Abstract

A probability-based model is developed to describe cross phase modulation in multichannel multilevel amplitude/phase modulated coherent systems. Standard deviation of nonlinear phase-shift is evaluated in 16-QAM coherent systems accordingly and by numerical simulation for different values of chromatic dispersion and symbol rate. Furthermore, an error analysis is provided to evaluate the accuracy of the model which demonstrates maximum relative error of 12% in the field of interest.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (2)

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010).
[CrossRef]

2009 (4)

V. Tavassoli and T. E. Darcie, “An analytical method for performance evaluation of a DQPSK channel in presence of OOK signal,” Proc. SPIE 7386, 73861C (2009).
[CrossRef]

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express 17(3), 1435–1441 (2009).
[CrossRef] [PubMed]

Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express 17, 13860–13868 (2009).
[CrossRef] [PubMed]

C. Xie, “Interchannel nonlinearities in coherent polarization-division multiplexed quadrature-phase-shift- keying systems,” IEEE Photon. Technol. Lett. 21, 274–276 (2009).
[CrossRef]

2008 (3)

2007 (1)

2006 (1)

2003 (1)

1999 (2)

1998 (1)

G. Bellotti, M. Varani, C. Francia, and A. Bononi, “Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation,” IEEE Photon. Technol. Lett. 10(12), 1745–1747 (1998).
[CrossRef]

Allen, C. T.

Barros, D. J. F.

Bellotti, G.

G. Bellotti, M. Varani, C. Francia, and A. Bononi, “Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation,” IEEE Photon. Technol. Lett. 10(12), 1745–1747 (1998).
[CrossRef]

Bononi, A.

G. Bellotti, M. Varani, C. Francia, and A. Bononi, “Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation,” IEEE Photon. Technol. Lett. 10(12), 1745–1747 (1998).
[CrossRef]

Buhl, L. L.

Cartaxo, A. V. T.

Chen, X.

Chen, Z.

Darcie, T. E.

V. Tavassoli and T. E. Darcie, “An analytical method for performance evaluation of a DQPSK channel in presence of OOK signal,” Proc. SPIE 7386, 73861C (2009).
[CrossRef]

Demarest, K. R.

Doerr, C. R.

Francia, C.

G. Bellotti, M. Varani, C. Francia, and A. Bononi, “Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation,” IEEE Photon. Technol. Lett. 10(12), 1745–1747 (1998).
[CrossRef]

Gnauck, A. H.

Goldfarb, G.

Ho, K. P.

K. P. Ho, “Cross-phase modulation-induced nonlinear phase noise for quadriphase-shift-keying signals,” in Impact of Nonlinearities on Fiber Optic Communications , S. Kumar ed. (Springer, 2011), pp. 325–341.
[CrossRef]

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

Hoshida, T.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express 17, 13860–13868 (2009).
[CrossRef] [PubMed]

Hui, R. Q.

Igarashi, K.

Ip, E.

Kahn, J. M.

Katoh, K.

Kikuchi, K.

Kim, H.

Kim, I.

Lau, A. P. T.

Li, G.

Li, L.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Li, X.

Liu, L.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Ly-Gagnon, D. S.

Magarini, M.

Mateo, E.

Mori, Y.

Nakashima, H.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Oda, S.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express 17, 13860–13868 (2009).
[CrossRef] [PubMed]

Rasmussen, J. C.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express 17, 13860–13868 (2009).
[CrossRef] [PubMed]

Tanimura, T.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Tao, Z.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express 17, 13860–13868 (2009).
[CrossRef] [PubMed]

Tavassoli, V.

V. Tavassoli and T. E. Darcie, “An analytical method for performance evaluation of a DQPSK channel in presence of OOK signal,” Proc. SPIE 7386, 73861C (2009).
[CrossRef]

Tsukarnoto, S.

Varani, M.

G. Bellotti, M. Varani, C. Francia, and A. Bononi, “Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation,” IEEE Photon. Technol. Lett. 10(12), 1745–1747 (1998).
[CrossRef]

Winzer, P. J.

Xie, C.

