JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 379 Numerical Comparison Between Distributed and Discrete Amplification in a Point-to-Point 40-Gb/s 40-WDM-Based Transmission System With Three Different Modulation Formats D. Dahan, Student Member, IEEE, and G. Eisenstein, Fellow, IEEE Abstract In this paper, we describe a detailed numerical investigation on the relative merits of gain flattened distributed Raman amplification (DRA) and discrete gain flattened amplifiers. We simulate a system with forty 40-Gb/s channels spaced at 100 GHz and compare the performance of three different modulation formats nonreturn-to-zero (NRZ), return-to-zero (RZ) and carrier-suppressed RZ (CS-RZ). Three types of amplifiers, multifrequency backward- and forward-pumped DRAs, and an idealized discrete gain flattened amplifier are examined for various signal powers and transmission distances. For the backward-pumped DRA, we also describe calculated tolerance limits imposed by incomplete dispersion slope compensation and polarization mode dispersion (PMD) level. Index Terms Distributed amplifiers, fiber nonlinearities, optical amplifiers, optical fiber dispersion, polarization mode dispersion (PMD), Raman scattering, wavelength division multiplexing (WDM). I. INTRODUCTION ADVANCES in wavelength division multiplexed (WDM) transmission systems have led to an almost complete usage of the available gain bandwidth in erbium-doped fiber amplifiers (EDFAs). Modified EDFAs with broader bandwidth have been demonstrated [1], but it is obvious that the role of other type of optical amplifiers, such as distributed Raman amplifiers (DRAs) will be increasingly significant. The DRA is attractive because its gain bandwidth and spectral allocation depend only on the pump wavelength. Moreover, the use of multiwavelength pumping schemes can be used to flatten the gain, as has been reported, for example, in [2]. Experiments in which DRAs have been exclusively used in dense WDM system have been reported [3], [4]. Understanding and quantifying all aspects of dense WDM systems calls for detailed modeling because many complicated mutually interacting nonlinear phenomena take place simultaneously. The complex propagation of multiwavelength optical pulses requires a careful physical formalism combined with large scale numerical computations. Manuscript received May 1, 2001; revised November 7, 2001. This work was supported by the European Commission through the METEOR project within the fifth framework of IST. The authors are with the Electrical Engineering Department, Technion Israel Institute of Technology, Haifa 32000, Israel (e-mail: gad@ee.technion.ac.il). Publisher Item Identifier S 0733-8724(02)01013-7. This paper describes a comprehensive numerical simulation of a dense point to point transmission system based on the IST-METEOR project specifications, which include 40 channels, each operating at 40 Gb/s with 100-GHz channel spacing [5]. The simulation compares discrete and distributed amplification for three separate modulation formats, nonreturn-to-zero (NRZ), return-to-zero (RZ), and carrier-suppressed RZ (CS-RZ), at different power levels and transmission distances. The discrete amplifier is modeled as an ideal (hypothetical) gain block with frequency independent gain and noise figure (NF db). Namely, its characteristics are superior to any practical broad-band gain-flattened EDFA. Distributed amplification is implemented by multiwavelength Raman amplification with either forward or backward pumping. II. SYSTEM DESCRIPTION The system is simulated with three types of transmission spans, as shown in Fig. 1. Each type uses one of the three amplification schemes, discrete gain block and forward- and backward-pumped DRA. Each transmission span consists of 75-km standard single-mode fiber (SSMF) whose dispersion and dispersion slope are completely compensated by 15 km of dispersion compensating fiber (DCF). All fiber nonlinearities, as well as first-order polarization mode dispersion (PMD) with a typical value of 0.15 ps/km, are included. For each configuration, the total transmission distance comprises one to five identical transmission spans. The backward and forward DRAs are optimized to get the best broad-band flat gain spectrum. Six pump sources at carefully chosen wavelengths were found to yield the best results ensuring a flat Raman gain spectrum at a level of 18.5 db, which is 0.5 db higher than the fiber loss in the transmission span. Raman amplification is a nonlinear scattering process that is highly polarization sensitive. Because PMD causes the polarization of the signal and the pumps to rotate with respect to one another over all possible states on the Poincaré sphere, we treat the pumps as being nonpolarized so that both orthogonal signal polarizations undergo Raman amplification during the transmission. In the transmission simulations, we consider NRZ, RZ, and CS-RZ modulation formats. Conventional RZ is generated from a 50% duty cycle electrical RZ voltage driving a Mach Zender modulator fed by a continuous wave (CW) optical signal. The resulting optical RZ signal has a duty cycle 0733-8724/02$17.00 2002 IEEE
