Abstract

We extend the theory of parametric noise amplification to the case of transmission systems employing multiple optical phase conjugators, demonstrating that the excess noise due to this process may be reduced in direct proportion to the number of phase conjugation devices employed. We further identify that the optimum noise suppression is achieved for an odd number of phase conjugators, and that the noise may be further suppressed by up to 3dB by partial digital back propagation (or fractional spans at the ends of the links).

© 2015 Optical Society of America

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References

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  1. D. Qian, M.-F. Huang, E. Ip, Y.-K. Huang, Y. Shao, J. Hu, and T. Wan, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Communications Conference, (OSA, 2011), paper PDPB5.
  2. X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P. I. Borel, and K. Carlson, “PDM-nyquist-32QAM for 450-Gb/s per-channel WDM transmission on the 50 GHz ITU-T Grid,” J. Lightwave Technol. 30(4), 553–559 (2012).
    [Crossref]
  3. J.-X. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. S. Bergano, “20 Tbit/s capacity transmission over 6,860km,” in Optical Fiber Communications Conference (OSA, 2011), paper PDPB4.
  4. 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]
  5. 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]
  6. P. Poggiolini, “Modeling of non-linear propagation in uncompensated coherent systems”, in Optical Fiber Communications Conference (OSA, 2013), paper OTh3G1.
    [Crossref]
  7. D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011).
    [Crossref] [PubMed]
  8. M. D. Pelusi, “Fiber looped phase conjugation of polarization multiplexed signals for pre-compensation of fiber nonlinearity effect,” Opt. Express 21(18), 21423–21432 (2013).
    [Crossref] [PubMed]
  9. G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
    [Crossref] [PubMed]
  10. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
    [Crossref]
  11. I. D. Phillips, M. Tan, M. F. C. Stephens, M. E. McCarthy, E. Giacoumidis, S. Sygletos, P. Rosa, S. Fabbri, S. T. Le, T. Kanesan, S. K. Turitsyn, N. J. Doran, P. Harper, and A. D. Ellis, “Exceeding the nonlinear-Shannon limit using Raman laser based amplification and optical phase conjugation,” in Optical Fiber Communications Conference (OSA, 2014), paper M3C1.
    [Crossref]
  12. S. Kilmurray, T. Fehenberger, P. Bayvel, and R. I. Killey, “Comparison of the nonlinear transmission performance of quasi-Nyquist WDM and reduced guard interval OFDM,” Opt. Express 20(4), 4198–4205 (2012).
    [Crossref] [PubMed]
  13. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
    [Crossref]
  14. D. Rafique and A. 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(4), 3449–3454 (2011).
    [Crossref] [PubMed]
  15. T. Tanimura, M. Nölle, J. K. Fischer, and C. Schubert, “Analytical results on back propagation nonlinear compensator with coherent detection,” Opt. Express 20(27), 28779–28785 (2012).
    [Crossref] [PubMed]
  16. G. Gao, X. Chen, and W. Shieh, “Influence of PMD on fiber nonlinearity compensation using digital back propagation,” Opt. Express 20(13), 14406–14418 (2012).
    [Crossref] [PubMed]
  17. A. D. Ellis, M. A. Sorokina, S. Sygletos, and S. K. Turitsyn, “Capacity limits in nonlinear fiber transmission,” in Asia Communications and Photonics Conference (OSA, 2013), paper AW4F.1.
    [Crossref]
