the pulse during its propagation in the fiber. All dispersion-management schemes attempt to cancel this phase factor so that the input signal can be restored. Actual implementation can be carried out at the transmitter, at the receiver, or along the fiber link. In the following sections we consider the three cases separately. 7.2 Precompensation Schemes This approach to dispersion management modifies the characteristics of input pulses at the transmitter before they are launched into the fiber link. The underlying idea can be understood from Eq. (7.1.4). It consists of changing the spectral amplitude ˜ A(0, ω ) of the input pulse in such a way that GVD-induced degradation is eliminated, or at least reduced substantially. Clearly, if the spectral amplitude is changed as ˜ A(0, ω ) → ˜ A(0, ω )exp(−i ω 2 β 2 L/2), (7.2.1) where L is the fiber length, GVD will be compensated exactly, and the pulse will retain its shape at the fiber output. Unfortunately, it is not easy to implement Eq. (7.2.1) in practice. In a simple approach, the input pulse is chirped suitably to minimize the GVD-induced pulse broadening. Since the frequency chirp is applied at the transmitter before propagation of the pulse, this scheme is called the prechirp technique. 7.2.1 Prechirp Technique A simple way to understand the role of prechirping is based on the theory presented in Section 2.4 where propagation of chirped Gaussian pulses in optical fibers is discussed. The input amplitude is taken to be A(0,t)=A 0 exp  − 1 + iC 2  t T 0  2  , (7.2.2) where C is the chirp parameter. As seen in Fig. 2.12, for values of C such that β 2 C < 0, the input pulse initially compresses in a dispersive fiber. Thus, a suitably chirped pulse can propagate over longer distances before it broadens outside its allocated bit slot. As a rough estimate of the improvement, consider the case in which pulse broadening by a factor of up to √ 2 is acceptable. By using Eq. (2.4.17) with T 1 /T 0 = √ 2, the transmission distance is given by L = C + √ 1 + 2C 2 1 +C 2 L D , (7.2.3) where L D = T 2 0 /| β 2 | is the dispersion length. For unchirped Gaussian pulses, C = 0 and L = L D . However, L increases by 36% for C = 1. Note also that L < L D for large values of C. In fact, the maximum improvement by a factor of √ 2 occurs for 282 CHAPTER 7. DISPERSION MANAGEMENT Figure 7.1: Schematic of the prechirp technique used for dispersion compensation: (a) FM output of the DFB laser; (b) pulse shape produced by external modulator; and (c) prechirped pulse used for signal transmission. (After Ref. [9]; c 1994 IEEE; reprinted with permission.) C = 1/ √ 2. These features clearly illustrate that the prechirp technique requires careful optimization. Even though the pulse shape is rarely Gaussian in practice, the prechirp technique can increase the transmission distance by a factor of about 2 when used with care. As early as 1986, a super-Gaussian model [2] suitable for nonreturn-to-zero (NRZ) transmission predicted such an improvement, a feature also evident in Fig. 2.14, which shows the results of numerical simulations for chirped super-Gaussian pulses. The prechirp technique was considered during the 1980s in the context of directly modulated semiconductor lasers [2]–[5]. Such lasers chirp the pulse automatically through the carrier-induced index changes governed by the linewidth enhancement fac- tor β c (see Section 3.5.3). Unfortunately, the chirp parameter C is negative (C = − β c ) for directly modulated semiconductor lasers. Since β 2 in the 1.55- µ m wavelength re- gion is also negative for standard fibers, the condition β 2 C < 0 is not satisfied. In fact, as seen in Fig. 2.12, the chirp induced during direct modulation increases GVD- induced pulse broadening, thereby reducing the transmission distance drastically. Sev- eral schemes during the 1980s considered the possibility of shaping the current pulse appropriately in such a way that the transmission distance improved over that realized without current-pulse shaping [3]–[5]. In the case of external modulation, optical pulses are nearly chirp-free. The prechirp technique in this case imposes a frequency chirp with a positive value of the chirp pa- rameter C so that the condition β 2 C < 0 is satisfied. Several schemes have been pro- posed for this purpose [6]–[12]. In a simple approach shown schematically in Fig. 7.1, the frequency of the DFB laser is first frequency modulated (FM) before the laser out- put is passed to an external modulator for amplitude modulation (AM). The resulting optical signal exhibits simultaneous AM and FM [9]. From a practical standpoint, FM 7.2. PRECOMPENSATION SCHEMES 283 of the optical carrier can be realized by modulating the current injected into the DFB laser by a small amount (∼1 mA). Although such a direct modulation of the DFB laser also modulates the optical power sinusoidally, the magnitude is small enough that it does not interfere with the detection process. It is clear from Fig. 7.1 