Abstract

In periodically dispersion managed long-haul transmission systems, waveform distortion is dominated by chromatic dispersion. As a result of the periodic waveform evolution, the nonlinear behavior also repeats itself in every dispersion period. It is shown that, under the weakly nonlinear assumption, nonlinear effects accumulated in a large number (K) of spans can be approximated by nonlinear effects accumulated in a single span with the same dispersion map and K times the nonlinearity. Thus, significant savings in computational load can be achieved in digital compensation of fiber nonlinearity using folded digital backward propagation (DBP). Simulation results show that the required computation for DBP of dispersion managed transoceanic transmission systems can be reduced by up to 2 orders of magnitude with negligible penalty using folded DBP.

©2011 Optical Society of America

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References

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  1. K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
    [Crossref]
  2. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008).
    [Crossref]
  3. A. Pilipetski, “Nonlinearity management and compensation in transmission systems,” in Proceedings of OFC/NFOEC 2010, paper OTuL5.
  4. R. Hui, K. R. Demarest, and C. T. Allen, “Cross-phase modulation in multispan WDM optical fiber systems,” J. Lightwave Technol. 17(6), 1018–1026 (1999).
    [Crossref]
  5. Q. Lin and G. P. Agrawa, “Effects of polarization-mode dispersion on cross-phase modulation in dispersion-managed wavelength-division-multiplexed systems,” J. Lightwave Technol. 22(4), 977–987 (2004).
    [Crossref]
  6. B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. 5(10), 1250–1253 (1993).
    [Crossref]
  7. T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, “Comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise,” J. Lightwave Technol. 21(9), 1933–1943 (2003).
    [Crossref]
  8. K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22(3), 779–783 (2004).
    [Crossref]
  9. K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
    [Crossref]
  10. L. B. Du and A. J. Lowery, “Fiber nonlinearity compensation for CO-OFDM systems with periodic dispersion maps,” Proceedings of OFC/NFOEC 2009, paper OTuO1.
  11. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008).
    [Crossref] [PubMed]
  12. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
    [Crossref]
  13. L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46(16), 1140–1141 (2010).
    [Crossref]
  14. F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed wdm transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
    [Crossref]
  15. E. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express 16(20), 16124–16137 (2008).
    [Crossref] [PubMed]
  16. E. F. Mateo and G. Li, “Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation,” Appl. Opt. 48(25), F6–F10 (2009).
    [Crossref] [PubMed]
  17. E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010).
    [Crossref] [PubMed]
  18. L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010).
    [Crossref] [PubMed]
  19. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15(23), 1351–1353 (1990).
    [Crossref] [PubMed]
  20. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21(1), 61–68 (2003).
    [Crossref]
  21. K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308(5-6), 417–425 (2003).
    [Crossref]
  22. V. A. J. M. Sleiffer, D. van den Borne, M. S. Alfiad, S. L. Jansen, and H. de Waardt, “Dispersion management in long-haul 111-Gb/s POLMUX-RZ-DQPSK transmission systems,” in Proceedings of LEOS Annual Meeting Conference 2009, pp.569–570.

2010 (4)

L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46(16), 1140–1141 (2010).
[Crossref]

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed wdm transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
[Crossref]

E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010).
[Crossref] [PubMed]

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (4)

2006 (2)

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
[Crossref]

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
[Crossref]

2004 (2)

2003 (3)

1999 (1)

1993 (1)

B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. 5(10), 1250–1253 (1993).
[Crossref]

1990 (1)

Abe, J.

Agrawa, G. P.

Allen, C. T.

Chen, X.

De Man, E.

de Waardt, H.

Demarest, K. R.

Du, L. B.

Duthel, T.

Fludger, C. R. S.

Geyer, J.

Goldfarb, G.

Gordon, J. P.

Hardcastle, I.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
[Crossref]

Ho, K.-P.

Holzlohner, R.

Hui, R.

Imamura, K.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
[Crossref]

Ip, E.

Ishida, K.

Kahn, J. M.

Kasahara, K.

Khoe Giok-Djan,

Kim, I.

Kinjo, K.

Kobayashi, T.

Kokura, K.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
[Crossref]

Kurtzke, B. C.

B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. 5(10), 1250–1253 (1993).
[Crossref]

Li, C.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
[Crossref]

Li, G.

Li, X.

Lin, Q.

Lowery, A. J.

Mateo, E.

Mateo, E. F.

Menyuk, C. R.

Mizuochi, T.

Mollenauer, L. F.

Motoshima, K.

Moubissi, A. B.

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308(5-6), 417–425 (2003).
[Crossref]

Mukasa, K.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
[Crossref]

Nakkeeran, K.

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308(5-6), 417–425 (2003).
[Crossref]

O’Sullivan, M.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
[Crossref]

Roberts, K.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
[Crossref]

Schmidt, E.-D.

Schulien, C.

Shimotakahara, I.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
[Crossref]

Sinkin, O. V.

Strawczynski, L.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
[Crossref]

Tchofo Dinda, P.

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308(5-6), 417–425 (2003).
[Crossref]

van den Borne, D.

Wuth, T.

Yagi, T.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
[Crossref]

Yaman, F.

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed wdm transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
[Crossref]

E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010).
[Crossref] [PubMed]

L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46(16), 1140–1141 (2010).
[Crossref]

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008).
[Crossref] [PubMed]

Zhu, L.