  18. L. B. Du, M. M. Morshed, and A. J. Lowery, “Fiber nonlinearity compensation for OFDM super-channels using optical phase conjugation,” Opt. Express 20(18), 19921–19927 (2012).
    [Crossref] [PubMed]
  19. H. Hu, R. M. Jopson, A. Gnauck, M. Dinu, S. Chandrasekhar, X. Liu, C. Xie, M. Montoliu, S. Randel, and C. McKinstrie, “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in Optical Fiber Communications Conference (OSA, 2014), paper M3C.2.
    [Crossref]
  20. I. Sackey, F. Da Ros, M. Jazayerifar, T. Richter, C. Meuer, M. Nölle, L. Molle, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation in 5 × 28-GBd PDM 16-QAM signal transmission over a dispersion-uncompensated link with backward-pumped distributed Raman amplification,” Opt. Express 22(22), 27381–27391 (2014).
    [Crossref] [PubMed]
  21. K. Solis-Trapala, M. D. Pelusi, H. N. Tan, T. Inoue, and S. Namiki, “Transmission optimized impairment mitigation by 12 Stage phase conjugation of WDM 24x48 Gb/s DP-QPSK signals,” in Optical Fiber Communications Conference, (OSA, 2015), paper Th3C.2.
    [Crossref]
  22. K. Solis-Trapala, T. Inoue, and S. Namiki, “Nearly-ideal optical phase conjugation based nonlinear compensation system,” in Optical Fiber Communications Conference, (OSA, 2014), paper W3F.8.
    [Crossref]
  23. M. H. Shoreh, “Compensation of nonlinearity impairments in coherent optical OFDM systems using multiple optical phase conjugate modules,” J. Opt. Commun. Netw. 6(6), 549–558 (2014).
    [Crossref]
  24. M. Morshed, L. B. Du, B. Foo, M. D. Pelusi, B. Corcoran, and A. J. Lowery, “Experimental demonstrations of dual polarization CO-OFDM using mid-span spectral inversion for nonlinearity compensation,” Opt. Express 22(9), 10455–10466 (2014).
    [Crossref] [PubMed]
  25. I. Sackey, F. Da Ros, J. K. Fischer, T. Richter, M. Jazayerifar, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation: mid-link spectral inversion versus digital backpropagation in 5×28-GBd PDM 16-QAM signal transmission,” J. Lightwave Technol. 33(9), 1821–1827 (2015).
    [Crossref]
  26. A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit,” presented at IEEE Summer Topical Meeting on Nonlinear Optical Signal Processing, Nassau, Bahamas, 13–15th July 2015.
  27. D. A. Cleland, C. H. F. Sturrock, and A. D. Ellis, “Precise modelling of four wave mixing products over 400km of step index fibre,” Electron. Lett. 28(12), 1171–1172 (1992).
    [Crossref]
  28. S. T. Le, M. E. McCarthy, N. Mac Suibhne, M. A. Z. Al-Khateeb, E. Giacoumidis, N. J. Doran, A. D. Ellis, and S. K. Turitsyn, “Demonstration of phase-conjugated subcarrier coding for fiber nonlinearity compensation in CO-OFDM transmission,” J. Lightwave Technol. 33(11), 2206–2212 (2015).
    [Crossref]
  29. M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices, (Cambridge University, 2008).
  30. D. Rafique and A. D. Ellis, “Nonlinearity compensation in multi-rate 28 Gbaud WDM systems employing optical and digital techniques under diverse link configurations,” Opt. Express 19(18), 16919–16926 (2011).
    [Crossref] [PubMed]
  31. R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
    [Crossref] [PubMed]
  32. P. Poggiolini, A. Carena, Y. Jiang, G. Bosco, V. Curri, and F. Forghieri, “Impact of low-OSNR operation on the performance of advanced coherent optical transmission systems,” in European Conference on Optical Communications (Systematic, 2014), paper Mo.4.3.2.
    [Crossref]
  33. E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightwave Technol. 32(16), 2862–2876 (2014).
    [Crossref]