that FM of the optical carrier, followed by external AM, generates a signal that consists of chirped pulses. The amount of chirp can be deter- mined as follows. Assuming that the pulse shape is Gaussian, the optical signal can be written as E(0,t)=A 0 exp(−t 2 /T 2 0 )exp[−i ω 0 (1 + δ sin ω m t)t], (7.2.4) where the carrier frequency ω 0 of the pulse is modulated sinusoidally at the frequency ω m with a modulation depth δ . Near the pulse center, sin( ω m t) ≈ ω m t, and Eq. (7.2.4) becomes E(0,t) ≈ A 0 exp  − 1 + iC 2  t T 0  2  exp(−i ω 0 t), (7.2.5) where the chirp parameter C is given by C = 2 δω m ω 0 T 2 0 . (7.2.6) Both the sign and magnitude of the chirp parameter C can be controlled by changing the FM parameters δ and ω m . Phase modulation of the optical carrier also leads to a positive chirp, as can be verified by replacing Eq. (7.2.4) with E(0,t)=A 0 exp(−t 2 /T 2 0 )exp[−i ω 0 t + i δ cos( ω m t)] (7.2.7) and using cos x ≈ 1 −x 2 /2. An advantage of the phase-modulation technique is that the external modulator itself can modulate the carrier phase. The simplest solution is to employ an external modulator whose refractive index can be changed electronically in such a way that it imposes a frequency chirp with C > 0 [6]. As early as 1991, a 5-Gb/s signal was transmitted over 256 km [7] using a LiNbO 3 modulator such that values of C were in the range 0.6–0.8. These experimental values are in agreement with the Gaussian-pulse theory on which Eq. (7.2.3) is based. Other types of semiconduc- tor modulators, such as an electroabsorption modulator [8] or a Mach–Zehnder (MZ) modulator [10], can also chirp the optical pulse with C > 0, and have indeed been used to demonstrate transmission beyond the dispersion limit [11]. With the development of DFB lasers containing a monolithically integrated electroabsorption modulator, the implementation of the prechirp technique has become quite practical. In a 1996 exper- iment, a 10-Gb/s NRZ signal was transmitted over 100 km of standard fiber using such a transmitter [12]. 7.2.2 Novel Coding Techniques Simultaneous AM and FM of the optical signal is not essential for dispersion compen- sation. In a different approach, referred to as dispersion-supported transmission, the frequency-shift keying (FSK) format is used for signal transmission [13]–[17]. The FSK signal is generated by switching the laser wavelength by a constant amount ∆ λ 284 CHAPTER 7. DISPERSION MANAGEMENT Figure 7.2: Dispersion compensation using FSK coding: (a) Optical frequency and power of the transmitted signal; (b) frequency and power of the received signal and the electrically decoded data. (After Ref. [13]; c 1994 IEEE; reprinted with permission.) between 1 and 0 bits while leaving the power unchanged (see Chapter 10). During propagation inside the fiber, the two wavelengths travel at slightly different speeds. The time delay between the 1 and 0 bits is determined by the wavelength shift ∆ λ and is given by ∆T = DL∆ λ , as shown in Eq. (2.3.4). The wavelength shift ∆ λ is chosen such that ∆T = 1/B. Figure 7.2 shows schematically how the one-bit delay produces a three-level optical signal at the receiver. In essence, because of fiber dispersion, the FSK signal is converted into a signal whose amplitude is modulated. The signal can be decoded at the receiver by using an electrical integrator in combination with a decision circuit [13]. Several transmission experiments have shown the usefulness of the dispersion- supported transmission scheme [13]–[15]. All of these experiments were concerned with increasing the transmission distance of a 1.55- µ m lightwave system operating at 10 Gb/s or more over the standard fibers. In 1994, transmission of a 10-Gb/s signal over 253 km of standard fiber was realized [13]. By 1998, in a 40-Gb/s field trial, the signal was transmitted over 86 km of standard fiber [15]. These values should be compared with the prediction of Eq. (7.1.2). Clearly, the transmission distance can be improved by a large factor by using the FSK technique when the system is properly designed [17]. Another approach for increasing the transmission distance consists of transmitting an optical signal whose bandwidth at a given bit rate is smaller compared with that of the standard on–off coding technique. One scheme makes use of the duobinary coding, which can reduce the signal bandwidth by 50% [18]. In the simplest duobinary scheme, the two successive bits in the digital bit stream are summed, forming a three-level duobinary code at half the bit rate. Since the GVD-induced degradation depends on the signal bandwidth, the transmission distance should improve for a reduced-bandwidth signal. This is indeed found to be the case experimentally [19]–[24]. In a 1994 experiment designed to compare the binary and duobinary schemes, a 7.2. PRECOMPENSATION SCHEMES 285 Figure 7.3: Streak-camera traces of the 16-Gb/s signal transmitted over 70 km of standard fiber (a) with and (b) without SOA-induced chirp. Bottom trace shows the background level in each case. (After Ref. [26]; c 1989 IEE; reprinted with permission.) 