Abstract

The impact of cross-phase modulation (XPM) and four-wave mixing (FWM) on electronic impairment compensation via backward propagation is analyzed. XPM and XPM+FWM compensation are compared by solving, respectively, the backward coupled Nonlinear Schrödinger Equation (NLSE) system and the total-field NLSE. The DSP implementations as well as the computational requirements are evaluated for each post-compensation system. A 12×100 Gb/s 16-QAM transmission system has been used to evaluate the efficiency of both approaches. The results show that XPM post-compensation removes most of the relevant source of nonlinear distortion. While DSP implementation of the total-field NLSE can ultimately lead to more precise compensation, DSP implementation using the coupled NLSE system can maintain high accuracy with better computation efficiency and low system latency.

© 2008 Optical Society of America

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  1. D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9,121-129 (1991).
    [CrossRef]
  2. S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-249 (1996).
    [CrossRef]
  3. C. Kurtzke, "Suppression of fiber nonlinearities by appropriate dispersion management," J. Lightwave Technol. 5, 1250-1253 (1993).
  4. J. Leibrich, C. Wree and W. Rosenkranz, "CF-RZ-DPSK for suppression of XPM on dispersion-managed longhaul optical WDMtransmission on standard single-mode fiber," IEEE Photon. Technol. Lett. 14, 155-157 (2002).
    [CrossRef]
  5. S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003).
    [CrossRef]
  6. K. Roberts, C. Li, L. Strawczynski, M. OSullivan, and I. Hardcatle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).
    [CrossRef]
  7. E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
    [CrossRef]
  8. 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, 880-889 (2008).
    [CrossRef] [PubMed]
  9. G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 2007).
  10. J. Leibrich and W. Rosenkranz, "Efficient numerical simulation of multichannel WDM transmission systems limited by XPM," IEEE Photon. Technol. Lett. 15, 395-397 (2003).
    [CrossRef]
  11. O. V. Sinkin, Holzlohner, J. Zweck, and C. Menyuk," "Optimization of the split-step Fourier method in modeling optical-fiber communications system," J. Lightwave Technol. 21, 61-68 (2003).
    [CrossRef]
  12. T. Schneider, Nonlinear optics in telecommunications, (Springer, 2004).
  13. G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
    [CrossRef]
  14. G. Goldfarb, G. Li and M. G. Taylor, "Orthogonal wavelength-division multiplexing using coherent detection," IEEE Photon. Technol. Lett. 19, 2015-2017 (2007).
    [CrossRef]
  15. X. Liu and D. A. Fishman, "A fast and reliable algorithm for electronic pre-equalization of SPM and chromatic dispersion," in OFC 1996, paper OThD4.
  16. A. J. Lowery, L. B. Du, and J. Armstrong, "Performance of optical OFDM in ultralong-haul WDM lightwave systems," J. Lightwave Technol. 25, 131-138 (2007).
    [CrossRef]
  17. M. Shtaif, M. Eiselt, and L. D. Garret, "Cross-phase modulation distortion measurements in multispan WDM systems," IEEE Photon. Technol. Lett. 12, 88-90 (2000).
    [CrossRef]
  18. P. P. Mitra and J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
    [CrossRef] [PubMed]
  19. J. M. Kahn and K. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Top. Quantum Electron. 10, 259-272 (2004).
    [CrossRef]
  20. J. Wang and K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightwave Technol. 10, 96-100 (1992).
    [CrossRef]
  21. T. Yu, W. M. Reimer, V. S. Grigoryan, and C. R. Menyuk, "A mean field approach for simulating wavelengthdivision multiplexed systems," IEEE Photon. Technol. Lett. 12, 443-445 (2000).
    [CrossRef]

2008

2007

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

G. Goldfarb, G. Li and M. G. Taylor, "Orthogonal wavelength-division multiplexing using coherent detection," IEEE Photon. Technol. Lett. 19, 2015-2017 (2007).
[CrossRef]

A. J. Lowery, L. B. Du, and J. Armstrong, "Performance of optical OFDM in ultralong-haul WDM lightwave systems," J. Lightwave Technol. 25, 131-138 (2007).
[CrossRef]

2006

K. Roberts, C. Li, L. Strawczynski, M. OSullivan, and I. Hardcatle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).
[CrossRef]

2004

J. M. Kahn and K. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Top. Quantum Electron. 10, 259-272 (2004).
[CrossRef]