2015 (3)

2014 (5)

2013 (2)

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

M. D. Pelusi, “Fiber looped phase conjugation of polarization multiplexed signals for pre-compensation of fiber nonlinearity effect,” Opt. Express 21(18), 21423–21432 (2013).
[Crossref] [PubMed]

2012 (5)

2011 (3)

2010 (2)

2001 (1)

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]

1992 (1)

D. A. Cleland, C. H. F. Sturrock, and A. D. Ellis, “Precise modelling of four wave mixing products over 400km of step index fibre,” Electron. Lett. 28(12), 1171–1172 (1992).
[Crossref]

Agrell, E.

Al-Khateeb, M. A. Z.

Alvarado, A.

Bayvel, P.

Borel, P. I.

Carlson, K.

Chandrasekhar, S.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Chen, X.

Chraplyvy, A. R.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Cleland, D. A.

D. A. Cleland, C. H. F. Sturrock, and A. D. Ellis, “Precise modelling of four wave mixing products over 400km of step index fibre,” Electron. Lett. 28(12), 1171–1172 (1992).
[Crossref]

Corcoran, B.

Cotter, D.

Da Ros, F.

Doran, N. J.

Du, L. B.

Durisi, G.

Ellis, A. D.

Fehenberger, T.

Fischer, J. K.

Foo, B.

Galdino, L.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Gao, G.

Giacoumidis, E.

Isaac, R.

Jazayerifar, M.

Karlsson, M.

Killey, R. I.

Kilmurray, S.

Le, S. T.

Liga, G.

Liu, X.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Lowery, A. J.

Mac Suibhne, N.

Magill, P.

Maher, R.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

McCarthy, M. E.

Meuer, C.

Mitra, P. P.

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]

Molle, L.

Morshed, M.

Morshed, M. M.

Nelson, L. E.

Nölle, M.

Peckham, D. W.

Pelusi, M. D.

Petermann, K.

Peucheret, C.

Rafique, D.

Richter, T.

Sackey, I.

Sato, M.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Savory, S. J.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Schubert, C.

Shi, K.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Shieh, W.

Shoreh, M. H.

Stark, J. B.

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]

Sturrock, C. H. F.

D. A. Cleland, C. H. F. Sturrock, and A. D. Ellis, “Precise modelling of four wave mixing products over 400km of step index fibre,” Electron. Lett. 28(12), 1171–1172 (1992).
[Crossref]

Tanimura, T.

Thomsen, B. C.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Tkach, R. W.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Turitsyn, S. K.

Winzer, P. J.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Xu, T.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
[Crossref] [PubMed]

Zhao, J.

Zhou, X.

Zhu, B.

Electron. Lett. (1)

D. A. Cleland, C. H. F. Sturrock, and A. D. Ellis, “Precise modelling of four wave mixing products over 400km of step index fibre,” Electron. Lett. 28(12), 1171–1172 (1992).
[Crossref]

J. Lightwave Technol. (5)

J. Opt. Commun. Netw. (1)

Nat. Photonics (1)

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Nature (1)

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]

Opt. Express (12)

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]

D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011).
[Crossref] [PubMed]

M. D. Pelusi, “Fiber looped phase conjugation of polarization multiplexed signals for pre-compensation of fiber nonlinearity effect,” Opt. Express 21(18), 21423–21432 (2013).
[Crossref] [PubMed]

G. Liga, T. Xu, A. Alvarado, R. I. Killey, and P. Bayvel, “On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission,” Opt. Express 22(24), 30053–30062 (2014).
[Crossref] [PubMed]

D. Rafique and A. 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(4), 3449–3454 (2011).
[Crossref] [PubMed]

T. Tanimura, M. Nölle, J. K. Fischer, and C. Schubert, “Analytical results on back propagation nonlinear compensator with coherent detection,” Opt. Express 20(27), 28779–28785 (2012).
[Crossref] [PubMed]

G. Gao, X. Chen, and W. Shieh, “Influence of PMD on fiber nonlinearity compensation using digital back propagation,” Opt. Express 20(13), 14406–14418 (2012).
[Crossref] [PubMed]

S. Kilmurray, T. Fehenberger, P. Bayvel, and R. I. Killey, “Comparison of the nonlinear transmission performance of quasi-Nyquist WDM and reduced guard interval OFDM,” Opt. Express 20(4), 4198–4205 (2012).
[Crossref] [PubMed]

L. B. Du, M. M. Morshed, and A. J. Lowery, “Fiber nonlinearity compensation for OFDM super-channels using optical phase conjugation,” Opt. Express 20(18), 19921–19927 (2012).
[Crossref] [PubMed]

M. Morshed, L. B. Du, B. Foo, M. D. Pelusi, B. Corcoran, and A. J. Lowery, “Experimental demonstrations of dual polarization CO-OFDM using mid-span spectral inversion for nonlinearity compensation,” Opt. Express 22(9), 10455–10466 (2014).
[Crossref] [PubMed]

I. Sackey, F. Da Ros, M. Jazayerifar, T. Richter, C. Meuer, M. Nölle, L. Molle, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation in 5 × 28-GBd PDM 16-QAM signal transmission over a dispersion-uncompensated link with backward-pumped distributed Raman amplification,” Opt. Express 22(22), 27381–27391 (2014).
[Crossref] [PubMed]