Zweck, J.

Appl. Opt. (1)

Electron. Lett. (1)

L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46(16), 1140–1141 (2010).
[Crossref]

IEEE Photon. J. (1)

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed wdm transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (2)

B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. 5(10), 1250–1253 (1993).
[Crossref]

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006).
[Crossref]

J. Lightwave Technol. (7)

R. Hui, K. R. Demarest, and C. T. Allen, “Cross-phase modulation in multispan WDM optical fiber systems,” J. Lightwave Technol. 17(6), 1018–1026 (1999).
[Crossref]

O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21(1), 61–68 (2003).
[Crossref]

T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, “Comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise,” J. Lightwave Technol. 21(9), 1933–1943 (2003).
[Crossref]

K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22(3), 779–783 (2004).
[Crossref]

Q. Lin and G. P. Agrawa, “Effects of polarization-mode dispersion on cross-phase modulation in dispersion-managed wavelength-division-multiplexed systems,” J. Lightwave Technol. 22(4), 977–987 (2004).
[Crossref]

C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008).
[Crossref]

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
[Crossref]

Opt. Express (4)

Opt. Fiber. Commun. (1)

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” Opt. Fiber. Commun. 3(5), 292–339 (2006).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (1)

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308(5-6), 417–425 (2003).
[Crossref]

Other (3)

V. A. J. M. Sleiffer, D. van den Borne, M. S. Alfiad, S. L. Jansen, and H. de Waardt, “Dispersion management in long-haul 111-Gb/s POLMUX-RZ-DQPSK transmission systems,” in Proceedings of LEOS Annual Meeting Conference 2009, pp.569–570.

A. Pilipetski, “Nonlinearity management and compensation in transmission systems,” in Proceedings of OFC/NFOEC 2010, paper OTuL5.

L. B. Du and A. J. Lowery, “Fiber nonlinearity compensation for CO-OFDM systems with periodic dispersion maps,” Proceedings of OFC/NFOEC 2009, paper OTuO1.

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Figures (4)

Fig. 1
Fig. 1 Folded DBP for a periodically dispersion managed fiber link with M × K spans.

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Fig. 2
Fig. 2 Block diagram of the dispersion managed WDM system.

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Fig. 3
Fig. 3 (a) Q-value vs. launching power per channel and (b) Q-value at optimum power vs. step number per span with RDPS = 0 ps/nm.

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Fig. 4
Fig. 4 (a) Q-value vs. folding factor K and (b) Q-value vs. RDPS.

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Equations (20)

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∂ A j ( z , t ) ∂ z = [ D + ε ⋅ N ( | A j ( z , t ) | 2 ) ] ⋅ A j ( z , t ) ,
A 1 ( 0 , t ) = a ( 0 , t ) ,
A j ( 0 , t ) = A j − 1 ( L , t )  for  j ≥ 2 ,
A j ( z , t ) = A j , l ( z , t ) + ε ⋅ A j , n l ( z , t ) .
∂ A j , l ( z , t ) ∂ z − D ⋅ A j , l ( z , t ) + ε ⋅ [ ∂ A j , n l ( z , t ) ∂ z − D ⋅ A j , n l ( z , t ) − N ( | A j , l ( z , t ) | 2 ) ⋅ A j , l ( z , t ) ] + O ( ε 2 ) = 0 ,
∂ A j , l ( z , t ) ∂ z = D ⋅ A j , l ( z , t ) ,
∂ A j , n l ( z , t ) ∂ z = D ⋅ A j , n l ( z , t ) + N ( | A j , l ( z , t ) | 2 ) ⋅ A j , l ( z , t ) .
A 1 , l ( 0 , t ) = a ( 0 , t ) ,
A j , l ( 0 , t ) = A j − 1 ( L , t )  for  j ≥ 2 ,
A j , n l ( 0 , t ) = 0.
A 1 , l ( L , t ) = a ( 0 , t ) ,
A 2 ( 0 , t ) = A 1 ( L , t ) = a ( 0 , t ) + ε ⋅ A 1 , n l ( L , t ) ,
A 2 , l ( z , t ) = A 1 , l ( z , t ) + ε ⋅ A ¯ ( z , t ) ,
A 2 , l ( L , t ) = a ( 0 , t ) + ε ⋅ A 1 , n l ( L , t ) .
| A 2 , l | 2 = | A 1 , l + ε ⋅ A ¯ | 2 = | A 1 , l | 2 + O ( ε ) ,
A 2 , n l ( L , t ) = A 1 , n l ( L , t ) .
A 2 ( L , t ) = A 2 , l ( L , t ) + ε ⋅ A 2 , n l ( L , t ) = a ( 0 , t ) + ε ⋅ 2 A 1 , n l ( L , t ) .
A N ( L , t ) = a ( 0 , t ) + ε ⋅ K A 1 , n l ( L , t ) ,
∂ A j ( z , t ) ∂ z = [ D + ε ⋅ K N ( | A j ( z , t ) | 2 ) ] ⋅ A j ( z , t ) .
∂ A j ( z , t ) ∂ z = [ D + ε ⋅ K ⋅ N ( | A j ( z , t ) | 2 ) ] ⋅ A j ( z , t ) .

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