Abstract

In this paper, the effect of fiber nonlinear effects on coherent optical WDM systems is investigated through numerical simulations. The analysis of the most relevant fiber nonlinear effects is made recurring to the Volterra series transfer function method, which allows us to quantify its impact on the transmission of multi-level modulated signals employing digital coherent receiver. The performance transmission is evaluated using vector analysis of the received signal’s constellation where firstly we validate against split-step simulations that VSTF is suitable for optimizing coherent optical WDM transmission; then we evaluate the different contributions of the fiber nonlinear distortions imposed on the coherent optical QPSK, 8PSK and 16QAM channels by co-propagating lower data rate intensity modulated channels.

© 2010 OSA

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  1. O. B-Pardo, “D. Mongardien, P. Bousselet, P. Tran, H. Mardoyan, I. Brylski, J. Renaudier, H. Bissesur, “Transmission of 2.6 Tb/s Using 100-Gb/s PDM-QPSK Paired With a Coherent Receiver Over a 401-km Unrepeatered Link,” IEEE Photon. Technol. Lett. 21(23), 1767–1769 (2009).
  2. R. Freund, D. Groß, M. Seimetz, L. Molle, and C. Caspar, “30 Gbit/s RZ-8-PSK Transmission over 2800 km Standard Single Mode Fibre without Inline Dispersion Compensation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMI5.
  3. 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]
  4. X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, and P. D. Magill, “High-Spectral-Efficiency 114-Gb/s Transmission Using PolMux-RZ-8PSK Modulation Format and Single-Ended Digital Coherent Detection Technique,” J. Lightwave Technol. 27(3), 146–152 (2009).
    [CrossRef]
  5. J. Renaudier, G. Charlet, O. Bertran-Pardo, H. Mardoyan, P. Tran, M. Salsi, and S. Bigo, “Transmission of 100 Gb/s coherent PDM-QPSK over 16 x 100 km of standard fiber with allerbium amplifiers,” Opt. Express 17(7), 5112–5119 (2009).
    [CrossRef] [PubMed]
  6. Y. Tang and W. Shieh, “Coherent Optical OFDM Transmission Up to 1Tb/s per Channel,” J. Lightwave Technol. 27(16), 3511–3517 (2009).
    [CrossRef]
  7. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009).
    [CrossRef] [PubMed]
  8. A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-Guard-Interval Coherent Optical OFDM for 100Gb/s Long-Haul WDM Transmission,” J. Lightwave Technol. 27(16), 3705–3713 (2009).
    [CrossRef]
  9. A. Carena, V. Curri, P. Poggiolini, and F. Forguieri, “Guard-Band for 111Gbit/s coherent PM-QPSK channels on legacy fiber link carrying 10 Gbit/s IMDD channels,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OThR7.
  10. A. Bononi, M. Bertolini, P. Serena, and G. Bellotti, “Cross-Phase Modulation Induced by OOK Channels on Higher-Rate DQPSK and Coherent QPSK Channels,” J. Lightwave Technol. 27(18), 3974–3983 (2009).
    [CrossRef]
  11. K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Transfer Function of Single-Mode Fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997).
    [CrossRef]
  12. K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Approach for Optimizing Fiber-Optic Communications Systems Design,” J. Lightwave Technol. 16(11), 2046–2055 (1998).
    [CrossRef]
  13. C. Xia and W. Rosenkranz, “Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering,” J. Lightwave Technol. 25(4), 996–1001 (2007).
    [CrossRef]
  14. X. Zhu, S. Kumar, S. Raghavan, Y. Mauro, and S. Lobanov, “Nonlinear Electronic Dispersion Compensation Techniques for Fiber-Optic Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWA56.
  15. R. Weidenfeld, M. Nazarathy, R. Noe, and I. Shpatzer, “Volterra Nonlinear Compensation of 112Gb/s Ultra-long-haul Coherent Optical OFDM based on Frequency-Shaped Decision Feedback,” in ECOC’09, paper 2.3.3 (2009).
  16. B. Xu and M. Brandt-Pearce, “Comparison of FWM- and XPM-Induced Crosstalk Using Volterra Series Transfer Function Method,” J. Lightwave Technol. 21(1), 40–53 (2003).
    [CrossRef]
  17. S. Kumar and D. Yang, “Second-Order Theory for Self-Phase Modulation and Cross-Phase Modulation in Optical Fibers,” J. Lightwave Technol. 23(6), 2073–2080 (2005).
    [CrossRef]
  18. J. Tang, “The Channel Capacity of a Multispan DWDM System Employing Dispersive Nonlinear Optical Fibers and an Ideal Coherent Optical Receiver,” J. Lightwave Technol. 20(7), 1095–1101 (2002).
    [CrossRef]
  19. A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(12), 1633–1635 (2000).
    [CrossRef]
  20. S. Kumar and L. Liu, “Reduction of nonlinear phase noise using optical phase conjugation in quasi-linear optical transmission systems,” Opt. Express 15(5), 2166–2177 (2007).
    [CrossRef] [PubMed]
  21. Q. Zhang, “Performance analysis and design of WDM based optical communications systems using a Volterra series method”, Ph.D dissertation, University of Virginia, 2001.
  22. M. Seimetz, “High-Order Modulation for Optical Fiber Transmission,” in Optical Sciences, W.T. Rhodes, ed. (Springer, Atlanta, GA., 2009).
  23. B. Xu and M. Brandt-Pearce, “Modified Volterra Series Transfer Function,” IEEE Photon. Technol. Lett. 14(1), 47–49 (2002).
    [CrossRef]
  24. R. Hassun, M. Flaherty, R. Matreci, and M. Taylor, “Effective evaluation of link quality using error vector magnitude techniques,” in Proceedings of IEEE Wireless Communications Conference (Institute of Electrical and Electronics Engineers, Boulder-CO, USA, 1997), pp 89–94.
  25. L. N. Binh, “Linear and nonlinear transfer function of single mode fiber for optical transmission systems,” J. Opt. Soc. Am. A 26(7), 1564–1575 (2009).
    [CrossRef]

