Abstract

Cross-phase modulation (XPM) has been considered as one of the ultimate obstacles for optical coherent dense wavelength division multiplexing (DWDM) systems. In order to facilitate the XPM analysis, a simplified model was proposed. The model reduced the distributed XPM phenomena to a lumped phase modulation. The XPM phase noise was generated by a linear system which was determined by the DWDM system parameters and whose inputs were undistorted pump channel intensity waveforms. The model limitations induced by the lumped phase modulation and undistorted pumps approximations were intensively discussed and verified. The simplified model showed a good agreement with simulations and experiments for a typical hybrid optical coherent system. Various XPM phenomena were explained by the proposed model.

© 2009 OSA

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References

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  1. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-753 .
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  9. X. Liu, and S. Chandrasekhar, “Suppression of XPM penalty on 40-Gb/s DQPSK resulting from 10-Gb/s OOK channels by dispersion management” in Tech. Digest of the Conference on Optical Fiber Communication,2008, paper OMQ6.
  10. S. Chandrasekhar and X. Liu, “Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid,” IEEE Photon. Technol. Lett. 19(22), 1801–1803 (2007).
    [CrossRef]
  11. A. S. Lenihan, G. E. Tudury, W. Astar, and G. M. Carter, “XPM-induced impairments in RZ-DPSK transmission in a multi-modulation format WDM system” in Tech. Digest of Conference on the Lasers and Electro-Optics, (CLEO)2005. paper CWO5.
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    [CrossRef]
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    [CrossRef]
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  15. K. P. Ho, “Error Probability of DPSK Signals With Cross-Phase Modulation Induced Nonlinear Phase Noise,” IEEE J. Sel. Top. Quantum Electron. 10(2), 421–427 (2004).

2008

2007

S. Chandrasekhar and X. Liu, “Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid,” IEEE Photon. Technol. Lett. 19(22), 1801–1803 (2007).
[CrossRef]

2005

X. Huang, L. Zhang, M. Zhang, and P. Ye, “Impact of nonlinear phase noise on direct-detection DQPSK WDM systems,” IEEE Photon. Technol. Lett. 17(7), 1423–1425 (2005).
[CrossRef]

2004

K. P. Ho, “Error Probability of DPSK Signals With Cross-Phase Modulation Induced Nonlinear Phase Noise,” IEEE J. Sel. Top. Quantum Electron. 10(2), 421–427 (2004).

1996

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. 14(3), 249–260 (1996).
[CrossRef]

Barros, D. J. F.

Chandrasekhar, S.

S. Chandrasekhar and X. Liu, “Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid,” IEEE Photon. Technol. Lett. 19(22), 1801–1803 (2007).
[CrossRef]

Chen, X.

Chiang, T. K.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. 14(3), 249–260 (1996).
[CrossRef]

Goldfarb, G.

Ho, K. P.

K. P. Ho, “Error Probability of DPSK Signals With Cross-Phase Modulation Induced Nonlinear Phase Noise,” IEEE J. Sel. Top. Quantum Electron. 10(2), 421–427 (2004).

Huang, X.

X. Huang, L. Zhang, M. Zhang, and P. Ye, “Impact of nonlinear phase noise on direct-detection DQPSK WDM systems,” IEEE Photon. Technol. Lett. 17(7), 1423–1425 (2005).
[CrossRef]

Ip, E.

Kagi, N.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. 14(3), 249–260 (1996).
[CrossRef]

Kahn, J. M.

Kazovsky, L. G.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. 14(3), 249–260 (1996).
[CrossRef]

Kikuchi, K.

Kim, I.

Lau, A. P. T.

Li, G.

Li, X.

Liu, X.

S. Chandrasekhar and X. Liu, “Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid,” IEEE Photon. Technol. Lett. 19(22), 1801–1803 (2007).
[CrossRef]

Marhic, M. E.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. 14(3), 249–260 (1996).
[CrossRef]

Mateo, E.

Yaman, F.

Ye, P.

X. Huang, L. Zhang, M. Zhang, and P. Ye, “Impact of nonlinear phase noise on direct-detection DQPSK WDM systems,” IEEE Photon. Technol. Lett. 17(7), 1423–1425 (2005).
[CrossRef]

Zhang, L.

X. Huang, L. Zhang, M. Zhang, and P. Ye, “Impact of nonlinear phase noise on direct-detection DQPSK WDM systems,” IEEE Photon. Technol. Lett. 17(7), 1423–1425 (2005).
[CrossRef]

Zhang, M.

X. Huang, L. Zhang, M. Zhang, and P. Ye, “Impact of nonlinear phase noise on direct-detection DQPSK WDM systems,” IEEE Photon. Technol. Lett. 17(7), 1423–1425 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. P. Ho, “Error Probability of DPSK Signals With Cross-Phase Modulation Induced Nonlinear Phase Noise,” IEEE J. Sel. Top. Quantum Electron. 10(2), 421–427 (2004).

