Chapter 10 Coherent Lightwave Systems The lightwave systems discussed so far are based on a simple digital modulation scheme in which an electrical bit stream modulates the intensity of an optical carrier inside the optical transmitter and the optical signal transmitted through the fiber link is incident directly on an optical receiver, which converts it to the original digital signal in the elec- trical domain. Such a scheme is referred to as intensity modulation with direct detection (IM/DD). Many alternative schemes, well known in the context of radio and microwave communication systems [1]–[6], transmit information by modulating the frequency or the phase of the optical carrier and detect the transmitted signal by using homodyne or heterodyne detection techniques. Since phase coherence of the optical carrier plays an important role in the implementation of such schemes, such optical communica- tion systems are called coherent lightwave systems. Coherent transmission techniques were studied during the 1980s extensively [7]–[16]. Commercial deployment of coher- ent systems, however, has been delayed with the advent of optical amplifiers although the research and development phase has continued worldwide. The motivation behind using the coherent communication techniques is two-fold. First, the receiver sensitivity can be improved by up to 20 dB compared with that of IM/DD systems. Second, the use of coherent detection may allow a more efficient use of fiber bandwidth by increasing the spectral efficiency of WDM systems. In this chap- ter we focus on the design of coherent lightwave systems. The basic concepts behind coherent detection are discussed in Section 10.1. In Section 10.2 we present new mod- ulation formats possible with the use of coherent detection. Section 10.3 is devoted to synchronous and asynchronous demodulation schemes used by coherent receivers. The bit-error rate (BER) for various modulation and demodulation schemes is considered in Section 10.4. Section 10.5 focuses on the degradation of receiver sensitivity through mechanisms such as phase noise, intensity noise, polarization mismatch, fiber disper- sion, and reflection feedback. The performance aspects of coherent lightwave systems are reviewed in Section 10.6 where we also discuss the status of such systems at the end of 2001. 478 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) 10.1. BASIC CONCEPTS 479 Figure 10.1: Schematic illustration of a coherent detection scheme. 10.1 Basic Concepts 10.1.1 Local Oscillator The basic idea behind coherent detection consists of combining the optical signal co- herently with a continuous-wave (CW) optical field before it falls on the photodetector (see Fig. 10.1). The CW field is generated locally at the receiver using a narrow- linewidth laser, called the local oscillator (LO), a term borrowed from the radio and microwave literature. To see how the mixing of the received optical signal with the LO output can improve the receiver performance, let us write the optical signal using complex notation as E s = A s exp[−i( ω 0 t + φ s )], (10.1.1) where ω 0 is the carrier frequency, A s is the amplitude, and φ s is the phase. The optical field associated with the local oscillator is given by a similar expression, E LO = A LO exp[−i( ω LO t + φ LO )], (10.1.2) where A LO , ω LO , and φ LO represent the amplitude, frequency, and phase of the local oscillator, respectively. The scalar notation is used for both E s and E LO after assuming that the two fields are identically polarized (polarization-mismatch issues are discussed later in Section 10.5.3). Since a photodetector responds to the optical intensity, the optical power incident at the photodetector is given by P = K|E s + E LO | 2 , where K is a constant of proportionality. Using Eqs. (10.1.1) and (10.1.2), P(t)=P s + P LO + 2  P s P LO cos( ω IF t + φ s − φ LO ), (10.1.3) where P s = KA 2 s , P LO = KA 2 LO , ω IF = ω 0 − ω LO . (10.1.4) The frequency ν IF ≡ ω IF /2 π is known as the intermediate frequency (IF). When ω 0 = ω LO , the optical signal is demodulated in two stages; its carrier frequency is first con- verted to an intermediate frequency ν IF (typically 0.1–5 GHz) before the signal is de- modulated to the baseband. It is not always necessary to use an intermediate frequency. 