## Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems |

Optics Express, Vol. 19, Issue 4, pp. 3449-3454 (2011)

http://dx.doi.org/10.1364/OE.19.003449

Acrobat PDF (1077 KB)

### Abstract

Limitations in the performance of coherent transmission systems employing digital back-propagation due to four-wave mixing impairments are reported for the first time. A significant performance constraint is identified, originating from four-wave mixing between signals and amplified spontaneous emission noise which induces a linear increase in the standard deviation of the received field with signal power, and linear dependence on transmission distance.

© 2011 OSA

## 1. Introduction

3. C. Weber, C.-A. Bunge, and K. Petermann, “Fiber Nonlinearities in Systems Using Electronic Predistortion of Dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. **27**(16), 3654–3661 (2009). [CrossRef]

3. C. Weber, C.-A. Bunge, and K. Petermann, “Fiber Nonlinearities in Systems Using Electronic Predistortion of Dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. **27**(16), 3654–3661 (2009). [CrossRef]

7. J. P. Gordon and H. A. Haus, “‘’Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. **11**(10), 665–667 (1986). [CrossRef] [PubMed]

8. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt. Lett. **15**(23), 1351–1353 (1990). [CrossRef] [PubMed]

9. R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. **15**(7), 1071–1082 (1997). [CrossRef]

10. D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. **9**(10), 1330–1334 (1991). [CrossRef]

12. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. **16**(2), 73–85 (2010). [CrossRef]

5. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. **26**(20), 3416–3425 (2008). [CrossRef]

## 2. Simulation setup

^{13}per polarization per channel, and the sample-rate was set to be 16 samples/symbol. The 112 Gb/s PM-QPSK signal was propagated over a non dispersion-managed link using single stage erbium doped fibre amplifier (EDFA). The link comprised

*60*× 80 km spans of single mode fibre (SMF) for transmission. The EDFA was modelled with a 4.5 dB noise figure and the total amplification gain was equal to the total loss in each span. The fibre had a loss (α) of 0.2 dB/km and a nonlinear coefficient (γ) of 1.4/W/km, and no inline optical dispersion compensation was used. Note that, we expect the findings of this report would remain valid, although at a higher transmission distance, given a fibre with lower loss, nonlinear coefficient and larger core area [13

13. J. Cai, Y. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “Transmission of 96x100G Pre‐Filtered PDM‐RZ‐QPSK Channels with 300% Spectral Efficiency over 10,608km and 400% Spectral Efficiency over 4,368km,” *in Proc. OFC 2010*, PDPB10 (2010).

## 3. Results and discussions

5. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. **26**(20), 3416–3425 (2008). [CrossRef]

12. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. **16**(2), 73–85 (2010). [CrossRef]

10. D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. **9**(10), 1330–1334 (1991). [CrossRef]

_{norm}) of the received field after DBP for radial (Fig. 3a) and angular jitter (Fig. 3b) for different dispersion coefficients. It can be seen that at lower signal power σ

_{norm}increases with decreasing OSNR for all the dispersion maps, as expected for a noise-limited system. For higher launch power levels, where the performance is affected by nonlinear effects, σ

_{norm}of the received field shows a linear increase with signal power, thus we may conclude that the actual constellation variance varies quadratically with signal launch power. This is in contrast to previously reported mechanisms for the nonlinear interaction between signal and noise, which tend to demonstrate a linear dependence on the signal power, is solely dependent on the noise power [8

8. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt. Lett. **15**(23), 1351–1353 (1990). [CrossRef] [PubMed]

12. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. **16**(2), 73–85 (2010). [CrossRef]

_{norm}with power would be expected for a FWM based signal-ASE interaction where the parametric amplification of ASE increases quadratically with signal power. The resonant enhancement or quasi phase matching of FWM along an amplified transmission line is well-known [14,15

15. K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. **13**(1), 88–93 (1995). [CrossRef]

*E*is the nonlinearly generated field,

_{FWM}*w*is the angular frequency,

*E*and

_{p}, E_{q}*E*are signal components,

_{r}**n*is the refractive index,

*L*is the span length,

*χ*is the nonlinearity coefficient, degeneracy factor

^{3}*D*is either three or six for degenerate and non-degenerate FWM and

*Δβ*is the effective propagation constant difference. For a modulated signal whose total bandwidth exceeds the phase matching bandwidth of a single fibre span (~3GHz for standard single mode fibre) integration of Eq. (1) over the continuous power spectral density (PSD).is required, accounting for contributions from both strongly and weakly phase matched contributions.

16. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express **18**(18), 19039–19054 (2010). [CrossRef] [PubMed]

*N*amplifier along the remainder of the link,where,

^{th}*I*is the nonlinear noise power spectral density,

_{SN-FWM}*I*is the signal power spectral density,

_{signal}*I*is the noise power spectral density from a single amplifier.

_{noise}*C*and

_{1}*C*represent weakly and strongly phase matched regimes, respectively.

_{2}*N*is the number of spans after a given amplifier,

*B*is signal bandwidth and

*β*the group velocity dispersion (D = −2πcβ

_{2}_{2}/λ

^{2}). From Eq. (2), treating the contribution from each amplifier as an independent random variable, with Gaussian statistics, the total nonlinear noise at the output of an

*M*-span system is,

16. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express **18**(18), 19039–19054 (2010). [CrossRef] [PubMed]

^{3/2}. Figure 4a shows the evolution of the noise σ

_{norm}with length for a signal launch power of 5 dBm, close to the optimum shown in Fig. 3, and again shows an excellent agreement with analytical prediction of (2). Figure 4a also shows the expected evolution in σ

_{norm}in the absence of nonlinearity, corresponding to noise loading at the receiver. Comparing the two curve fits reveals that the signal-ASE FWM process becomes dominant in this system after ~5,000 km for PM-QPSK.

17. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. **28**(4), 423–433 (2010). [CrossRef]

18. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature **411**(6841), 1027–1030 (2001). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” |

2. | D. Rafique, M. Forzati, and J. Mårtensson, “Impact of Nonlinear Fibre Impairments in 112 Gb/s PM-QPSK Transmission with 43 Gb/s and 10.7 Gb/s Neighbours,” |

3. | C. Weber, C.-A. Bunge, and K. Petermann, “Fiber Nonlinearities in Systems Using Electronic Predistortion of Dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. |

4. | F. Yaman and G. Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photonics Technol. Lett. |

5. | E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. |

6. | D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010). |

7. | J. P. Gordon and H. A. Haus, “‘’Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. |

8. | J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt. Lett. |

9. | R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. |

10. | D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. |

11. | J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. |

12. | A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. |

13. | J. Cai, Y. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “Transmission of 96x100G Pre‐Filtered PDM‐RZ‐QPSK Channels with 300% Spectral Efficiency over 10,608km and 400% Spectral Efficiency over 4,368km,” |

14. | A. D. Ellis, and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in |

15. | K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. |

16. | X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express |

17. | A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. |

18. | P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: October 27, 2010

Revised Manuscript: December 9, 2010

Manuscript Accepted: December 10, 2010

Published: February 8, 2011

**Citation**

Danish Rafique and Andrew D. Ellis, "Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems," Opt. Express **19**, 3449-3454 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3449

Sort: Year | Journal | Reset

### References

- S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proc. ECOC 2008, Mo.3.D.1 (2008).
- D. Rafique, M. Forzati, and J. Mårtensson, “Impact of Nonlinear Fibre Impairments in 112 Gb/s PM-QPSK Transmission with 43 Gb/s and 10.7 Gb/s Neighbours,” in Proc. ICTON 2010, paper We.D1.6 (2010).
- C. Weber, C.-A. Bunge, and K. Petermann, “Fiber Nonlinearities in Systems Using Electronic Predistortion of Dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. 27(16), 3654–3661 (2009). [CrossRef]
- F. Yaman and G. Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photonics Technol. Lett. 1, 144–152 (2009).
- E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]
- D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010).
- J. P. Gordon and H. A. Haus, “‘’Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11(10), 665–667 (1986). [CrossRef] [PubMed]
- J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt. Lett. 15(23), 1351–1353 (1990). [CrossRef] [PubMed]
- R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. 15(7), 1071–1082 (1997). [CrossRef]
- D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. 9(10), 1330–1334 (1991). [CrossRef]
- J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, pp1104 (2000).
- A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16(2), 73–85 (2010). [CrossRef]
- J. Cai, Y. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “Transmission of 96x100G Pre‐Filtered PDM‐RZ‐QPSK Channels with 300% Spectral Efficiency over 10,608km and 400% Spectral Efficiency over 4,368km,” in Proc. OFC 2010, PDPB10 (2010).
- A. D. Ellis, and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in Non-Linear Effects in Fibre Communications, IEE Colloquium on, 6/1–6/4, (1990).
- K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995). [CrossRef]
- X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010). [CrossRef] [PubMed]
- A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010). [CrossRef]
- P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.