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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 18 — Sep. 4, 2006
  • pp: 8065–8071
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Multi-level optimization of a fiber transmission system via nonlinearity management

J. D. Ania-Castañón, S.K. Turitsyn, A. Tonello, S. Wabnitz, and E. Pincemin  »View Author Affiliations


Optics Express, Vol. 14, Issue 18, pp. 8065-8071 (2006)
http://dx.doi.org/10.1364/OE.14.008065


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Abstract

Nonlinearity management is explored as a complete tool to obtain maximum transmission reach in a WDM fiber transmission system, making it possible to optimize multiple system parameters, including optimal dispersion pre-compensation, with fast simulations based on the continuous-wave approximation.

© 2006 Optical Society of America

1. Introduction

In addition to many other attractive features such as reducing noise and being applicable to any spectral band, distributed Raman amplification offers the possibility to manage the signal power evolution along the transmission span. Indeed, the possibility of exerting control over the signal power profile and perform direct nonlinearity management [1–4

1 . R. Gabitov and P. M. Lushnikov , “ Nonlinearity management in a dispersion-managed system ,” Opt. Lett. 27 , 113 – 115 ( 2002 ) [CrossRef]

] allows for the balancing of the penalties originated from noise accumulation and from nonlinear impairments, thus leading to increased system reach or expanded performance margins [5

5 . S. Bigo , “ Optimizing terrestrial systems for 40Gbit/s channel rate ,” Proceedings of the 31 st European Conference on Optical Communications 5 , pp. 137 – 157 ( 2005 )

].

Despìte the many advantages that can be derived from implementing distributed amplification in optical transmission systems, the introduction of new degrees of freedom for system optimization make finding the best possible configuration a daunting task. In this paper we present a detailed discussion of the successive steps involved in the application of the nonlinearity management technique to transmission system optimization, including dispersion pre-compensation.

For illustration, but without loss of generality, we consider a WDM transmission system with hybrid Raman/EDFA amplification. The basic cell of our system is schematically depicted on Fig. 1: a span of standard single-mode fiber (SSMF) is followed by a -100 ps/nm/km dispersion-compensating fiber (DCF) module. Distributed Raman amplification (DRA) with bi-directional pumping is used in the SSMF section, whereas an Erbium-doped fiber amplifier (EDFA) with a noise figure of 4.5 dB provides additional amplification at the end of the span. We shall consider a wavelength-division multiplexed (WDM) transmission, with 16-channels. The SSMF span length is not fixed, but rather it is one of the multiple system design parameters that will be subject to our optimization procedure.

Fig. 1. System Schematic.

2. Optimization of the amplification scheme/span length

Following the approach that was presented in refs. [3

3 . J.D. Ania-Castañón , I.O. Nasieva , N. Kurukitkoson , S.K. Turitsyn , C. Borsier , and E. Pincemin , “ Nonlinearity management in fiber transmission systems with hybrid amplification ,” Opt. Commun. 233 , 353 – 357 ( 2004 ). [CrossRef]

,4

4 . J.D. Ania-Castañón , I.O. Nasieva , S.K. Turitsyn , N. Brochier , and E. Pincemin , “ Optimal span length in high-speed transmission systems with hybrid Raman-erbium-doped fiber amplification ,” Opt. Lett. 30 , 23 – 25 ( 2005 ) [CrossRef] [PubMed]

], the first step involves optimising the amplification scheme in terms of two key parameters. Namely: η1 which is the ratio between Raman gain and total span gain (to compensate for total span loss), and η2 which is the ratio between the backward and total Raman pump powers in the SSMF. Nonlinear impairments are qualitatively assessed by calculating the channel nonlinear phase shift (NPS) per span, whereas the system output optical signal-to-noise ratio (OSNR) over 1 nm measures the impact of noise accumulation. Given that a full optimisation analysis requires taking into account both span length (i.e., the length L of the SSMF) and output OSNR, we are facing a complex 4-dimensional optimization problem that we are solving in the frame of the well known CW model for the evolution of the average powers of signals and pumps (including double-Rayleigh backscattering and amplified spontaneous emission as sources of noise) [12

12 . S. Namiki and Y. Emori , “ Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes ,” J. Sel. Top. Quantum Electron. , 7 , 3 – 16 ( 2001 ) [CrossRef]

]. As a key optimization parameter, the function NPS (η1, η2, L) is computed for multiple values of the output OSNR level. We fix the total transmission distance to an arbitrary long length (e.g., to 900 km), so the number of spans will be adjusted automatically as we vary the span length L. Figure 2 shows the NPS vs. η1 and L for a value of η2 equal to 1 and an OSNR of 20 dB at the receiver (i.e., after the total transmission distance).