10-Gb/s signal could be transmitted over distances 30 to 40 km longer by replacing binary coding with duobinary coding [19]. The duobinary scheme can be combined with the prechirping technique. Indeed, transmission of a 10-Gb/s signal over 160 km of a standard fiber has been realized by combining duobinary coding with an external modulator capable of producing a frequency chirp with C > 0 [19]. Since chirping in- creases the signal bandwidth, it is hard to understand why it would help. It appears that phase reversals occurring in practice when a duobinary signal is generated are primarily responsible for improvement realized with duobinary coding [20]. A new dispersion- management scheme, called the phase-shaped binary transmission, has been proposed to take advantage of phase reversals [21]. The use of duobinary transmission increases signal-to-noise requirements and requires decoding at the receiver. Despite these short- comings, it is useful for upgrading the existing terrestrial lightwave systems to bit rates of 10 Gb/s and more [22]–[24]. 7.2.3 Nonlinear Prechirp Techniques A simple nonlinear prechirp technique, demonstrated in 1989, amplifies the trans- mitter output using a semiconductor optical amplifier (SOA) operating in the gain- saturation regime [25]–[29]. As discussed in Section 6.2.4, gain saturation leads to time-dependent variations in the carrier density, which, in turn, chirp the amplified pulse through carrier-induced variations in the refractive index. The amount of chirp is given by Eq. (6.2.23) and depends on the input pulse shape. As seen in Fig. 6.8, the chirp is nearly linear over most of the pulse. The SOA not only amplifies the pulse but also chirps it such that the chirp parameter C > 0. Because of this chirp, the input pulse can be compressed in a fiber with β 2 < 0. Such a compression was observed in an experiment in which 40-ps input pulses were compressed to 23 ps when they were propagated over 18 km of standard fiber [25]. The potential of this technique for dispersion compensation was demonstrated in a 1989 experiment by transmitting a 16-Gb/s signal, obtained from a mode-locked 286 CHAPTER 7. DISPERSION MANAGEMENT external-cavity semiconductor laser, over 70 km of fiber [26]. Figure 7.3 compares the streak-camera traces of the signal obtained with and without dispersion compensation. From Eq. (7.1.2), in the absence of amplifier-induced chirp, the transmission distance at 16 Gb/s is limited by GVD to about 14 km for a fiber with D = 15 ps/(km-nm). The use of the amplifier in the gain-saturation regime increased the transmission distance fivefold, a feature that makes this approach to dispersion compensation quite attractive. It has an added benefit that it can compensate for the coupling and insertion losses that invariably occur in a transmitter by amplifying the signal before it is launched into the optical fiber. Moreover, this technique can be used for simultaneous compensation of fiber losses and GVD if SOAs are used as in-line amplifiers [29]. A nonlinear medium can also be used to prechirp the pulse. As discussed in Section 2.6, the intensity-dependent refractive index chirps an optical pulse through the phe- nomenon of self-phase modulation (SPM). Thus, a simple prechirp technique consists of passing the transmitter output through a fiber of suitable length before launching it into the fiber link. Using Eq. (2.6.13), the optical signal at the fiber input is given by A(0,t)=  P(t)exp[i γ L m P(t)], (7.2.8) where P(t) is the power of the pulse, L m is the length of the nonlinear medium, and γ is the nonlinear parameter. In the case of Gaussian pulses for which P(t)=P 0 exp(−t 2 /T 2 0 ), the chirp is nearly linear, and Eq. (7.2.8) can be approximated by A(0,t) ≈  P 0 exp  − 1 + iC 2  t T 0  2  exp(−i γ L m P 0 ), (7.2.9) where the chirp parameter is given by C = 2 γ L m P 0 .For γ > 0, the chirp parameter C is positive, and is thus suitable for dispersion compensation. Since γ > 0 for silica fibers, the transmission fiber itself can be used for chirping the pulse. This approach was suggested in a 1986 study [30]. It takes advantage of higher- order solitons which pass through a stage of initial compression (see Chapter 9) . Figure 7.4 shows the GVD-limited transmission distance as a function of the average launch power for 4- and 8-Gb/s lightwave systems. It indicates the possibility of doubling the transmission distance by optimizing the average power of the input signal to about 3mW. 7.3 Postcompensation Techniques Electronic techniques can be used for compensation of GVD within the receiver. The philosophy behind this approach is that even though the optical signal has been de- graded by GVD, one may be able to equalize the effects of dispersion electronically if the fiber acts as a linear system. It is relatively easy to compensate for dispersion if a