480 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS In fact, there are two different coherent detection techniques to choose from, depend- ing on whether or not ω IF equals zero. They are known as homodyne and heterodyne detection techniques. 10.1.2 Homodyne Detection In this coherent-detection technique, the local-oscillator frequency ω LO is selected to coincide with the signal-carrier frequency ω 0 so that ω IF = 0. From Eq. (10.1.3), the photocurrent (I = RP, where R is the detector responsivity) is given by I(t)=R(P s + P LO )+2R  P s P LO cos( φ s − φ LO ). (10.1.5) Typically, P LO  P s , and P s + P LO ≈ P LO . The last term in Eq. (10.1.5) contains the information transmitted and is used by the decision circuit. Consider the case in which the local-oscillator phase is locked to the signal phase so that φ s = φ LO . The homodyne signal is then given by I p (t)=2R  P s P LO . (10.1.6) The main advantage of homodyne detection is evident from Eq. (10.1.6) if we note that the signal current in the direct-detection case is given by I dd (t)=RP s (t). Denoting the average optical power by ¯ P s , the average electrical power is increased by a factor of 4P LO / ¯ P s with the use of homodyne detection. Since P LO can be made much larger than ¯ P s , the power enhancement can exceed 20 dB. Although shot noise is also enhanced, it is shown later in this section that homodyne detection improves the signal-to-noise ratio (SNR) by a large factor. Another advantage of coherent detection is evident from Eq. (10.1.5). Because the last term in this equation contains the signal phase explicitly, it is possible to trans- mit information by modulating the phase or frequency of the optical carrier. Direct detection does not allow phase or frequency modulation, as all information about the signal phase is lost. The new modulation formats for coherent systems are discussed in Section 10.2. A disadvantage of homodyne detection also results from its phase sensitivity. Since the last term in Eq. (10.1.5) contains the local-oscillator phase φ LO explicitly, clearly φ LO should be controlled. Ideally, φ s and φ LO should stay constant except for the inten- tional modulation of φ s . In practice, both φ s and φ LO fluctuate with time in a random manner. However, their difference φ s − φ LO can be forced to remain nearly constant through an optical phase-locked loop. The implementation of such a loop is not sim- ple and makes the design of optical homodyne receivers quite complicated. In addition, matching of the transmitter and local-oscillator frequencies puts stringent requirements on the two optical sources. These problems can be overcome by the use of heterodyne detection, discussed next. 10.1.3 Heterodyne Detection In the case of heterodyne detection the local-oscillator frequency ω LO is chosen to differ form the signal-carrier frequency ω 0 such that the intermediate frequency ω IF is 10.1. BASIC CONCEPTS 481 in the microwave region ( ν IF ∼ 1 GHz). Using Eq. (10.1.3) together with I = RP, the photocurrent is now given by I(t)=R(P s + P LO )+2R  P s P LO cos( ω IF t + φ s − φ LO ). (10.1.7) Since P LO  P s in practice, the direct-current (dc) term is nearly constant and can be removed easily using bandpass filters. The heterodyne signal is then given by the alternating-current (ac) term in Eq. (10.1.7) or by I ac (t)=2R  P s P LO cos( ω IF t + φ s − φ LO ). (10.1.8) Similar to the case of homodyne detection, information can be transmitted through amplitude, phase, or frequency modulation of the optical carrier. More importantly, the local oscillator still amplifies the received signal by a large factor, thereby improving the SNR. However, the SNR improvement is lower by a factor of 2 (or by 3 dB) compared with the homodyne case. This reduction is referred to as the heterodyne- detection penalty. The origin of the 3-dB penalty can be seen by considering the signal power (proportional to the square of the current). Because of the ac nature of I ac , the average signal power is reduced by a factor of 2 when I 2 ac is averaged over a full cycle at the intermediate frequency (recall that the average of cos 2 θ over θ is 1 2 ). The advantage gained at the expense of the 3-dB penalty is that the receiver design is considerably simplified because an optical phase-locked loop is no longer needed. Fluctuations in both φ s and φ LO still need to be controlled using narrow-linewidth semi- conductor lasers for both optical sources. However, as discussed in Section 10.5.1, the linewidth requirements are quite moderate when an asynchronous demodulation scheme is used. This feature makes the heterodyne-detection scheme quite suitable for practical implementation in coherent lightwave systems. 