380 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 Fig. 1. Schematics of the transmission link for the three amplifier schemes: (a) backward and (b) forward six-wavelength-pumped DRA and (c) discrete flattened amplifier. of 62.5%. The CS-RZ is generated by two cascaded differential Mach Zender modulators; the first modulates a CW signal with NRZ electrical data driven at 40 Gb/s, and the second is modulated by a 20-GHz sinusoidal signal while the modulator is biased at [6]. The resultant duty cycle is 87.5%. Temporal and spectral representations of the three signal types are shown schematically in Fig. 2. The multiplexer and demultiplexer are modeled as parabolic tapered horn array waveguide gratings with a bandwidth of 78 GHz. III. DISTRIBUTED RAMAN AMPLIFICATION In this section, we compare the relative merits of the forward and backward pumping configurations in DRAs and address the definitions of gain and NF. A. Power Analysis The Raman fiber amplifier uses the intrinsic properties of the silica fiber for amplification; when the transmission fiber is used as the gain medium, this is called distributed amplification. The amplification is produced by stimulated Raman scattering (SRS), which occurs when a pump photon is scattered by a glass molecule to a lower frequency photon while, at the same time, the residual energy is absorbed by the molecule as optical phonons (transition between vibrational states). This lower frequency photon is coherently added to the signal photons [7]. The performance of distributed Raman amplification is limited by Raman amplified spontaneous emission (ASE), Rayleigh scattering of ASE, and multipath interference (MPI) due to the double Rayleigh backscattering (DRBS) of the signal. In the latter case, the signal power is Rayleigh backscattered, amplified by SRS, scattered back again to its original propagation direction, and amplified for a second time. This MPI depends on several factors, such as the Raman gain, the signal power, the fiber length, and the fiber effective area [8]. The power evolution of the forward propagating signal, pump, and noise, respectively noted as and, is
DAHAN AND EISENSTEIN: POINT-TO-POINT 40-Gb/s 40-WDM-BASED TRANSMISSION SYSTEM 381 Fig. 2. Frequency and temporal representation of NRZ, RZ, and CS-RZ modulation formats at 40 Gb/s. governed by (1), shown at the bottom of the page, where is the fiber loss, is the Rayleigh backscattering coefficient, is the fiber effective section, and is the Raman gain at the frequency for a pump at the frequency. The last two terms in the pump power equation (1b) refer to the pump depletion induced by the pumps at lower frequencies and by (1a) (1b) (1c)
382 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 the channels, respectively, and the last term at the noise power equation refers to the ASE generated at the frequency by the pump at with being the excess noise factor defined as (2) where is Planck s constant, is the NF resolution, is Boltzmann s constant, and is the temperature. Because the spontaneous emission process is polarization independent, it is twice as efficient as the stimulated emission process. The equations of the backward-propagating waves (,, and ) are obtained from (1) by inverting the sign of the propagation operator and replacing the forward waves by the backward ones and vice versa. Although these equations refer to a simultaneous backwardand forward-pumping scheme, we solve them numerically for an 18.5-dB gain forward- or backward-multipumping scheme, respectively. This type of equation system is a typical two-point boundary value problem; the initial values of the forward- and backward-propagating waves at the opposite fiber ends are known. It is solved by using an iterative method to guess the missing values at each step of a fourth-order Runge Kutta algorithm. The power evolutions along the transmission span of the backward- and forward-multipumping schemes are shown in Fig. 3. The figure shows the evolution of the 40 signal channels, the pumps, and the ASE noise as well as the DRBS noise