heterodyne receiver is used for signal detection (see Section 10.1). A heterodyne receiver first converts the optical signal into a microwave signal at the intermediate fre- quency ω IF while preserving both the amplitude and phase information. A microwave bandpass filter whose impulse response is governed by the transfer function H( ω )=exp[−i( ω − ω IF ) 2 β 2 L/2], (7.3.1) 7.3. POSTCOMPENSATION TECHNIQUES 287 Figure 7.4: Dispersion-limited transmission distance as a function of launch power for Gaus- sian (m = 1) and super-Gaussian (m = 3) pulses at bit rates of 4 and 8 Gb/s. Horizontal lines correspond to the linear case. (After Ref. [30]; c 1986 IEE; reprinted with permission.) where L is the fiber length, should restore to its original form the signal received. This conclusion follows from the standard theory of linear systems (see Section 4.3.2) by us- ing Eq. (7.1.4) with z = L. This technique is most practical for dispersion compensation in coherent lightwave systems [31]. In a 1992 transmission experiment, a 31.5-cm-long microstrip line was used for dispersion equalization [32]. Its use made it possible to transmit the 8-Gb/s signal over 188 km of standard fiber having a dispersion of 18.5 ps/(km-nm). In a 1993 experiment, the technique was extended to homodyne detection using single-sideband transmission [33], and the 6-Gb/s signal could be recovered at the receiver after propagating over 270 km of standard fiber. Microstrip lines can be designed to compensate for GVD acquired over fiber lengths as long as 4900 km for a lightwave system operating at a bit rate of 2.5 Gb/s [34]. As discussed in Chapter 10, use of a coherent receiver is often not practical. An electronic dispersion equalizer is much more practical for a direct-detection receiver. A linear electronic circuit cannot compensate GVD in this case. The problem lies in the fact that all phase information is lost during direct detection as a photodetector responds to optical intensity only (see Chapter 4). As a result, no linear equalization technique can recover a signal that has spread outside its allocated bit slot. Nevertheless, several nonlinear equalization techniques have been developed that permit recovery of the de- graded signal [35]–[38]. In one method, the decision threshold, normally kept fixed at the center of the eye diagram (see Section 4.3.3), is varied depending on the preced- ing bits. In another, the decision about a given bit is made after examining the analog waveform over a multiple-bit interval surrounding the bit in question [35]. The main difficulty with all such techniques is that they require electronic logic circuits, which 288 CHAPTER 7. DISPERSION MANAGEMENT must operate at the bit rate and whose complexity increases exponentially with the number of bits over which an optical pulse has spread because of GVD-induced pulse broadening. Consequently, electronic equalization is generally limited to low bit rates and to transmission distances of only a few dispersion lengths. An optoelectronic equalization technique based on a transversal filter has also been proposed [39]. In this technique, a power splitter at the receiver splits the received optical signal into several branches. Fiber-optic delay lines introduce variable delays in different branches. The optical signal in each branch is converted into photocurrent by using variable-sensitivity photodetectors, and the summed photocurrent is used by the decision circuit. The technique can extend the transmission distance by about a factor of 3 for a lightwave system operating at 5 Gb/s. 7.4 Dispersion-Compensating Fibers The preceding techniques may extend the transmission distance of a dispersion-limited system by a factor of 2 or so but are unsuitable for long-haul systems for which GVD must be compensated along the transmission line in a periodic fashion. What one needs for such systems is an all-optical, fiber-based, dispersion-management technique [40]. A special kind of fiber, known as the dispersion-compensating fiber (DCF), has been developed for this purpose [41]–[44]. The use of DCF provides an all-optical technique that is capable of compensating the fiber GVD completely if the average optical power is kept low enough that the nonlinear effects inside optical fibers are negligible. It takes advantage of the linear nature of Eq. (7.1.3). To understand the physics behind this dispersion-management technique, consider the situation in which each optical pulse propagates through two fiber segments, the second of which is the DCF. Using Eq. (7.1.4) for each fiber section consecutively, we obtain A(L,t)= 1 2 π  ∞ −∞ ˜ A(0, ω )exp  i 2 ω 2 ( β 21 L 1 + β 22 L 2 ) −i ω t  d ω , (7.4.1) where L = L 1 + L 2 and β 2 j is the GVD parameter for the fiber segment of length L j ( j = 1, 2). If the DCF is chosen such that the ω 2 phase term vanishes, the pulse will recover its original shape at the end of DCF. The condition for perfect dispersion compensation is thus β 21 L 1 + β 22 L 2 = 0, or D 1 L 1 + D 2 L 2 = 0. (7.4.2) Equation (7.4.2) shows that the DCF must have normal GVD at 1.55 µ m(D 2 < 0) because D 1 > 0 for standard telecommunication fibers. Moreover, its length should be chosen to satisfy L 2 = −(D 1 /D 2 )L 1 . (7.4.3) For practical reasons, L 2 should be as small as possible. This is possible only if the DCF has a large negative value of D 2 . Although the idea of using a DCF has been around since 1980 [40], it was only after the advent of optical amplifiers around the 1990 that the development of DCFs [...]