10.1.4 Signal-to-Noise Ratio The advantage of coherent detection for lightwave systems can be made more quanti- tative by considering the SNR of the receiver current. For this purpose, it is necessary to extend the analysis of Section 4.4 to the case of heterodyne detection. The receiver current fluctuates because of shot noise and thermal noise. The variance σ 2 of current fluctuations is obtained by adding the two contributions so that σ 2 = σ 2 s + σ 2 T , (10.1.9) where σ 2 s = 2q(I + I d )∆ f, σ 2 T =(4k B T /R L )F n ∆ f. (10.1.10) The notation used here is the same as in Section 4.4. The main difference from the analysis of Section 4.4 occurs in the shot-noise contribution. The current I in Eq. (10.1.10) is the total photocurrent generated at the detector and is given by Eq. (10.1.5) or Eq. (10.1.7), depending on whether homodyne or heterodyne detection is employed. In practice, P LO  P s , and I in Eq. (10.1.10) can be replaced by the dominant term RP LO for both cases. 482 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS The SNR is obtained by dividing the average signal power by the average noise power. In the heterodyne case, it is given by SNR = I 2 ac  σ 2 = 2R 2 ¯ P s P LO 2q(RP LO + I d )∆ f + σ 2 T . (10.1.11) In the homodyne case, the SNR is larger by a factor of 2 if we assume that φ s = φ LO in Eq. (10.1.5). The main advantage of coherent detection can be seen from Eq. (10.1.11). Since the local-oscillator power P LO can be controlled at the receiver, it can be made large enough that the receiver noise is dominated by shot noise. More specifically, σ 2 s  σ 2 T when P LO  σ 2 T /(2qR∆ f ). (10.1.12) Under the same conditions, the dark-current contribution to the shot noise is negligible (I d  RP LO ). The SNR is then given by SNR ≈ R ¯ P s q∆ f = η ¯ P s h ν ∆ f , (10.1.13) where R = η q/h ν was used from Eq. (4.1.3). The use of coherent detection allows one to achieve the shot-noise limit even for p–i–n receivers whose performance is generally limited by thermal noise. Moreover, in contrast with the case of avalanche photodiode (APD) receivers, this limit is realized without adding any excess shot noise. It is useful to express the SNR in terms of the number of photons, N p , received within a single bit. At the bit rate B, the signal power ¯ P s is related to N p as ¯ P s = N p h ν B. Typically, ∆ f ≈ B/2. By using these values of ¯ P s and ∆ f in Eq. (10.1.13), the SNR is given by a simple expression SNR = 2 η N p . (10.1.14) In the case of homodyne detection, SNR is larger by a factor of 2 and is given by SNR = 4 η N p . Section 10.4 discusses the dependence of the BER on SNR and shows how receiver sensitivity is improved by the use of coherent detection. 10.2 Modulation Formats As discussed in Section 10.1, an important advantage of using the coherent detection techniques is that both the amplitude and the phase of the received optical signal can be detected and measured. This feature opens up the possibility of sending information by modulating either the amplitude, or the phase, or the frequency of an optical carrier. In the case of digital communication systems, the three possibilities give rise to three modulation formats known as amplitude-shift keying (ASK), phase-shift keying (PSK), and frequency-shift keying (FSK) [1]–[6]. Figure 10.2 shows schematically the three modulation formats for a specific bit pattern. In the following subsections we consider each format separately and discuss its implementation in practical lightwave systems. 10.2. MODULATION FORMATS 483 Figure 10.2: ASK, PSK, and FSK modulation formats for a specific bit pattern shown on the top. 10.2.1 ASK Format The electric field associated with an optical signal can be written as [by taking the real part of Eq. (10.1.1)] E s (t)=A s (t)cos[ ω 0 t + φ s (t)]. (10.2.1) In the case of ASK format, the amplitude A s is modulated while keeping ω 0 and φ s constant. For binary digital modulation, A s takes one of the two fixed values during each bit period, depending on whether 1 or 0 bit is being transmitted. In most practical situations, A s is set to zero during transmission of 0 bits. The ASK format is then called on–off keying (OOK) and is identical with the