2003

O. V. Sinkin, Holzlohner, J. Zweck, and C. Menyuk," "Optimization of the split-step Fourier method in modeling optical-fiber communications system," J. Lightwave Technol. 21, 61-68 (2003).
[CrossRef]

O. V. Sinkin, Holzlohner, J. Zweck, and C. Menyuk," "Optimization of the split-step Fourier method in modeling optical-fiber communications system," J. Lightwave Technol. 21, 61-68 (2003).
[CrossRef]

S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003).
[CrossRef]

J. Leibrich and W. Rosenkranz, "Efficient numerical simulation of multichannel WDM transmission systems limited by XPM," IEEE Photon. Technol. Lett. 15, 395-397 (2003).
[CrossRef]

2002

J. Leibrich, C. Wree and W. Rosenkranz, "CF-RZ-DPSK for suppression of XPM on dispersion-managed longhaul optical WDMtransmission on standard single-mode fiber," IEEE Photon. Technol. Lett. 14, 155-157 (2002).
[CrossRef]

2001

P. P. Mitra and J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

2000

T. Yu, W. M. Reimer, V. S. Grigoryan, and C. R. Menyuk, "A mean field approach for simulating wavelengthdivision multiplexed systems," IEEE Photon. Technol. Lett. 12, 443-445 (2000).
[CrossRef]

M. Shtaif, M. Eiselt, and L. D. Garret, "Cross-phase modulation distortion measurements in multispan WDM systems," IEEE Photon. Technol. Lett. 12, 88-90 (2000).
[CrossRef]

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

1996

S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-249 (1996).
[CrossRef]

1993

C. Kurtzke, "Suppression of fiber nonlinearities by appropriate dispersion management," J. Lightwave Technol. 5, 1250-1253 (1993).

1992

J. Wang and K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightwave Technol. 10, 96-100 (1992).
[CrossRef]

1991

D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9,121-129 (1991).
[CrossRef]

Armstrong, J.

Benedetto, S.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

Boroditsky, M.

S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003).
[CrossRef]

Bosco, G.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

Carena, A.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

Chen, X.

Chraplyvy, A. R.

D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9,121-129 (1991).
[CrossRef]

Curri, V.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

Du, L. B.

Eiselt, M.

M. Shtaif, M. Eiselt, and L. D. Garret, "Cross-phase modulation distortion measurements in multispan WDM systems," IEEE Photon. Technol. Lett. 12, 88-90 (2000).
[CrossRef]

Feuer, M.D.

S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003).
[CrossRef]

Garret, L. D.

M. Shtaif, M. Eiselt, and L. D. Garret, "Cross-phase modulation distortion measurements in multispan WDM systems," IEEE Photon. Technol. Lett. 12, 88-90 (2000).
[CrossRef]

Gaudino, R.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

Goldfarb, G.

Grigoryan, V. S.

T. Yu, W. M. Reimer, V. S. Grigoryan, and C. R. Menyuk, "A mean field approach for simulating wavelengthdivision multiplexed systems," IEEE Photon. Technol. Lett. 12, 443-445 (2000).
[CrossRef]

Ho, K.

J. M. Kahn and K. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Top. Quantum Electron. 10, 259-272 (2004).
[CrossRef]

Holzlohner, O. V.

Huang, S.

S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003).
[CrossRef]

Inuzuka, F.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Kahn, J. M.

J. M. Kahn and K. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Top. Quantum Electron. 10, 259-272 (2004).
[CrossRef]

Kim, I.

Koga, M.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Kurtzke, C.

C. Kurtzke, "Suppression of fiber nonlinearities by appropriate dispersion management," J. Lightwave Technol. 5, 1250-1253 (1993).

Leibrich, J.

J. Leibrich and W. Rosenkranz, "Efficient numerical simulation of multichannel WDM transmission systems limited by XPM," IEEE Photon. Technol. Lett. 15, 395-397 (2003).
[CrossRef]

J. Leibrich, C. Wree and W. Rosenkranz, "CF-RZ-DPSK for suppression of XPM on dispersion-managed longhaul optical WDMtransmission on standard single-mode fiber," IEEE Photon. Technol. Lett. 14, 155-157 (2002).
[CrossRef]

Li, C.

K. Roberts, C. Li, L. Strawczynski, M. OSullivan, and I. Hardcatle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).
[CrossRef]

Li, G.

Li, X.

Lowery, A. J.

Marcuse, D.

D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9,121-129 (1991).
[CrossRef]

Mateo, E.

Menyuk, C. R.