C. Xie, “Interchannel nonlinearities in coherent polarization-division multiplexed quadrature-phase-shift- keying systems,” IEEE Photon. Technol. Lett. 21, 274–276 (2009).
[CrossRef]

Xu, A.

Yaman, F.

Yan, W.

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system,” Opt. Express 17, 13860–13868 (2009).
[CrossRef] [PubMed]

Zhang, C.

Zhang, F.

Zhu, L.

IEEE J. Sel. Top. Quantum Electron. (1)

Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

C. Xie, “Interchannel nonlinearities in coherent polarization-division multiplexed quadrature-phase-shift- keying systems,” IEEE Photon. Technol. Lett. 21, 274–276 (2009).
[CrossRef]

G. Bellotti, M. Varani, C. Francia, and A. Bononi, “Intensity distortion induced by cross-phase modulation and chromatic dispersion in optical-fiber transmissions with dispersion compensation,” IEEE Photon. Technol. Lett. 10(12), 1745–1747 (1998).
[CrossRef]

J. Lightwave Technol. (5)

Opt. Express (6)

Proc. SPIE (1)

V. Tavassoli and T. E. Darcie, “An analytical method for performance evaluation of a DQPSK channel in presence of OOK signal,” Proc. SPIE 7386, 73861C (2009).
[CrossRef]

Other (2)

K. P. Ho, “Cross-phase modulation-induced nonlinear phase noise for quadriphase-shift-keying signals,” in Impact of Nonlinearities on Fiber Optic Communications , S. Kumar ed. (Springer, 2011), pp. 325–341.
[CrossRef]

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

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Figures (6)

Fig. 1
Fig. 1

(a)16-QAM constellation (b)Three 16-QAM intensity levels decay along the fiber. The signal amplitude for a random bit-stream is shown at three different positions; beginning, middle and end of the link with waveform distortion caused by CD.

Fig. 2
Fig. 2

Relative error between Eq. (3) and the approximation given in Eq. (5) are shown with NW , number of walk-off symbols.

Fig. 3
Fig. 3

Standard deviation of nonlinear phase shift vs. launched power for different values of dispersion parameters (ps/(km.nm)) for a 2 channel system (one pump - one probe) at (a)10 GBaud symbol rate, (b)15 GBaud symbol rate and (c)20 GBaud symbol rate. Solid lines are results from the model and dashed lines are results from CNLSE for effective core area of 80μm2.

Fig. 4
Fig. 4

(a) Standard deviation of nonlinear phase shift,σϕ (in degrees) with dispersion for two sybmol rates (10 and 20 Gbaud) and launched power of 26 mW. Solid lines are results from the model and circles and squares are results from CNLSE. (b) Standard deviation of nonlinear phase shift,σϕ (in degrees) with launched power for two-pump and four-pump systems. channels are 50 GHz apart and probe is in the middle. Fiber’s dispersion is 16 ps/(nm.km) and symbol rate is 15 Gbaud. Solid lines are results from the model and triangles are results from CNLSE.

Fig. 5
Fig. 5

Standard deviation of received signal’s phase is given in degrees as a function of number of spans for fiber dispersions of 8 and 20 ps/(nm.km) at 15 Gbaud. Solid lines are results from the model and triangles are results from CNLSE.

Fig. 6
Fig. 6

Contour diagram of Err (error between σϕ driven from model and σϕ from CNLSE in percent) for different values of fiber dispersion and symbol rates.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

N W = B S L e D λ 2 Δ ν / c
Φ ( m ) = 2 γ ( m 1 ) L s m L s e α z d z
σ ϕ 2 = P e 2 Σ Φ m 2
P e 2 = 1 4 { ( P 1 2 + 2 P 2 2 + P 3 2 ) ( P 1 + 2 P 2 + P 3 ) 2 }
σ ϕ 2 = 2 P e 2 γ 2 L e α N W
σ ϕ t 2 = Σ σ ϕ i 2
σ ϕ t = N s σ ϕ
Err = 100 × σ ϕ σ ϕ S σ ϕ S

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