modulation scheme commonly used for noncoherent (IM/DD) digital lightwave systems. The implementation of ASK for coherent systems differs from the case of the direct-detection systems in one important aspect. Whereas the optical bit stream for direct-detection systems can be generated by modulating a light-emitting diode (LED) or a semiconductor laser directly, external modulation is necessary for coherent com- munication systems. The reason behind this necessity is related to phase changes that 484 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS invariably occur when the amplitude A s (or the power) is changed by modulating the current applied to a semiconductor laser (see Section 3.5.3). For IM/DD systems, such unintentional phase changes are not seen by the detector (as the detector responds only to the optical power) and are not of major concern except for the chirp-induced power penalty discussed in Section 5.4.4. The situation is entirely different in the case of coherent systems, where the detector response depends on the phase of the received signal. The implementation of ASK format for coherent systems requires the phase φ s to remain nearly constant. This is achieved by operating the semiconductor laser continuously at a constant current and modulating its output by using an external mod- ulator (see Section 3.6.4). Since all external modulators have some insertion losses, a power penalty incurs whenever an external modulator is used; it can be reduced to below 1 dB for monolithically integrated modulators. As discussed in Section 3.64, a commonly used external modulator makes use of LiNbO 3 waveguides in a Mach–Zehnder (MZ) configuration [17]. The performance of external modulators is quantified through the on–off ratio (also called extinction ratio) and the modulation bandwidth. LiNbO 3 modulators provide an on–off ratio in excess of 20 and can be modulated at speeds up to 75 GHz [18]. The driving voltage is typically 5 V but can be reduced to near 3 V with a suitable design. Other materials can also be used to make external modulators. For example, a polymeric electro-optic MZ modulator required only 1.8 V for shifting the phase of a 1.55- µ m signal by π in one of the arms of the MZ interferometer [19]. Electroabsorption modulators, made using semiconductors, are often preferred be- cause they do not require the use of an interferometer and can be integrated mono- lithically with the laser (see Section 3.6.4). Optical transmitters with an integrated electroabsorption modulator capable of modulating at 10 Gb/s were available commer- cially by 1999 and are used routinely for IM/DD lightwave systems [20]. By 2001, such integrated modulators exhibited a bandwidth of more than 50 GHz and had the potential of operating at bit rates of up to 100 Gb/s [21]. They are likely to be employed for coherent systems as well. 10.2.2 PSK Format In the case of PSK format, the optical bit stream is generated by modulating the phase φ s in Eq. (10.2.1) while the amplitude A s and the frequency ω 0 of the optical carrier are kept constant. For binary PSK, the phase φ s takes two values, commonly chosen to be 0 and π . Figure 10.2 shows the binary PSK format schematically for a specific bit pattern. An interesting aspect of the PSK format is that the optical intensity remains constant during all bits and the signal appears to have a CW form. Coherent detection is a necessity for PSK as all information would be lost if the optical signal were detected directly without mixing it with the output of a local oscillator. The implementation of PSK requires an external modulator capable of changing the optical phase in response to an applied voltage. The physical mechanism used by such modulators is called electrorefraction. Any electro-optic crystal with proper orientation can be used for phase modulation. A LiNbO 3 crystal is commonly used in practice. The design of LiNbO 3 -based phase modulators is much simpler than that of an amplitude modulator as a Mach–Zehnder interferometer is no longer needed, and 10.2. MODULATION FORMATS 485 a single waveguide can be used. The phase shift δφ occurring while the CW signal passes through the waveguide is related to the index change δ n by the simple relation δφ =(2 π / λ )( δ n)l m , (10.2.2) where l m is the length over which index change is induced by the applied voltage. The index change δ n is proportional to the applied