... zω 2 /2), it is evident that an optical filter whose transfer function cancels this phase will restore the signal Unfortunately, no optical filter (except for an optical fiber) has a transfer function suitable for compensating the GVD exactly Nevertheless, several optical filters have provided partial GVD compensation by mimicking the ideal transfer function Consider an optical filter with the transfer... management in long-haul systems 7.8 Long-Haul Lightwave Systems This chapter has so far focused on lightwave systems in which dispersion management helps to extend the transmission distance from a value of ∼10 km to a few hundred kilometers The important question is how dispersion management can be used for long-haul systems for which transmission distance is several thousand kilometers If the optical signal... 7.9 High-Capacity Systems Modern WDM lightwave systems use a large number of channels to realize a system capacity of more than 1 Tb/s For such systems, the dispersion-management technique should be compatible with the broad bandwidth occupied by the multichannel signal In this section we discuss the dispersion-management issues relevant for high-capacity systems 7.9 HIGH-CAPACITY SYSTEMS 311 7.9.1... smaller than the amplifier bandwidth 7.5 OPTICAL FILTERS 291 Figure 7.6: Dispersion management in a long-haul fiber link using optical filters after each amplifier Filters compensate for GVD and also reduce amplifier noise Optical filters can be made using an interferometer which, by its very nature, is sensitive to the frequency of the input light and acts as an optical filter because of its frequency-dependent... also tunable [80] 7.7 Optical Phase Conjugation Although the use of optical phase conjugation (OPC) for dispersion compensation was proposed in 1979 [81], it was only in 1993 that the OPC technique was implemented experimentally; it has attracted considerable attention since then [82]–[103] In contrast with other optical schemes discussed in this chapter, the OPC is a nonlinear optical technique This... this reason, several other all-optical schemes have been developed for dispersion management Most of them can be classified under the category of optical equalizing filters Interferometric filters are considered in this section while the next section is devoted to fiber gratings The function of optical filters is easily understood from Eq (7.1.4) Since the GVD affects the optical signal through the spectral... simplifies the system design Typically L m = LA ≈ 80 km for terrestrial lightwave systems but is reduced to about 50 km for submarine systems Because of cost considerations, most laboratory experiments use a fiber loop in which the optical signal is forced to recirculate many times to simulate a long-haul 7.8 LONG-HAUL LIGHTWAVE SYSTEMS 307 lightwave system Figure 7.15 shows such a recirculating fiber loop... compensated by choosing an optical filter such that φ2 = −β2 L The pulse will recover perfectly only if |H(ω )| = 1 and the cubic and higher-order terms in the Taylor expansion in Eq (7.5.2) are negligible Figure 7.6 shows schematically how such an optical filter can be combined with optical amplifiers such that both fiber losses and GVD can be compensated simultaneously Moreover, the optical filter can also... the input power, and the amplifier spacing, and may decrease to below 3000 km, depending on the operating parameters [96] The use of OPC for long-haul lightwave systems requires periodic use of optical amplifiers and phase conjugators These two optical elements can be combined into one by using parametric amplifiers, which not only generate the phase-conjugated signal through the FWM process but also amplify... using an optical amplifier A loss of 6 dB was due to a 3-dB fiber coupler used to separate the reflected signal from the incident signal This amount can be reduced to about 1 dB using an optical circulator, a three-port device that transfers power one port to another in a circular fashion Even then, relatively high losses and narrow bandwidths of FP filters limit their use in practical lightwave systems . advent of optical amplifiers, fiber losses are no longer a major limiting factor for optical communication systems. Indeed, mod- ern lightwave systems are. third-generation terrestrial systems operating near 1.55 µ m and using optical transmitters containing a distributed feedback (DFB) laser. Such systems generally