Abstract

An improved split-step method (SSM) for digital backward propagation (DBP) applicable to wavelength-division multiplexed (WDM) transmission with polarization-division multiplexing (PDM) is presented. A coupled system of nonlinear partial differential equations, derived from the Manakov equations, is used for DBP. The above system enables the implementation of DBP on a channel-by-channel basis, where only the effect of phase-mismatched four-wave mixing (FWM) is neglected. A novel formulation of the SSM for PDM-WDM systems is presented where new terms are included in the nonlinear step to account for inter-polarization mixing effects. In addition, the effect of inter-channel walk-off is included. This substantially reduces the computational load compared to the conventional SSM.

© 2011 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  5. 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]
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    [CrossRef]
  8. F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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2010

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

E. Ip, “Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission,” J. Lightwave Technol. 28(6), 939–951 (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]

2009

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]

P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems,” Opt. Express 17(3), 1385–1403 (2009).
[CrossRef] [PubMed]

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

X. Liu, F. Buchali, and R. W. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
[CrossRef]

F. Yaman and G. Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photonics J. 1(2), 144–152 (2009).
[CrossRef]

2008

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]

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

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental Demonstration of Fiber Impairment Compensation Using the Split-Step Finite-Impulse-Response Filtering Method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

E. F. 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]

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(1), 9–11 (2007).
[CrossRef]

2004

M. G. Taylor, “Coherent Detection Method using DSP for Demodulation of Signal and Subsequent Equalization of Propagation Impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

2003

O. 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]

2001

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]

Bayvel, P.

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

Buchali, F.

X. Liu, F. Buchali, and R. W. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
[CrossRef]

Carena, A.

P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems,” Opt. Express 17(3), 1385–1403 (2009).
[CrossRef] [PubMed]

Chen, X.

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]

Chen, Z.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

Curri, V.

P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems,” Opt. Express 17(3), 1385–1403 (2009).
[CrossRef] [PubMed]

Forghieri, F.

P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems,” Opt. Express 17(3), 1385–1403 (2009).
[CrossRef] [PubMed]

Fürst, C.

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

Gao, Y.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

Goldfarb, G.

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental Demonstration of Fiber Impairment Compensation Using the Split-Step Finite-Impulse-Response Filtering Method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[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]

Herbst, S.

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

Holbein, L.

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

Holzlohner, R.

O. 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]

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(1), 9–11 (2007).
[CrossRef]

Ip, E.

E. Ip, “Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission,” J. Lightwave Technol. 28(6), 939–951 (2010).
[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]

Kahn, J. M.

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

Killey, R. I.

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

Kim, I.

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]

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(1), 9–11 (2007).
[CrossRef]

Li, G.

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]

F. Yaman and G. Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photonics J. 1(2), 144–152 (2009).
[CrossRef]

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]

E. F. 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]

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]

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental Demonstration of Fiber Impairment Compensation Using the Split-Step Finite-Impulse-Response Filtering Method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

Li, J.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

Li, L.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

Li, X.

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]

Liu, X.

X. Liu, F. Buchali, and R. W. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
[CrossRef]

Luo, Y.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

Mateo, E.

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]

Mateo, E. F.

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]

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]

E. F. 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]

Menyuk, C. R.

O. 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]

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]

Poggiolini, P.

P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems,” Opt. Express 17(3), 1385–1403 (2009).
[CrossRef] [PubMed]

Sinkin, O.

O. 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]

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]

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(1), 9–11 (2007).
[CrossRef]

Taylor, M. G.

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental Demonstration of Fiber Impairment Compensation Using the Split-Step Finite-Impulse-Response Filtering Method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

M. G. Taylor, “Coherent Detection Method using DSP for Demodulation of Signal and Subsequent Equalization of Propagation Impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

Tkach, R. W.

X. Liu, F. Buchali, and R. W. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
[CrossRef]

Waegemans, R.

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

Watts, P.

R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009).
[CrossRef] [PubMed]

Xu, A.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

Yaman, F.

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]

F. Yaman and G. Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photonics J. 1(2), 144–152 (2009).
[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]

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(1), 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(1), 9–11 (2007).
[CrossRef]

Zhang, F.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

Zhu, L.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

E. F. 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]

Zweck, J.

O. 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]

Appl. Opt.

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]

Electron. Lett.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental Demonstration of Intra-channel Nonlinearity Mitigation in Coherent QPSK Systems with Nonlinear Electrical Equalizer,” Electron. Lett. 46(5), 353–355 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

M. G. Taylor, “Coherent Detection Method using DSP for Demodulation of Signal and Subsequent Equalization of Propagation Impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[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(1), 9–11 (2007).
[CrossRef]

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental Demonstration of Fiber Impairment Compensation Using the Split-Step Finite-Impulse-Response Filtering Method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

IEEE Photonics J.

F. Yaman and G. Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photonics J. 1(2), 144–152 (2009).
[CrossRef]

J. Lightwave Technol.

E. Ip, “Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission,” J. Lightwave Technol. 28(6), 939–951 (2010).
[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]

X. Liu, F. Buchali, and R. W. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
[CrossRef]

O. 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]

Nature

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

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Figures (5)

Fig. 1
Fig. 1

(A): Block diagram for the implementation of one step using the advanced SSM..The XPM and Xpol modules are shown below. (B) Sketch of the XPM module including the filtering for walk-off factorization. For conventional SSFM, the FFT, IFFT and filters W m q are removed. (C) Block of the Xpol module including the filtering for walk-off factorization. For conventional SSFM, the FFT, IFFT and filters W m q are removed.