By drawing a series of such plots, sweeping through different values of η2 (see animation associated to Fig. 2) and of the OSNR, we can find the span length and amplifier configuration that minimize the NPS for any given value of the OSNR (please note that since we will consider all possible target OSNRs, the initial choice of total transmission length used to produce the contour plots becomes irrelevant). So far the input signal power is a free parameter, to be adjusted in order to achieve the target OSNR at a given system reach.

Both the optimal span length and η1 depend quite strongly on the pump split ratio characterized by η2. With full forward Raman pumping (η2 = 0, not see animation), a short span length of about 30 km SSMF and a 50% splitting of the gain between Raman and EDFA (i.e., η1 = 0.5) amplifiers give the best system performance. The optimal span length and relative contribution from the Raman amplifier to the total gain increase gradually as the backward Raman pump grows larger until η2 reaches a value of 0.75, for which the optimal span length is 60 km and the optimal η1~0.6. Finally, for η2 = 1 (as shown in Fig. 2), the optimal span length decreases to 50 km, again with an optimal η1~0.6.

By considering the optimum solution for each possible value of η2, we see that nonlinear penalties are reduced (always at the same OSNR level of 20 dB) as the gain contribution from forward Raman pumping decreases. The best result for the whole 3-dimensional space defined by a fixed value of the OSNR is then obtained for: η1 = 0.6, η2 = 1, and L = 50 km.

Fig. 2. NPS vs. η1 and L, with η2 = 1, for an OSNR of 20 dB after 900 km (Animation shows results for different values of η2) [Media 1]

Fig. 3. Max reach (Km) vs. Span length and input power for 16-channel OOK RZ-50% transmission, with no dispersion pre-compensation or average dispersion optimization.

3. Optimization of the pre-compensation length

Finding the optimal pre-compensation for a given transmission system is essential in order to minimise the impact of both intra-channel and inter-channel distortions. In Ref. [7

7 . R.I. Killey , H.J. Thiele , V. Mikhailov , and P. Bayvel , “ Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber ,” Photon. Technol. Lett. 12 , 1624 – 1626 ( 2000 ) [CrossRef]

], Killey et al. provided a simple criterion for optimum pre-compensation in dispersion-managed systems with lumped amplification that has been confirmed for on-off keying systems with direct detection. Namely, the Dpre should be chosen so that pulses are compressed to a minimum duration at a distance z’ within the nonlinear length of each span, where

0z'PineαSzdz=z'LPineαSzdz,
(1)

with Dpre = -DSMF z’, from which

Dpre=DSMFαSln(21+eαSL)NDres2.
(2)

Dres is the residual dispersion if average dispersion is different from zero, and N represents the number of spans. Such optimal Dpre minimizes both pulse overlap within the nonlinear length, and maximizes the reversal of timing jitter build-up in the second half of the nonlinear span. In the case of a system with distributed amplification, signal power evolution within the span is not trivial, but the above procedure can be still generalized and an equivalent relation can be obtained which is valid for any amplification scheme:

0z'PS(z)dz=z'LPS(z)dz,
(3)

where Ps can be analytically estimated only if pump depletion is neglected.

In general, it will be simpler to obtain the optimal distance z’ by numerically integrating the signal power and finding the z’ that verifies the above condition. This is equivalent to finding the point within the SSMF where the accumulated NPS reaches half of its total value, or the NPS barycentric, as proposed in [8

8 . I. Joindot , “ Dispersion map optimization in hybrid Raman/erbium-doped fiber amplifier-based 40-Gb/s link ,” Photon. Technol. Lett. 17 , 1555 - 1557 ( 2005 ) [CrossRef]

]. This simple procedure permits to find the optimal pre-compensation length for any given amplifier configuration and span length, once again without the need for time-consuming full system simulations. For illustration, Fig. 4 shows in a contour plot the optimal pre-compensation lengths (in km) of DCF, superimposed on top of the NPS vs. η1 and L, for the case of η2 = 1, a target OSNR of 20 dB at 900 km, and 16 WDM channels.