D. Rafique and A. D. Ellis, “Nonlinearity compensation in multi-rate 28 Gbaud WDM systems employing optical and digital techniques under diverse link configurations,” Opt. Express 19(18), 16919–16926 (2011).
[Crossref] [PubMed]

Sci. Rep. (1)

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, “Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation,” Sci. Rep. 5, 8214 (2015).
[Crossref] [PubMed]

Other (11)

P. Poggiolini, A. Carena, Y. Jiang, G. Bosco, V. Curri, and F. Forghieri, “Impact of low-OSNR operation on the performance of advanced coherent optical transmission systems,” in European Conference on Optical Communications (Systematic, 2014), paper Mo.4.3.2.
[Crossref]

K. Solis-Trapala, M. D. Pelusi, H. N. Tan, T. Inoue, and S. Namiki, “Transmission optimized impairment mitigation by 12 Stage phase conjugation of WDM 24x48 Gb/s DP-QPSK signals,” in Optical Fiber Communications Conference, (OSA, 2015), paper Th3C.2.
[Crossref]

K. Solis-Trapala, T. Inoue, and S. Namiki, “Nearly-ideal optical phase conjugation based nonlinear compensation system,” in Optical Fiber Communications Conference, (OSA, 2014), paper W3F.8.
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, “The impact of phase conjugation on the nonlinear-Shannon limit,” presented at IEEE Summer Topical Meeting on Nonlinear Optical Signal Processing, Nassau, Bahamas, 13–15th July 2015.

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices, (Cambridge University, 2008).

H. Hu, R. M. Jopson, A. Gnauck, M. Dinu, S. Chandrasekhar, X. Liu, C. Xie, M. Montoliu, S. Randel, and C. McKinstrie, “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in Optical Fiber Communications Conference (OSA, 2014), paper M3C.2.
[Crossref]

D. Qian, M.-F. Huang, E. Ip, Y.-K. Huang, Y. Shao, J. Hu, and T. Wan, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Communications Conference, (OSA, 2011), paper PDPB5.

A. D. Ellis, M. A. Sorokina, S. Sygletos, and S. K. Turitsyn, “Capacity limits in nonlinear fiber transmission,” in Asia Communications and Photonics Conference (OSA, 2013), paper AW4F.1.
[Crossref]

I. D. Phillips, M. Tan, M. F. C. Stephens, M. E. McCarthy, E. Giacoumidis, S. Sygletos, P. Rosa, S. Fabbri, S. T. Le, T. Kanesan, S. K. Turitsyn, N. J. Doran, P. Harper, and A. D. Ellis, “Exceeding the nonlinear-Shannon limit using Raman laser based amplification and optical phase conjugation,” in Optical Fiber Communications Conference (OSA, 2014), paper M3C1.
[Crossref]

P. Poggiolini, “Modeling of non-linear propagation in uncompensated coherent systems”, in Optical Fiber Communications Conference (OSA, 2013), paper OTh3G1.
[Crossref]

J.-X. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. S. Bergano, “20 Tbit/s capacity transmission over 6,860km,” in Optical Fiber Communications Conference (OSA, 2011), paper PDPB4.

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Figures (7)