Fig. 2
Fig. 2

Simulated TX-RX configuration with polarization diverse coherent detection.

Fig. 3
Fig. 3

DBP performance results for a PDM 16-QAM WDM system consisting of 24 channels at 200 Gb/s. DBP1 is SPM compensation. DBP2 is incoherent inter-channel compensation. DBP3 is coherent inter-channel compensation.

Fig. 4
Fig. 4

Q-factor per channel for the different DBP cases. Each case is shown at the respective optimum power.

Fig. 5
Fig. 5

Q-factors as functions of step size for the inter-channel compensation cases DBP2 and DBP3.

Tables (1)

Tables Icon

Table 1 Summary of results for a 200 Gb/s PDM WDM system consisting in 24 channels with a 50 GHz channel spacing. Transmission is 10 × 100 km. Letter ‘-a’ stands for advanced SSFM and ‘-c’ stands for conventional SSFM.

Equations (27)

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E ( x , y ) z + α 2 E ( x , y ) + i β 2 2 2 E ( x , y ) t 2 + β 3 6 3 E ( x , y ) t 3 + i 8 9 γ ( | E ( x , y ) | 2 + | E ( y , x ) | 2 ) E ( x , y ) = 0 ,
E ^ x m z + ( α 2 + L m + i C x m ) E ^ x m + i K m E ^ y m = 0 , E ^ y m z + ( α 2 + L m + i C y m ) E ^ y m + i K m * E ^ x m = 0 ,
K m = 8 9 γ ( q m E ^ y q * E ^ x q ) ,
E ^ ( x , y ) m ( t , z + h ) = F - 1 { F [ E ^ ( x , y ) m ( t , z ) ] H m ( ω , h ) } ,
H m ( ω , h ) = exp [ ( i β 2 ( ω m Δ ω ) 2 2 + i β 3 ( ω m Δ ω ) 3 6 ) h ]
E x m z + i C x m e α z E x m + i K m e α z E y m = 0 , E y m z + i C y m e α z E y m + i K m * e α z E x m = 0 ,
E ( x , y ) m = E ( x , y ) m 0 exp ( i z z + h C ( x , y ) m e α z d z ) .
η m = 1 z K m e α z d z ,
E x m z + i η m E y m = 0 , E y m z + i η m * E x m = 0 ,
E ( x , y ) m = a ( x , y ) e i | η m | z + b ( x , y ) e i | η m | z ,
E x m = E x m 0 cos ( | η m | z ) i E y m 0 η m | η m | sin ( | η m | z ) , E y m = E y m 0 cos ( | η m | z ) i E x m 0 η m * | η m | sin ( | η m | z ) ,
E x m ( t , z + h ) = E x m ( t , z ) e i ϕ x m cos ( | Q m | ) i E y m ( t , z ) e i ϕ y m Q m sinc ( | Q m | ) , E y m ( t , z + h ) = E y m ( t , z ) e i ϕ y m cos ( | Q m | ) i E x m ( t , z ) e i ϕ x m Q m * sinc ( | Q m | ) ,
ϕ ( x , y ) m = z z + h C ( x , y ) m e α z d z ,
Q m = z z + h K m e α z d z .
ϕ ( x , y ) m ( t , z + h ) = h e f f C ( x , y ) m ( t , z ) ,
Q m ( t , z + h ) = h e f f K m ( t , z ) ,
K m ( t , z ) = 8 9 γ ( q m E y q * ( t d m q z , z ) E x q ( t d m q z , z ) ) ,
K m ( ω , z ) = 8 9 γ ( q m E y q * ( ω , z ) E x q ( ω , z ) e i d m q ω z ) .
Q m ( t , z + h ) = 8 9 γ [ F 1 { q m E ^ y q * ( ω , z ) E ^ x q ( ω , z ) W m q ( ω , h ) } ] ,
W m q ( ω , h ) = e α h i d m q ω z 1 α i d m q ω .
W m q ( ω , h ) = e ( α i d m q ω ) h 1 α i d m q ω e ( α i d m q ω ) h / 2 h e f f = e α h 1 α e α h / 2
τ W = 2 π | β 2 | ( N 1 ) Δ f × h , τ H = 2 π | β 2 | B × h .
P W = 2 π | β 2 | ( N 1 ) Δ f × h × S , P H = 2 π | β 2 | B × h × S .
O P D B P 2 c = n steps [ 4 ( M + P H ) log 2 ( M + P H ) + 2 ( M + P H ) + 18 M ] / 2 M ,
O P D B P 3 c = n steps [ 4 ( M + P H ) log 2 ( M + P H ) + 2 ( M + P H ) + 36 M ] / 2 M .
O P D B P 2 a = n steps [ 8 ( M + P W ) log 2 ( M + P W ) + ( 2 N + 6 ) ( M + P W ) + 16 M ] / 2 M ,
O P D B P 3 a = n steps [ 10 ( M + P W ) log 2 ( M + P W ) + ( 3 N + 5 ) ( M + P W ) + 33 M ] / 2 M .

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