voltage, which is chosen such that δφ = π . Thus, a phase shift of π can be imposed on the optical carrier by applying the required voltage for the duration of each “1” bit. Semiconductors can also be used to make phase modulators, especially if a multi- quantum-well (MQW) structure is used. The electrorefraction effect originating from the quantum-confinement Stark effect is enhanced for a quantum-well design. Such MQW phase modulators have been developed [22]–[27] and are able to operate at a bit rate of up to 40 Gb/s in the wavelength range 1.3–1.6 µ m. Already in 1992, MQW devices had a modulation bandwidth of 20 GHz and required only 3.85 V for introducing a π phase shift when operated near 1.55 µ m [22]. The operating voltage was reduced to 2.8 V in a phase modulator based on the electroabsorption effect in a MQW waveguide [23]. A spot-size converter is sometimes integrated with the phase modulator to reduce coupling losses [24]. The best performance is achieved when a semiconductor phase modulator is monolithically integrated within the transmitter [25]. Such transmitters are quite useful for coherent lightwave systems. The use of PSK format requires that the phase of the optical carrier remain stable so that phase information can be extracted at the receiver without ambiguity. This re- quirement puts a stringent condition on the tolerable linewidths of the transmitter laser and the local oscillator. As discussed later in Section 10.5.1, the linewidth requirement can be somewhat relaxed by using a variant of the PSK format, known as differential phase-shift keying (DPSK). In the case of DPSK, information is coded by using the phase difference between two neighboring bits. For instance, if φ k represents the phase of the kth bit, the phase difference ∆ φ = φ k − φ k−1 is changed by π or 0, depending on whether kth bit is a 1 or 0 bit. The advantage of DPSK is that the transmittal signal can be demodulated successfully as long as the carrier phase remains relatively stable over a duration of two bits. 10.2.3 FSK Format In the case of FSK modulation, information is coded on the optical carrier by shifting the carrier frequency ω 0 itself [see Eq. (10.2.1)]. For a binary digital signal, ω 0 takes two values, ω 0 + ∆ ω and ω 0 −∆ ω , depending on whether a 1 or 0 bit is being trans- mitted. The shift ∆ f = ∆ ω /2 π is called the frequency deviation. The quantity 2∆ f is sometimes called tone spacing, as it represents the frequency spacing between 1 and 0 bits. The optical field for FSK format can be written as E s (t)=A s cos[( ω 0 ±∆ ω )t + φ s ], (10.2.3) where + and −signs correspond to 1 and 0 bits. By noting that the argument of cosine can be written as ω 0 t +( φ s ±∆ ω t), the FSK format can also be viewed as a kind of 486 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS PSK modulation such that the carrier phase increases or decreases linearly over the bit duration. The choice of the frequency deviation ∆ f depends on the available bandwidth. The total bandwidth of a FSK signal is given approximately by 2∆ f + 2B, where B is the bit rate [1]. When ∆ f  B, the bandwidth approaches 2∆ f and is nearly independent of the bit rate. This case is often referred to as wide-deviation or wideband FSK. In the opposite case of ∆ f B, called narrow-deviation or narrowband FSK, the bandwidth approaches 2B. The ratio β FM = ∆f /B, called the frequency modulation (FM) index, serves to distinguish the two cases, depending on whether β FM  1or β FM  1. The implementation of FSK requires modulators capable of shifting the frequency of the incident optical signal. Electro-optic materials such as LiNbO 3 normally produce a phase shift proportional to the applied voltage. They can be used for FSK by applying a triangular voltage pulse (sawtooth-like), since a linear phase change corresponds to a frequency shift. An alternative technique makes use of Bragg scattering from acoustic waves. Such modulators are called acousto-optic modulators. Their use is somewhat cumbersome in the bulk form. However, they can be fabricated in compact form using surface acoustic waves on a slab waveguide. The device structure is similar to that of an acousto-optic filter used for wavelength-division multiplexing (WDM) applications (see Section 8.3.1). The maximum frequency shift is typically limited to below 1 GHz for such modulators. The simplest method for producing an FSK signal makes