contribution to the signal channels. For both configurations, Raman amplification also affects the pumps themselves. The longest wavelength pumps drain energy to the shortest wavelength pumps, which are directly responsible for signal amplification. In the backward-pumped case, the shortest wavelength pumps contribute more gain at the end of the transmission fiber. As a result, the highest gain is achieved in the second half of the fiber, but the high gain is accompanied by large noise. The forward-pumped case exhibits the highest gain in the first half of the fiber, where the pump and signal powers are the highest. The signal power exhibits a maximum near the first quarter of the fiber that increases the nonlinear effects. The output optical signal-to-noise ratio (OSNR) is 33 db in the forward-pumped configuration, compared to 25 db in the backward case. The DRBS is also shown, and as expected for an 18.5 db gain, we get a signal-to-drbs ratio larger than 42 db for both configurations [8]. B. ON OFF Gain and Effective NF The distributed Raman amplification takes place during the signal propagation in the fiber. Hence, the usual definitions for gain and NF should include the fiber loss. In order to compare its performances with that of a discrete amplifier, the DRA must be considered as lumped at the end of the transmission fiber, so that the loss contribution to the NF is removed. In such a case, the corresponding effective NF may be negative because the equivalent discrete amplifier is not physically realizable. The reason Fig. 3. Power evolution through the transmission fiber in the (a) backward and (b) forward six-wavelength-pumped DRA. for this is that the DRA is equivalent to placing a string of line amplifiers in the transmission fiber. Thus, when the signal propagates through the fiber, it always has a higher level than when the pumps are off. The gain is compared on a pump ON OFF basis; it is defined as the output signal power when pumps are on, divided by the output signal power with pumps off. Hansen et al. [9] provide the following expression for the effective noise figure: NF (3) where is the ON OFF gain, is the amplified simultaneous emission power measured over the bandwidth, and is the photon energy. Fig. 4 shows the gain and equivalent noise figure for the backward- and forward-pumping configurations. For both schemes, we achieved more than 18-dB flattened gain over 33 nm with a 0.8-dB peak-to-peak ripple with a total pump power less than 800 mw. To achieve the flat gain, six pumps were used with the following set of pump wavelengths: 1395, 1418, 1425, 1432, 1449, and 1463 nm. The forward-pumping scheme requires slightly higher pump powers to enable this
DAHAN AND EISENSTEIN: POINT-TO-POINT 40-Gb/s 40-WDM-BASED TRANSMISSION SYSTEM 383 Fig. 4. Gain and effective NF of the (a) backward and (b) forward sixwavelength-pumped DRA. gain, and its NF is better than in the backward-pumped scheme because of its higher output OSNR. IV. COMPARISON BETWEEN DISTRIBUTED AND DISCRETE AMPLIFIERS In order to simulate the performances of the three amplifiers with the three modulation formats, several approximations were made to reduce the computation time according to the total transmission distance (up to 450 km), the pump, and the signal power levels. Rayleigh backscattering of the noise and DRBS are negligible because an optical isolator is placed at the beginning of each transmission span to limit the Rayleigh backscattering process to one span at a time. Furthermore, optical signal to DRBS noise ratio is more than 20 db higher than the OSNR. The CW theory of stimulated Raman scattering, as described in (1), needs to be modified when we consider pulsed signals and CW pumps. In a multipumping configuration, the pumps pumps and signal pumps interactions are governed by a set of coupled amplitude equations [7] [see (4) at the bottom of the page], which include the effects of dispersion, self-phase modulation (SPM), and cross-phase modulation (XPM). Because the detuning between the pumps and signal is large, we neglect the FWM process. In (4), is the complex amplitude of the channel signal or the th pump respectively. Equation (4) includes effects of fiber loss through, of group velocity, second- and third-order dispersions through,, and, respectively, of fractional contribution of Raman effect through and of fiber nonlinearity through. Several simplifications of (4) have been considered and used. In a WDM system, the complex envelope of the signal is composed of several time-varying channels. Pattern-dependent crosstalk induced by pump depletion and pump noise