WEDNESDAY AFTERNOON / OFC 2003 / VOL. 1 / 305 Wednesday, March 26 1607. [6] Y. Zhu et al., Electron. Lett. 38, 895 (2002). [7] Y. Hadjar, N.J. Traynor, OFC '02, paper ThB1. [8] J.-C. Bouteiller et al., OFC '02, post-deadline paper FB3. [9] S.B. Papernyi, V.I. Karpov, W.R.L. Clements, OF C'02, post-deadline paper FB4. [10] M. Vasilyev, to be published. [11] A. Artamonov et al., OFC '02, paper WB6. [12] C.R.S. Fludger et al., OFC '02, paper WB4. [13] P.J. Winzer, K. Sherman, and M. Zirngibl, OF C'02, paper WB5. [14] S. Gray, M. Vasilyev, K. Jepsen, OFC '01, paper MA2. [15] R.-J. Essiambre et al., IEEE Photon. Technol. Lett. 14, 914 (2002). [16] A. Kobyakov, M. Vasilyev, A.F. Evans, OFC’03, paper WB2. [17] J. Bromage et al., OFC '02, paper TuR3. [18] M. Mehendale, M. Vasilyev, A. Kobyakov, M. Williams, S. Tsuda, Electron. Lett. 38, 648 (2002). [19] I. Tomkos, M. Vasilyev, J.-K. Rhee, M. Mehendale, B. Hallock, B. Szalabofka, M. Williams, S. Tsuda, M. Sharma, OFC '02, post- deadline paper FC1. [20] I. Tomkos, M. Vasilyev, J.-K. Rhee, M. Mehendale, B. Hallock, B. Szalabofka, M. Will- iams, S. Tsuda, M. Sharma, ECOC '02, post-dead- line paper PD2.1. [21] B. Zhu et al., ECOC '01, post-deadline paper PD.M.1.8. [22] F. Liu et al., OFC '02, post-deadline paper FC7. WB2 2:00 PM Performance Analysis of Raman Amplifiers Based on Dispersion-Managed Fibers A. Kobyakov, M. Vasilyev, A. Evans, Corning Inc., Corning, NY, Email: KobyakovA@corning.com. We optimize bidirectionally-pumped Raman amplifiers based on dispersion-managed fibers (DMFs). We show that, in terms of the signal-to- noise ratio, performance of the optimized DMF amplifier is only a few dB away from that of an ideal distributed amplifier. 1. Introduction In the past several years, distributed Raman amplification in high-capacity transmission sys- tems established itself as a viable alternative to doped-fiber amplifiers (see, e.g., [1] and refer- ences therein). Recently, several studies have been devoted to optimizing the performance of distributed amplifiers by minimizing the com- bined effect of amplified spontaneous emission (ASE), double Rayleigh backscattering (DRBS), and nonlinearity [2-4]. Restrictions imposed on relative intensity noise of Raman pumps have also been studied [5]. Dispersion-managed fibers (DMFs) consisting of positive (+D) and negative (-D) dispersion fibers emerged as a result of a search for further improvement of system perfor- mance [6,7]. Dispersion-slope compensation and high pumping efficiency in the smaller-effective area -D fiber, combined with improved noise per- formance [8], make DMF a strong candidate for the fiber of choice in next-generation high-capac- ity transmission systems. Several recent experi- ments demonstrated impressive performance of all-Raman DMF-based wavelength-division mul- tiplexed systems [9,10]. It is not clear, however, how closely the DMF can approach the limit of an ideal distributed amplifier. In this paper we quan- tify this difference by optimizing pumping condi- tions of the all-Raman DMF-based system as a function of fiber parameters and post-span com- ponent loss. 2. Analysis The on-off Raman gain in a DMF G R can be found from the undepleted pump approximation [1,3,8] as where γ(z)=g R (z)P R /[A eff (z)α p (z)], α p , g R , and A eff are the dimensionless Raman interaction strength in a non-polarization maintaining fiber, loss at the pump wavelength, Raman coefficient, and effec- tive area of the fiber, respectively; is the normalized pump evolution due to com- bined forward and backward pumping, k=P f (0)/ P R is the ratio of forward pump power to the total launched pump power P R , and L is the span length. The total gain G(z) is related to the on-off gain as G(z)=G R (z)p s (z). It is also assumed that linear signal attenuation and pump attenuation p p (z) include lumped loss at the point of fiber splice z = z splice . Similarly to single fiber [3], the effective lumped noise figure (NF) of