use of the direct-modulation capability of semiconductor lasers. As discussed in Section 3.5.2, a change in the op- erating current of a semiconductor laser leads to changes in both the amplitude and frequency of emitted light. In the case of ASK, the frequency shift or the chirp of the emitted optical pulse is undesirable. But the same frequency shift can be used to ad- vantage for the purpose of FSK. Typical values of frequency shifts are ∼ 1 GHz/mA. Therefore, only a small change in the operating current (∼ 1 mA) is required for pro- ducing the FSK signal. Such current changes are small enough that the amplitude does not change much from from bit to bit. For the purpose of FSK, the FM response of a distributed feedback (DFB) laser should be flat over a bandwidth equal to the bit rate. As seen in Fig. 10.3, most DFB lasers exhibit a dip in their FM response at a frequency near 1 MHz [28]. The rea- son is that two different physical phenomena contribute to the frequency shift when the device current is changed. Changes in the refractive index, responsible for the fre- quency shift, can occur either because of a temperature shift or because of a change in the carrier density. The thermal effects contribute only up to modulation frequencies of about 1 MHz because of their slow response. The FM response decreases in the frequency range 0.1–10 MHz because the thermal contribution and the carrier-density contribution occur with opposite phases. Several techniques can be used to make the FM response more uniform. An equal- ization circuit improves uniformity but also reduces the modulation efficiency. Another technique makes use of transmission codes which reduce the low-frequency compo- nents of the data where distortion is highest. Multisection DFB lasers have been devel- oped to realize a uniform FM response [29]–[35]. Figure 10.3 shows the FM response of a two-section DFB laser. It is not only uniform up to about 1 GHz, but its modula- tion efficiency is also high. Even better performance is realized by using three-section 10.3. DEMODULATION SCHEMES 487 Figure 10.3: FM response of a typical DFB semiconductor laser exhibiting a dip in the frequency range 0.1–10 MHz. (After Ref. [12]; c 1988 IEEE; reprinted with permission.) DBR lasers described in Section 3.4.3 in the context of tunable lasers. Flat FM re- sponse from 100 kHz to 15 GHz was demonstrated [29] in 1990 in such lasers. By 1995, the use of gain-coupled, phase-shifted, DFB lasers extended the range of uni- form FM response from 10 kHz to 20 GHz [33]. When FSK is performed through direct modulation, the carrier phase varies continuously from bit to bit. This case is often referred to as continuous-phase FSK (CPFSK). When the tone spacing 2∆ f is chosen to be B/2( β FM = 1 2 ), CPFSK is also called minimum-shift keying (MSK). 10.3 Demodulation Schemes As discussed in Section 10.1, either homodyne or heterodyne detection can be used to convert the received optical signal into an electrical form. In the case of homo- dyne detection, the optical signal is demodulated directly to the baseband. Although simple in concept, homodyne detection is difficult to implement in practice, as it re- quires a local oscillator whose frequency matches the carrier frequency exactly and whose phase is locked to the incoming signal. Such a demodulation scheme is called synchronous and is essential for homodyne detection. Although optical phase-locked loops have been developed for this purpose, their use is complicated in practice. Het- erodyne detection simplifies the receiver design, as neither optical phase locking nor frequency matching of the local oscillator is required. However, the electrical signal oscillates rapidly at microwave frequencies and must be demodulated from the IF band to the baseband using techniques similar to those developed for microwave commu- nication systems [1]–[6]. Demodulation can be carried out either synchronously or asynchronously. Asynchronous demodulation is also called incoherent in the radio communication literature. In the optical communication literature, the term coherent detection is used in a wider sense. A lightwave system is called coherent as long as it uses a local oscillator irrespective of the demodulation technique used to convert the IF signal to baseband frequencies. This section focuses on the synchronous and asynchronous demodulation schemes for heterodyne systems. [...]