T. Yu, W. M. Reimer, V. S. Grigoryan, and C. R. Menyuk, "A mean field approach for simulating wavelengthdivision multiplexed systems," IEEE Photon. Technol. Lett. 12, 443-445 (2000).
[CrossRef]

Mitra, P. P.

P. P. Mitra and J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Petermann, K.

J. Wang and K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightwave Technol. 10, 96-100 (1992).
[CrossRef]

Poggiolini, P.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

Reimer, W. M.

T. Yu, W. M. Reimer, V. S. Grigoryan, and C. R. Menyuk, "A mean field approach for simulating wavelengthdivision multiplexed systems," IEEE Photon. Technol. Lett. 12, 443-445 (2000).
[CrossRef]

Roberts, K.

K. Roberts, C. Li, L. Strawczynski, M. OSullivan, and I. Hardcatle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).
[CrossRef]

Rosenkranz, W.

J. Leibrich and W. Rosenkranz, "Efficient numerical simulation of multichannel WDM transmission systems limited by XPM," IEEE Photon. Technol. Lett. 15, 395-397 (2003).
[CrossRef]

J. Leibrich, C. Wree and W. Rosenkranz, "CF-RZ-DPSK for suppression of XPM on dispersion-managed longhaul optical WDMtransmission on standard single-mode fiber," IEEE Photon. Technol. Lett. 14, 155-157 (2002).
[CrossRef]

Shirasaki, M.

S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-249 (1996).
[CrossRef]

Shtaif, M.

M. Shtaif, M. Eiselt, and L. D. Garret, "Cross-phase modulation distortion measurements in multispan WDM systems," IEEE Photon. Technol. Lett. 12, 88-90 (2000).
[CrossRef]

Sinkin, O. V.

Stark, J. B.

P. P. Mitra and J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Strawczynski, L.

K. Roberts, C. Li, L. Strawczynski, M. OSullivan, and I. Hardcatle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).
[CrossRef]

Takada, A.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Taylor, M. G.

G. Goldfarb, G. Li and M. G. Taylor, "Orthogonal wavelength-division multiplexing using coherent detection," IEEE Photon. Technol. Lett. 19, 2015-2017 (2007).
[CrossRef]

Tkach, R. W.

D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9,121-129 (1991).
[CrossRef]

Wang, J.

J. Wang and K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightwave Technol. 10, 96-100 (1992).
[CrossRef]

Watanabe, S.

S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-249 (1996).
[CrossRef]

Woodward, S. L.

S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003).
[CrossRef]

Wree, C.

J. Leibrich, C. Wree and W. Rosenkranz, "CF-RZ-DPSK for suppression of XPM on dispersion-managed longhaul optical WDMtransmission on standard single-mode fiber," IEEE Photon. Technol. Lett. 14, 155-157 (2002).
[CrossRef]

Yaman, F.

Yamazaki, E.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Yonenaga, K.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Yu, T.

T. Yu, W. M. Reimer, V. S. Grigoryan, and C. R. Menyuk, "A mean field approach for simulating wavelengthdivision multiplexed systems," IEEE Photon. Technol. Lett. 12, 443-445 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. M. Kahn and K. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Top. Quantum Electron. 10, 259-272 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Shtaif, M. Eiselt, and L. D. Garret, "Cross-phase modulation distortion measurements in multispan WDM systems," IEEE Photon. Technol. Lett. 12, 88-90 (2000).
[CrossRef]

J. Leibrich and W. Rosenkranz, "Efficient numerical simulation of multichannel WDM transmission systems limited by XPM," IEEE Photon. Technol. Lett. 15, 395-397 (2003).
[CrossRef]

J. Leibrich, C. Wree and W. Rosenkranz, "CF-RZ-DPSK for suppression of XPM on dispersion-managed longhaul optical WDMtransmission on standard single-mode fiber," IEEE Photon. Technol. Lett. 14, 155-157 (2002).
[CrossRef]

S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003).
[CrossRef]

K. Roberts, C. Li, L. Strawczynski, M. OSullivan, and I. Hardcatle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).
[CrossRef]

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-397 (2000).
[CrossRef]

G. Goldfarb, G. Li and M. G. Taylor, "Orthogonal wavelength-division multiplexing using coherent detection," IEEE Photon. Technol. Lett. 19, 2015-2017 (2007).
[CrossRef]

T. Yu, W. M. Reimer, V. S. Grigoryan, and C. R. Menyuk, "A mean field approach for simulating wavelengthdivision multiplexed systems," IEEE Photon. Technol. Lett. 12, 443-445 (2000).
[CrossRef]

J. Lightwave Technol.

D. Marcuse, A. R. Chraplyvy and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9,121-129 (1991).
[CrossRef]

S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-249 (1996).
[CrossRef]

C. Kurtzke, "Suppression of fiber nonlinearities by appropriate dispersion management," J. Lightwave Technol. 5, 1250-1253 (1993).