Fig. 1
Fig. 1 Principle of the reduction of parametric noise amplification through repeated optical phase conjugation showing; top row, a typical transmission link comprising electronic pre-distortion, amplifiers and fibres, OPC devices and electronic post compensation; lower rows show the evolution of parametrically amplified noise contribution from each amplifier (normalized to the signal power) along the transmission link where blue or red indicates normal or conjugated signal respectively. Each row represents the parametrically amplified noise from a single amplifier. The first column of numbers illustrates the absolute magnitudes of the parametrically amplified noise contribution from each amplifier (normalized to that of a single span) at the output of the link. The green trapezoids indicate the virtual parametric noise amplification added during electronic post compensation of a single span and the second column the (lower) parametrically amplified noise contribution from each amplifier after DSP. Parametrically amplified noise from last three spans not shown.
Fig. 2
Fig. 2 Nonlinear threshold curves for conventional transmission (blue), ideal digital back propagation (orange) and ideal optical phase conjugation (red) for an 4,800km, 5 THz bandwidth system calculated using Eqs. (5) and (6). Arrows illustrate the approximated signal-to-noise ratio gains predicted by Eq. (10) for large numbers of amplifiers, but neglecting strongly phase matched terms (i.e. μDBP = μ0 = 2.μOPC). Also shows performance with 300 GHz digital back propagation bandwidth (Green) and the difference between exact (solid) and approximated (dotted) calculations. The inset shows the peaks after compensation on an expanded scale.
Fig. 3
Fig. 3 Optimization of digital signal processing based nonlinear compensation showing (a) the impact of shifting signal processing from the transmitter to the receiver for three different transmission lengths, and (b) the variation in the performance enhancement with system length for three different splits of DSP load. Other system parameters are the same as in Fig. (2). Note ΔSNR is the change in NLC gain from ( ( 3 2 SN R 0 ) 3/2 ) .
Fig. 4
Fig. 4 (a) Increase in signal to noise ratio enhancement for different numbers of OPC devices in a 120 span system, plotted as a function of the number of stages of receiver digital back propagation. Colors represent different numbers of OPC devices as shown in the legend, ranging from no OPC’s (bottom curve, corresponding to Fig. 3, left) up to one OPC device per in line amplifier. (b) the SNR improvement as a function of the number of OPC devices, assuming optimized DSP, with approximate (blue) and exact (red) analytical predictions. Note ΔSNR is the change in NLC gain from ( ( 3 2 SN R 0 ) 3/2 )
Fig. 5
Fig. 5 Impact of DSP bandwidth as a function of the number of OPC devices. System parameters not otherwise specified are as listed in Fig. 2.
Fig. 6
Fig. 6 Performance improvement observed for a variable number of OPC devices considering Eq. (11)(crosses) and a numerically simulated single channel transmission system (filled disks) for single channel (blue), and for 3 channel (red) and full C band (green) WDM systems propagated over a 32x80km of ideal Raman amplified link. Inset shows same data with OPC count shown on a logarithmic scale.
Fig. 7
Fig. 7 Comparison of numerically simulated and theoretically predicted performance for a 3 channel WDM transmission comprising ideal Raman amplification and multiple OPCs (number of OPCs: blue-0, green-1, orange-3, red-7, purple-15, black-31).

Equations (11)

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SN R 0 = P S N P N +ηlog( B 2 2 f w 2 )( N P S 3 + n=1 N n P S 2 P N )+η n=1 N ( n π + 2 αL { nLog( n )n+1 } ) P S 2 P N
P PAN =η P S 2 P N ( N Even s=1 N S f( | s N d | ) + N Odd s=1 N S f( | s N S + N d | ) )
f n ( s )=Log( B DBP 2 2 f w 2 )s+ s π + 2 αL ( sLog( s )s+1 )
f b ( s )=Log( B WDM 2 2 f w 2 )sLog( B DBP 2 2 f w 2 )s
S ¯ =( N Even + N Odd 2 , N Even N Odd , N Even , N Odd ) D ¯ ¯ =( N S 2 2( N D 2 N D N S ), 2 N S N S 2 N D 0 0 0 ( N d 1 )+( N S N d ) 0 0 ( N d )+( N S N d 1 ) ) E ¯ = ( log( B WDM 2 2 f w 2 )+ 1 π 2 αL , log( B DBP 2 2 f w 2 )+ 1 π 2 αL , 2 αL , 2 αL ) T
P PAN =η P S 2 P N S ¯ D ¯ ¯ E ¯ P NLS =η P S 3 N T ( E 1 - E 2 )
SN R DPC = P S N P N +η P S 2 P N ( ( Log( B WDM 2 2 f w 2 )+ 1 π 2 αL ) N 2 +N 2 + 2 αL ( H( N )+N ) )
SN R DBP = P S N P N +η P S 2 P N ( ( Log( B WDM 2 2 f w 2 )+ 1 π 2 αL ) N 2 N 2 + 2 αL ( H( N1 )+N ) )
SN R OPC1 = P S N P N +η P S 2 P N ( ( Log( B WDM 2 2 f w 2 )+ 1 π 2 αL ) N 2 4 + 2 αL ( H( N 2 )Log( N 2 1 )+N ) )
SN R i = ( 3 2 SN R 0 ) 3 2 ( μ 0 μ i ) 1 2
ΔSNR= SN R OPC N OPC ( 3 2 SN R 0 ) 3 2 N OPC +1

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