... 1990 [2] R E Ziemer, Principles of Communications; Systems, Modulation and Noise, Wiley, New York, 1994 [3] L W Couch II, Digital and Analog Communication Systems, 5th ed., Prentice Hall, Upper Saddle River, NJ, 1995 [4] M S Roden, Analog and Digital Communication Systems, Prentice Hall, Upper Saddle River, NJ, 1995 [5] B P Lathi, Modern Digital and Analog Communication Systems, Oxford University Press,... K Kikuchi, Coherent Optical Fiber Communications, Kluwer Academic, Boston, 1988 [12] R A Linke and A H Gnauck, J Lightwave Technol 6, 1750 (1988) [13] J R Barry and E A Lee, Proc IEEE 78, 1369 (1990) [14] P S Henry and S D Persoinick, Eds., Coherent Lightwave Communications, IEEE Press, Piscataway, NJ, 1990 [15] S Betti, G de Marchis, and E Iannone, Coherent Optical Communication Systems, Wiley, New... in phase diversity ASK receivers [106] Nonlinear effects in optical fibers discussed in Section 2.6 also limit the coherent system, depending on the optical power launched into the fiber [107] Stimulated Raman scattering is not likely to be a limiting factor for single-channel coherent systems but becomes important for multichannel coherent systems (see Section 7.3.3) On the other hand, stimulated Brillouin... single-channel coherent systems The SBS threshold depends on both the modulation format and the bit rate, and its effects on coherent systems have been studied extensively [108]–[110] Nonlinear refraction converts intensity fluctuations into phase fluctuation through self- (SPM) and cross-phase modulation (XPM) [107] The effects of SPM become important for long-haul systems using cascaded optical amplifiers... 1980s to demonstrate the potential of coherent lightwave systems Their main objective was to show that coherent receivers are more sensitive than IM/DD receivers This section focuses on the system performance issues while reviewing the state of the art of coherent lightwave systems 10.6.1 Asynchronous Heterodyne Systems Asynchronous heterodyne systems have attracted the most attention in practice simply... used for long-haul coherent systems using in-line optical amplifiers for increasing the transmission distance A 1991 experiment realized a transmission distance of 2223 km at 2.5 Gb/s by using 25 erbiumdoped fiber amplifiers at approximately 80-km intervals [126] The performance of long-haul coherent systems is affected by the amplifier noise as well as by the nonlinear effects in optical fibers Their design... long-haul coherent systems [102]–[104] 10.5.5 Other Limiting Factors Several other factors can degrade the performance of coherent lightwave systems and should be considered during system design Reflection feedback is one such limiting factor The effect of reflection feedback on IM/DD systems has been discussed in Section 5.4.5 Essentially the same discussion applies to coherent lightwave systems Any feedback... both of which cannot be tolerated for coherent systems The use of optical isolators within the transmitter may be necessary for controlling the effects of optical feedback Multiple reflections between two reflecting surfaces along the fiber cable can convert phase noise into intensity noise and affect system performance as discussed in Section 5.4.5 For coherent systems such conversion can occur even inside... NJ, 1990 [15] S Betti, G de Marchis, and E Iannone, Coherent Optical Communication Systems, Wiley, New York, 1995 [16] S Ryu, Coherent Lightwave Communication Systems, Artec House, Boston, 1995 [17] F Heismann, S K Korotky, and J J Veselka, in Optical Fiber Telecommunications III, Vol B, I P Kaminow and T L Loch, Eds., Academic Press, San Diego, CA, 1997, Chap 8 [18] K Noguchi, O Mitomi, and H Miyazawa,... photons/bit were needed by an optically demodulated DPSK receiver designed with an optical preamplifier [119] In another variant, the transmitter sends a PSK signal but the receiver is designed to detect the phase difference such that a local oscillator is not needed [120] Considerable work has been done to quantify the performance of various 508 CHAPTER 10 COHERENT LIGHTWAVE SYSTEMS DPSK and FSK schemes . lightwave systems are reviewed in Section 10.6 where we also discuss the status of such systems at the end of 2001. 478 Fiber -Optic Communications Systems, . the optical carrier plays an important role in the implementation of such schemes, such optical communica- tion systems are called coherent lightwave systems.