From Fig. 4, it is easy to see that the optimal pre-compensation length for the best system configuration (η1 = 0.6, η2 = 1, and L = 50 km) is approximately equal to 3.8 km, instead of the 2.2 km that would have been predicted by (2) . Note that Killey et al’s method for calculating the pre-compensation length in lumped amplification systems is obtained under the assumption that nonlinearities are accumulated in the transmission span only, and not in the DCF. This hypothesis is still valid in the present case involving DRA in the SSMF, and loss in the DCF.

Fig. 4. Optimal pre-compensation lengths (red dash) and accumulated NPS (black) vs. η1 and L, for the case of η2 = 1 OSNR = 20 dB

In order to verify and confirm the accuracy of the optimal pre-compensation criterion discussed above, we carried out full numerical transmission simulations where we monitored the maximum transmission distance for channel 8 vs. pre-compensation DCF length. Our aim here was to find the best system configuration for the 16-channel OOK RZ-50% Gaussian signal transmission at 40 Gbit/s per channel.

As shown in Fig. 5, these simulations confirm that the optimal length of pre-compensation DCF (for zero average system dispersion) is between 3.8 km and 4 km. Such pre-compensation enables an increase in the transmission distance for channel 8 from 1400 up to 1755 km. In addition, as shown in Fig. 5, we observed as expected, a drift in the optimal pre-compensation length towards shorter DCFs as the absolute value of (negative) span average dispersion is increased by varying the length of the DCF on each span. The DCF used is designed to match both the dispersion and dispersion slope accumulated in the SMF, so similar amounts of residual dispersion are accumulated in all the channels. As it can be seen, however, the observed drifting is slower than what is predicted by Killey’s correction factor of -NDres / 2. Indeed, we have verified that the drift is directly dependent on the amplification configuration, defined by parameters η1 and η2. This fact suggests that the nonlinear signal evolution along the span modifies its response to accumulated dispersion, and highlights the need for further adjustment of the correction term when applying the pre-chirp selection rule to systems with non-zero average dispersion using distributed or hybrid amplification. For the configuration under study here, we achieved a maximum transmission distance (measured over SSMF and DCF) of 2164 km with an average dispersion of -0.3 ps/nm/km, and a pre-compensation length of 1.5 km.

Fig. 5 Reach (Km) vs. pre-compensation length and average dispersion for the optimal span configuration and input average power. White dashed line: expected drift with average dispersion according to Killey’s formula.

4. Conclusion

Acknowledgments

J. D. Ania-Castañón wishes to acknowledge the EPSRC for their economic support of this research through grant EP/C011880/1.

References and links

1 .

R. Gabitov and P. M. Lushnikov , “ Nonlinearity management in a dispersion-managed system ,” Opt. Lett. 27 , 113 – 115 ( 2002 ) [CrossRef]

2 .

R. Driben , B. A. Malomed , and U. Mahlab , “ Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links ,” Opt. Commun. 232 , 129 – 138 ( 2004 ) [CrossRef]

3 .

J.D. Ania-Castañón , I.O. Nasieva , N. Kurukitkoson , S.K. Turitsyn , C. Borsier , and E. Pincemin , “ Nonlinearity management in fiber transmission systems with hybrid amplification ,” Opt. Commun. 233 , 353 – 357 ( 2004 ). [CrossRef]

4 .

J.D. Ania-Castañón , I.O. Nasieva , S.K. Turitsyn , N. Brochier , and E. Pincemin , “ Optimal span length in high-speed transmission systems with hybrid Raman-erbium-doped fiber amplification ,” Opt. Lett. 30 , 23 – 25 ( 2005 ) [CrossRef] [PubMed]

5 .

S. Bigo , “ Optimizing terrestrial systems for 40Gbit/s channel rate ,” Proceedings of the 31 st European Conference on Optical Communications 5 , pp. 137 – 157 ( 2005 )

6 .

R.-J. Essiambre , P. Winzer , J. Bromage , and C. H. Kim , “ Design of Bidirectionally Pumped Fiber Amplifiers Generating Double Rayleigh Backscattering ,” Photon. Technol. Lett. 14 , 914 – 916 ( 2002 ) [CrossRef]

7 .

R.I. Killey , H.J. Thiele , V. Mikhailov , and P. Bayvel , “ Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber ,” Photon. Technol. Lett. 12 , 1624 – 1626 ( 2000 ) [CrossRef]

8 .

I. Joindot , “ Dispersion map optimization in hybrid Raman/erbium-doped fiber amplifier-based 40-Gb/s link ,” Photon. Technol. Lett. 17 , 1555 - 1557 ( 2005 ) [CrossRef]

9 .