transfer to the signal influence both the gain and the noise and lead to signal-quality degradation [10], [11]. These effects are predominant in forward pumping, but the averaging effect introduced by backward pumping moderates them. In order to properly compare the two cases, we neglect the pattern effects and consider the pumps to be pure CW signals and the pump depletion to be caused by the average signal power. Because the pumps are treated as CW light, they induce only a constant phase shift, which is irrelevant. Then, we can consider the net absorption coefficients defined by (5) at the bottom of the next page. All of these considerations lead to the conclusion that only the power evolution has to be considered for the pumps. Finally, (4) becomes (6), shown at the bottom of the next page. Equation (6) gives a new numerical approach to derive the signal amplitude evolution in the presence of SRS. The ASE noise computation is derived from (1c). The numerical calculation uses our own numerical model for the fiber transmission part. It is developed in MATLAB (Mathworks, Natick, MA 01760-2098 USA) and integrated in the Virtual Photonics (Holmdel, NJ 07733 USA) software environment. We modified (6) in order to take into account the two orthogonal polarizations in the signal equation and we used the coarse step method approach to simulate dispersion, nonlinearities and first-order PMD. Special care is taken in resizing the (4)
384 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 PMD level to its original value in the statistical sense and in distributing uniformly the optical state of polarization on the Poincaré sphere [12]. The calculations were done for a single run through the fiber spans but, due to the statistical nature of PMD, several runs followed by averaging may yield somewhat more accurate results. The distributed amplifier characteristics are the ones discribed in the previous chapter, while the discrete amplifier has a frequency independent gain ( db) and noise figure (NF db). For each format, the system simulated the transmission of a 128-bit-long pseudorandom binary sequence at 40 Gb/s for two values of total average launched signal power into the fiber, 3.4 mw and 6.8 mw. For the case of 3.4-mW total average launched signal power, the calculated factors as a function of distance are discribed in Fig. 5 where the factor extrema and mean values for the 40 channels are shown separately for each modulation format at the output of each transmission span. The factors we use are in the electrical domain obtained from a calculated detected eye diagram. Fig. 5(a) describes the case of backward-pumped Raman amplification where we observe that the worst results are obtained for the NRZ format but even it reaches a factor larger than 6.8 (BER ) at an effective transmission distance of 375 km. The RZ format is found to be somewhat better than the CS-RZ. Results for forward-pumped Raman amplification are shown in Fig. 5(b). This configuration achieves good performances for low launched power and because of its higher sensitivity to nonlinear effects, CS-RZ yields the best results. Fig. 5(c) shows the results for the discrete amplification case. We note that it is not possible to exceed 225 km with any format because of the low OSNR. It order to get error-free transmission, the amplification span has to be reduced to 60 km (50 km SMF 10 km DCF), which produces an OSNR enhancement. It is interesting to note, however, that due to the low power level, the RZ format achieves higher factor values than does the CS-RZ. Fig. 6 describes the system performance for the higher total launched signal power (6.8 mw). The backward-pumped configuration shown in Fig. 6(a) is, again, the best choice with even better performances for all the modulation formats. However, for this power, the forward-pumping scheme has a rather poor performance; NRZ drops drastically after 150 km and RZ drops after 225 km. The CS-RZ format achieves good performances because of the high nonlinear regime. Indeed, 40-Gb/s systems Fig. 5. Q factor range for (a) backward-pumped DRA, (b) forward-pumped DRA, and (c) ideal discrete amplifier with 3.4-mW total average input launched power. are mainly limited by SPM, whose effective length increases in the presence of Raman gain [13], whereas the CS-RZ format is more tolerant to SPM [6]. The ideal discrete amplifier [Fig. 6(c)] (5) (6)