IEEE Photon. Technol. Lett.

S. Chandrasekhar and X. Liu, “Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid,” IEEE Photon. Technol. Lett. 19(22), 1801–1803 (2007).
[CrossRef]

X. Huang, L. Zhang, M. Zhang, and P. Ye, “Impact of nonlinear phase noise on direct-detection DQPSK WDM systems,” IEEE Photon. Technol. Lett. 17(7), 1423–1425 (2005).
[CrossRef]

J. Lightwave Technol.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. 14(3), 249–260 (1996).
[CrossRef]

Opt. Express

Other

S. Oda, T. Tanimura, T. Hoshida, C. Ohshima, H. Nakashima, Z. Tao, and J. C. Rasmussen, “112 Gb/s DP-QPSK transmission using a novel nonlinear compensator in digital coherent receiver” in Tech. Digest of the Conference on Optical Fiber Communication,2009, paper OThR6.

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Compensation of chromatic dispersion and nonlinearity using simplified digital backpropagation” in Coherent Optical Technologies and Applications (Optical Society of America, 2008), paper CWB1.

K. P. Ho, Phase-Modulated Optical Communication Systems, (Springer, 2005), Chap. 8.3.

T. Tanimura, S. Oda, M. Yuki, H. Zhang, L. Li, Z. Tao, H. Nakashima, T. Hoshida, K. Nakamura, and J. C. Rasmussen, “Non-linearity tolerance of direct detection and coherent receivers for 43 Gb/s RZ-DQPSK signals with co-propagating 11.1 Gb/s NRZ signals over NZ-DSF” in Tech. Digest of the Conference on Optical Fiber Communication,2008, paper OTuM4.

X. Liu, and S. Chandrasekhar, “Suppression of XPM penalty on 40-Gb/s DQPSK resulting from 10-Gb/s OOK channels by dispersion management” in Tech. Digest of the Conference on Optical Fiber Communication,2008, paper OMQ6.

O. Vassilieva, T. Hoshida, J. C. Rasmussen, and T. Naito, “Symbol rate dependency of XPM phase noise penalty on QPSK-based modulation formats” in Tech. Digest of the European Conference on Optical Communication,2008, paper We.1.E.4.
[CrossRef]

W. Yan, Z. Tao, L. Li, L. Liu, S. Oda, T. Hoshida, and J. C. Rasmussen, “A Linear Model for Nonlinear Phase Noise Induced by Cross-phase Modulation” in Tech. Digest of the Conference on Optical Fiber Communication,2009, paper OTuD5.

A. S. Lenihan, G. E. Tudury, W. Astar, and G. M. Carter, “XPM-induced impairments in RZ-DPSK transmission in a multi-modulation format WDM system” in Tech. Digest of Conference on the Lasers and Electro-Optics, (CLEO)2005. paper CWO5.

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Figures (8)

Fig. 1.
Fig. 1.

Simplified model of XPM phase noise. (a) N-span M-channel DWDM system, (b) System with lumped XPM phase noise modulation, (c) Linear model of XPM phase noise

Fig. 2.
Fig. 2.

System setup of hybrid transmission NZ-DSF: non-zero dispersion shifted fiber, DCF: dispersion compensation fiber, PC: polarization controller, MUX: optical multiplexer

Fig. 3.
Fig. 3.

(a) auto-correlation and (b) waveform of the XPM phase noise. simulation: results obtained by solving the nonlinear Schrödinger Equation, model: results by the proposed model.

Fig. 4.
Fig. 4.

XPM phase noise auto-correlation of zero in-line dispersion compensation system with (a) 11 Gb/s NRZ pump and (b) 11 Gbaud RZ-QPSK pump, simulation: results obtained by solving the nonlinear Schrödinger Equation, model: results by the proposed model

Fig. 5.
Fig. 5.

Impact of polarization: (a) reduction of XPM phase noise, (b) independence of normalized auto-correlation

Fig. 6.
Fig. 6.

System performance of simplified model and real experiment (a) 450km (b) 900km

Fig. 7.
Fig. 7.

Normalized auto-correlations of XPM phase noise after transmission over (a) 450km and (b) 900km.

Fig. 8.
Fig. 8.

Dependences of XPM phase noise on (a) fiber launch power, (b) dispersion compensation (DC) ratio, (c) DWDM channel spacing, (d) guard spacing, (e) total channel number, (f) pump OOK channel bit rate. HWHM: the half-width half-magnitude of auto-correlation. std. the standard deviation of phase noise

Equations (2)

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H12 (f)=2γ 1exp(αL+j2πfd12L)αj2πfd12 2γα ×11j2πd12fα
τ12 =[d12L+DDCFLDCF(λ1λ2)]

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