A. Carena , V. Curri , and P. Poggliolini , “ On the optimization of hybrid Raman/erbium-doped fiber amplifiers ,” Photon. Technol. Lett. 13 , 1170 - 1172 ( 2001 ) [CrossRef]

10 .

J. Park , J. Park , D. Lee , N.Y. Kim , H. Lee , and N. Park , “ Nonlinear phase shift scanning method for the optimal design of Raman transmission systems ,” J. Lightwave Technol. 24 , 1257 – 1268 ( 2006 ) [CrossRef]

11 .

J.-C. Bouteiller , J. Bromage , H.-J. Thiele , L. E. Nelson , K. Brar , and S. Stulz , “ An optimization process for Raman-amplified long-span transmission ,” Photon. Technol. Lett. 16 , 326 – 328 ( 2004 ) [CrossRef]

12 .

S. Namiki and Y. Emori , “ Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes ,” J. Sel. Top. Quantum Electron. , 7 , 3 – 16 ( 2001 ) [CrossRef]

13 .

L.K. Wickham , R.-J. Essiambre , A.H. Gnauk , P.J. Winzer , and A.R. Chralpyvy , “ Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission ,” Photon. Technol. Lett. 16 , 1591 – 1593 ( 2004 ) [CrossRef]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 17, 2006
Revised Manuscript: August 14, 2006
Manuscript Accepted: August 15, 2006
Published: September 1, 2006

Citation
J. D. Ania-Castañón, S. K. Turitsyn, A. Tonello, S. Wabnitz, and E. Pincemin, "Multi-level optimization of a fiber transmission system via nonlinearity management," Opt. Express 14, 8065-8071 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8065


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References

  1. R. Gabitov, P. M. Lushnikov, "Nonlinearity management in a dispersion-managed system," Opt. Lett. 27, 113-115 (2002) [CrossRef]
  2. R. Driben, B. A. Malomed, and U. Mahlab, "Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links," Opt. Commun. 232, 129-138 (2004) [CrossRef]
  3. J.D. Ania-Castañón, I.O. Nasieva, N. Kurukitkoson, S.K. Turitsyn, C. Borsier and E. Pincemin, "Nonlinearity management in fiber transmission systems with hybrid amplification," Opt. Commun. 233, 353-357 (2004). [CrossRef]
  4. J.D. Ania-Castañón, I.O. Nasieva, S.K. Turitsyn, N. Brochier and E. Pincemin, "Optimal span length in high-speed transmission systems with hybrid Raman-erbium-doped fiber amplification," Opt. Lett. 30, 23-25 (2005) [CrossRef] [PubMed]
  5. S. Bigo, "Optimizing terrestrial systems for 40Gbit/s channel rate," Proceedings of the 31st European Conference on Optical Communications 5, pp. 137-157 (2005)
  6. R.-J. Essiambre, P. Winzer,J. Bromage, and C. H. Kim, "Design of Bidirectionally Pumped Fiber Amplifiers Generating Double Rayleigh Backscattering," Photon. Technol. Lett. 14, 914-916 (2002) [CrossRef]
  7. R.I. Killey, H.J. Thiele, V. Mikhailov and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," Photon. Technol. Lett. 12, 1624-1626 (2000) [CrossRef]
  8. I. Joindot, "Dispersion map optimization in hybrid Raman/erbium-doped fiber amplifier-based 40-Gb/s link," Photon. Technol. Lett. 17, 1555 - 1557 (2005) [CrossRef]
  9. A. Carena, V. Curri, P. Poggliolini, "On the optimization of hybrid Raman/erbium-doped fiber amplifiers," Photon. Technol. Lett. 13, 1170 - 1172 (2001) [CrossRef]
  10. J. Park, J. Park, D. Lee, N.Y. Kim, H. Lee and N. Park, "Nonlinear phase shift scanning method for the optimal design of Raman transmission systems," J. Lightwave Technol. 24, 1257-1268 (2006) [CrossRef]
  11. J.-C. Bouteiller, J. Bromage, H.-J. Thiele, L. E. Nelson, K. Brar, and S. Stulz, "An optimization process for Raman-amplified long-span transmission," Photon. Technol. Lett. 16, 326-328 (2004) [CrossRef]
  12. S. Namiki, and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," J. Sel. Top. Quantum Electron., 7, 3-16 (2001) [CrossRef]
  13. L.K. Wickham, R.-J. Essiambre, A.H. Gnauk, P.J. Winzer, and A.R. Chralpyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," Photon. Technol. Lett. 16, 1591-1593 (2004) [CrossRef]

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