DAHAN AND EISENSTEIN: POINT-TO-POINT 40-Gb/s 40-WDM-BASED TRANSMISSION SYSTEM 385 A. Tolerance to the Dispersion Slope Common techniques can achieve essentially total dispersion compensation. However, in high-bit-rate dense WDM (DWDM) systems, one also needs to completely compensate the slope dispersion, which is usually very difficult because it requires that the relative dispersion slope of the DCF be equal to the relative dispersion slope of the SSMF over a wide spectral bandwidth [14]. We have studied the effect of incomplete dispersion slope compensation for the three modulation formats, and the results are summarized in Fig. 7. The figure shows, for each modulation format, the minimum achieved factor over the 40 channels with respect to the effective transmission distance and the dispersion slope compensation efficiency. The second-order dispersion level is assumed to be perfectly compensated in all cases. The NRZ format is the most robust because its temporal pulsewidth is inherently wider (and, correspondingly, the spectral width is narrower) compared with RZ and CS-RZ, which behave rather similarly. However, CS-RZ achieves longer distances when the dispersion slope compensation efficiency deviates by approximately 5% from its optimum value, and it is more robust than RZ when the dispersion slope is overestimated. Fig. 6. Q factor range for (a) backward-pumped DRA, (b) forward-pumped DRA, and (c) ideal discrete amplifier with 6.8-mW total average input launched power. has better results than those found in the lower power case because of the higher OSNR. Good performances are achieved for up to 300 km in the NRZ case and up to 375 km for RZ and CS-RZ. V. BACKWARD-PUMPED DRA: APPLICATIONS The improved OSNR performance of DRA does not stem from an inherently lower noise compared to that of an EDFA. Rather, distributed amplification moderates the effect of noise and enables OSNR optimization. Furthermore, backward-pumped DRA is the configuration of choice for achieving error-free transmission because of its higher tolerance to nonlinearities. In this section, we address two more issues, incomplete dispersion slope compensation and different PMD levels. We use backward-pumped DRA and a total average launched power of 6.8 mw and the three modulation formats. B. Tolerance to PMD At 40 Gb/s, PMD becomes one of the major limiting factors for systems and may need to be compensated. However, PMD can be tolerated as long as it induces pulse broadening of less than 10% of the time bit slot (2.5 ps). Fig. 8 shows the minimum achieved factor over the 40 channels with respect to the effective transmission distance and the PMD value. NRZ is more sensitive than RZ and CS-RZ to PMD. The main reason of this is that, in RZ formats, the energy is more confined and larger differential group delays (DGDs) are required to cause the energy to leak out from the bit slot, which produces intersymbol interferences [15]. For a given distance, RZ is more tolerant to PMD than CS-RZ because it has a smaller duty cycle. However for a given PMD value, CS-RZ can reach longer distances. Sunnerud et al. [16] have given an exact analytic expression for the pulse broadening in presence of PMD. Alo, because there is an optimum input pulsewidth that gives the shortest output pulsewidth in the case of chromatic dispersion, a similar property exists for PMD. VI. CONCLUSION We have compared the performance of DRAs to that of an ideal discrete amplifier. Our comparison was based on a numerical simulation, which included NRZ, RZ, and CS-RZ modulation formats at 40 Gb/s. This study has shown the benefit of using backward-pumped distributed Raman amplification in term of OSNR improvement and tolerances to nonlinearities. Neglecting the pattern effects and pump noise transfer make the
386 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 Fig. 7. Contour plots illustrating the dependence of the minimum Q factor on the slope dispersion compensation for (A) NRZ, (B) RZ, and (C) CS-RZ. forward pumping ideal, even though it leads to lower performance results than the backward pumping. This latter allows the attainment of error-free transmissions at distances where the most ideal amplifier fails with low total average launched power into the fiber, and the typical NRZ distance limitation at 40 Gb/s can be increased.
DAHAN AND EISENSTEIN: POINT-TO-POINT 40-Gb/s 40-WDM-BASED TRANSMISSION SYSTEM 387 Fig. 8. Contour plots illustrating the dependence of the minimum Q factor on PMD for (A) NRZ, (B) RZ, and (C) CS-RZ. Our discussion also stresses the tolerance limits imposed by dispersion slope compensation as well as PMD for the three modulation formats in the case of backward pumped DRA. It has shown a balance between good tolerances of NRZ for dispersion slope compensation and the robustness of RZ and CS-RZ to PMD.