O. V. Sinkin, Holzlohner, J. Zweck, and C. Menyuk," "Optimization of the split-step Fourier method in modeling optical-fiber communications system," J. Lightwave Technol. 21, 61-68 (2003).
[CrossRef]

A. J. Lowery, L. B. Du, and J. Armstrong, "Performance of optical OFDM in ultralong-haul WDM lightwave systems," J. Lightwave Technol. 25, 131-138 (2007).
[CrossRef]

J. Wang and K. Petermann, "Small signal analysis for dispersive optical fiber communication systems," J. Lightwave Technol. 10, 96-100 (1992).
[CrossRef]

Nature

P. P. Mitra and J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Opt. Express

Other

X. Liu and D. A. Fishman, "A fast and reliable algorithm for electronic pre-equalization of SPM and chromatic dispersion," in OFC 1996, paper OThD4.

T. Schneider, Nonlinear optics in telecommunications, (Springer, 2004).

G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 2007).

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Figures (11)

Fig. 1.
Fig. 1.

Block diagram of the DSP implementation of the total-field NLSE.

Fig. 2.
Fig. 2.

Block diagram of the DSP implementation of coupled NLSEs.

Fig. 3.
Fig. 3.

SSFM backward propagation diagram for a M-spans optical link.

Fig. 4.
Fig. 4.

Transmission scheme for a coherently detected 16-QAM/WDM system. Red lines represent connections in the optical domain whereas blue lines stand for electrical connections.

Fig. 5.
Fig. 5.

Constellation and eye diagrams for one of the central channels (PT =9 dBm). (A) Back-to-back (Q=29.8 dB); (B) Dispersion compensation (Q=8.3 dB) and (C) XPM compensation with 30 steps per span (Q=13.3 dB).

Fig. 6.
Fig. 6.

Received Q-factor for Δf=50 GHz with: (A) XPM compensation via C-NLSE and (B) FWM compensation via T-NLSE.

Fig. 7.
Fig. 7.

Q-factor map, as a function of the launched power and the step size (Δf=50 GHz). (A) XPM compensation, (B) FWM compensation. The white spot indicates the optimum power and characteristic step size location.

Fig. 8.
Fig. 8.

Received Q-factor for Δf=100 GHz with: (A) XPM compensation via C-NLSE and (B) XPM+FWM compensation via T-NLSE.

Fig. 9.
Fig. 9.

Q-factor and step size for XPM and FWM compensation within the 50 and 100 GHz grids. Dashed lines indicate the characteristic step size for each case

Fig. 10.
Fig. 10.

Q-factor map, as a function of the launched power and the step size (Δf=100 GHz). (A) XPM compensation, (B) FWM compensation. The white spot indicates the optimum power and characteristic step size location.

Fig. 11.
Fig. 11.

Received Q-factor as a function of the step size for XPM post-compensation using intra-step walk-off modeling.

Equations (10)

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E z + α 2 E + i β 2 2 2 E t 2 β 3 6 3 E t 3 i γ E 2 E = 0 ,
E m z + α 2 E m + i β 2 2 2 E m t 2 β 3 6 3 E m t 3 i γ ( 2 q I E q 2 E m 2 ) E m = 0 .
L nl = 1 γ P T 2 N 1 N , L wo = 1 2 π β 2 ( N 1 ) Δ f B ,
i γ ( 2 q I E q 2 E m 2 ) E m i γ [ [ r s l m ] I E r E s E l * exp ( i δ k r s l m z ) ] ,
δ k r s l m = k r + k s k l k m = 1 2 β 2 Δ ω 2 [ r 2 + s 2 ( r + s m ) 2 m 2 ] .
δ k max = 1 4 β 2 ( N 1 ) 2 Δ ω 2 .
L fwm = 1 π 2 β 2 ( N 1 ) 2 Δ f 2 .
h wo = τ r L wo , h fwm = ϕ fwm L fwm ,
C fwm C xpm = h xpm N h fwm = π κ 2 ( N 1 ) Δ f N B ,
τ fwm τ xpm = h xpm h fwm = π κ 2 ( N 1 ) Δ f B .

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