an inhomogeneous fiber can be calculated as [8] where n sp ={1-exp[-h∆ν/(k B T fib )]} -1 is the sponta- neous emission factor that depends on the fiber temperature T fib and the pump-signal frequency difference ∆ν (h and k B are Planck and Boltzmann constants, respectively); T F < 1 is transmittance of a passive fiber, and α RBS is Rayleigh backscatter coefficient. For consistency, we have included the effect of backscattered ASE [second term in brackets in (1)] that starts to matter at high Raman gains [8]. We will evaluate the performance of the DMF with respect to some idealistic all-Raman system with minimum impairments. As such, we con- sider a single fiber-based system with the same total span loss as for the DMF (equal to fiber loss plus splice loss) and impaired solely by forward propagating ASE. Thus, our reference system is an ideal distributed amplifier with optimum trade- off between ASE and nonlinearity. One can show that in the absence of DRBS this condition is sat- isfied for a flat gain profile G(z) = 1. To ensure equal nonlinear penalties in both systems, we scale signal power to the DMF in such a way that the nonlinear phase shift in both spans is the same (here λ is the signal wavelength and n 2 is nonlinear Kerr coefficient of the fiber). Thus, if P ref is the input signal power to the single fiber span, the signal power to the DMF span is P DMF = P ref /R NL where for equal trans- mittances T F of the DMF and a single fiber In (2), α s,ref is the absorption coefficient at the sig- nal wavelength in a single fiber and Under these assumptions the ratio of electric sig- nal-to-noise-ratios (SNR) after N spans is given by [3] as where for single fiber F ref =1+2n sp ln(1/T F ). In the DMF-based system, we also account for the post- span loss T L of system components such as a gain-flattening filter or an add-drop multiplexer, so that T F G R (L)T L =1 and the total NF after one span After substituting these relations into expression for ∆SNR, modified to include detector quantum efficiency Ș, we obtain (3) where the NF of the DMF includes the contribution from the DRBS cross- talk and is effective electrical filter bandwidth that accounts for optical signal bandwidth [3]. 3. Results and discussion Parameters of a generic DMF [6] we use to illus- trate our analysis are listed in Table 1. We assume the ratio between the lengths of +D and -D sec- tions to be 2, splice loss at signal and pump wave- lengths to be 0.3 dB, =8 GHz, n sp =1.13. Relevant parameters of a sin- gle fiber are α s,ref = 0.21 dB/km. A eff,ref = 55 µm 2 , n 2,ref =2.2 x 10 -20 m 2 /W, and P ref = 0.5 mW. First, we evaluate the performance of a single span (N = 1) without post-span loss (T L =1). As can be seen from Fig. 1a, the optimum amount of forward pumping weakly depends on span length and amounts to k opt ≈0.3-0.4. This ratio is deter- mined by the two key performance factors - the total NF F DMF and the nonlinear factor R NL that have opposite trends with increasing k (Fig. 1b). Minimum of their product corresponds to k opt (dotted curve in Fig. 1b). For short spans, the per- formance advantage due to forward pumping is small (<0.3 dB). It increases with the span length and reaches ~2 dB for L =100 km (Fig. 1a). (a)         ′ ′ ′ α ′ γ = ∫ z p p R z d z p z z z G 0 ) ( ) ( ) ( exp ) (         ′ ′ α − +         ′ ′ α − − = ∫ ∫ z p L z p p z d z k z d z k z p 0 ) ( exp ) ( exp ) 1 ( ) (         ′ ′ α − = ∫ z s s z d z z p 0 ) ( exp ) ( (1) ∫ λ π = φ L eff in NL dz z G z A z n P 0 2 ) ( ) ( ) ( 2 (2) ( ) ∫ α = L eff F ref s NL dz z G z A z n T R 0 DMF 2 , ) ( ) ( ) ( / 1 ln , ref n z n z n , 2 DMF 2 2 ) ( ) ( = . ref eff eff eff A z A z A , DMF ) ( ) ( = ( ) ( ) 1 1 1 1 1 SNR SNR SNR total DMF DMF + − + − = = ∆ F N F N R ref NL ref eff e F NL ref B h X T R P F F ν + = 9 5 ASE DMF DMF eff e F NL ref B h X T R P F F ν + = 9 5 ASE DMF DMF ∫ ∫ ′ ′ ′ α α = L z L dz z d z G z z G z X ) ( ) ( ) ( ) ( 2 RBS 0 2 RBS eff e B eff e B