388 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 ACKNOWLEDGMENT D. Dahan wishes to thank the French Embassy in Israel for support while serving as a scientific cooperant. REFERENCES [1] D. Lowe, R. D. Muro, and S. Wilson, 75 nm continuous gain using a novel EDFA topology, in Proc. ECOC 2000, vol. 2, 2000, pp. 175 176. [2] H. Kidorf, K. Rottwitt, M. Vissov, M. Ma, and E. Rabarijaona, Pump interactions in a 100 nm bandwidth Raman amplifier, IEEE Photon. Technol. Lett., vol. 11, pp. 530 532, May 1999. [3] B. Mikkelson, G. Raybon, B. Zhu, J. Essiambre, P. G. Bernasconi, K. Dreyer, L. W. Stulz, and S. N. Knudsen, High spectral efficiency (0.53 bit/s/hz) WDM transmission of 160 Gb/s per wavelength over 400 km of fiber, in Proc. OFC 01, 2001, ThF2, pp. 1 3. [4] H. Nakamoto, T. Tanaka, N. Shimojoh, T. Naito, I. Yokota, A. Sugiyama, T. Ueki, and M. Suyama, 1.05 Tb/s WDM transmission over 8,186 km using distributed Raman amplifier repeaters, in Proc. 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Fludger, V. Handerek, and R. J. Mears, Pump to signal RIN transfer in Raman fiber amplifiers, J. Lightwave Technol., vol. 19, pp. 1140 1148, Aug. 2001. [12] D. Marcuse, C. R. Menyuk, and P. K. A. Wai, Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence, J. Lightwave Technol., vol. 9, pp. 1735 1745, Sept. 1997. [13] A. F. Evans, J. Grochocinski, A. Rahman, C. Reynolds, and M. Vasilyev, Distributed amplification: How Raman gain impacts other fiber nonlinearities, in Proc. OFC 01, 2001, MA7, pp. 1 3. [14] L. Gruner-Nielson, S. N. Knudsen, B. Edvol, P. Kristensen, T. Veng, and D. Magnussen, Dispersion compensating fibers and perspectives for future developments, in Proc. ECOC 2000, vol. 1, 2000, pp. 91 92. [15] H. Sunnerud, M. Karlsson, and P. A. Anderkson, A comparison between NRZ and RZ data formats with respect to PMD induced system degradation, in Proc. OFC 01, 2001, WT3, pp. 1 3. [16], Analytical theory for PMD-compensation, IEEE Photon. Technol. Lett., vol. 12, pp. 50 52, Jan. 2000. D. Dahan (S 02) was born in France in 1976. He received the engineer s diploma degree from the Ecole Superieure d Electricité (Supélec), Paris, France, in 1999 and the M.Sc. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 1999. He is currently pursuing the Ph.D. degree in electrical engineering at the Technion Israel Institute of Technology, Haifa, Israel. From March 2000 to June 2001, he was a Research Assistant in the optical communication laboratory at the Technion as part of French national service as a scientific cooperant. His current research interests are in the field of nonlinear optical amplifiers. G. Eisenstein (S 80 M 80 SM 90 F 99) received the B.Sc. degree from the University of Santa Clara, Santa Clara, CA, in 1975 and the M.Sc. and Ph.D. degrees from the University of Minnesota, Minneapolis, in 1978 and 1980, respectively. In 1980, he joined AT&T Bell Laboratories, where he was a member of the Technical Staff in the Photonic Circuits Research Department. His research at AT&T Bell Laboratories was in the fields of diode laser dynamics, high-speed optoelectronic devices, optical amplification, optical communication systems, and thin-film technology. In 1989, he joined the faculty of the Technion Israel Institute of Technology, Haifa, Israel, where he holds the Dianne and Mark Seiden Chair of Electrooptics in Electrical Engineering and serves as the head of the Barbara and Norman Seiden Advanced Optoelectronics Center. His current research interests include fiber-optic systems and components for such systems, microwave photonic systems, dynamics of quantum well lasers and bipolar heterojunction phototransistors, nonlinear semiconductor optical amplifiers, and compact short-pulse generators. He has published more than 200 journal and conference papers, and he lectures regularly in all major fiber-optics and diode-laser conferences and serves on numerous technical program committees. He is an Associate Editor of the IEEE JOURNAL OF QUANTUM ELECTRONICS.