2009 (9)

O. B-Pardo, “D. Mongardien, P. Bousselet, P. Tran, H. Mardoyan, I. Brylski, J. Renaudier, H. Bissesur, “Transmission of 2.6 Tb/s Using 100-Gb/s PDM-QPSK Paired With a Coherent Receiver Over a 401-km Unrepeatered Link,” IEEE Photon. Technol. Lett. 21(23), 1767–1769 (2009).

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]

X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, and P. D. Magill, “High-Spectral-Efficiency 114-Gb/s Transmission Using PolMux-RZ-8PSK Modulation Format and Single-Ended Digital Coherent Detection Technique,” J. Lightwave Technol. 27(3), 146–152 (2009).
[CrossRef]

J. Renaudier, G. Charlet, O. Bertran-Pardo, H. Mardoyan, P. Tran, M. Salsi, and S. Bigo, “Transmission of 100 Gb/s coherent PDM-QPSK over 16 x 100 km of standard fiber with allerbium amplifiers,” Opt. Express 17(7), 5112–5119 (2009).
[CrossRef] [PubMed]

Y. Tang and W. Shieh, “Coherent Optical OFDM Transmission Up to 1Tb/s per Channel,” J. Lightwave Technol. 27(16), 3511–3517 (2009).
[CrossRef]

Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009).
[CrossRef] [PubMed]

A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-Guard-Interval Coherent Optical OFDM for 100Gb/s Long-Haul WDM Transmission,” J. Lightwave Technol. 27(16), 3705–3713 (2009).
[CrossRef]

A. Bononi, M. Bertolini, P. Serena, and G. Bellotti, “Cross-Phase Modulation Induced by OOK Channels on Higher-Rate DQPSK and Coherent QPSK Channels,” J. Lightwave Technol. 27(18), 3974–3983 (2009).
[CrossRef]

L. N. Binh, “Linear and nonlinear transfer function of single mode fiber for optical transmission systems,” J. Opt. Soc. Am. A 26(7), 1564–1575 (2009).
[CrossRef]

2007 (2)

2005 (1)

2003 (1)

2002 (2)

2000 (1)

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(12), 1633–1635 (2000).
[CrossRef]

1998 (1)

1997 (1)

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Transfer Function of Single-Mode Fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997).
[CrossRef]

Bellotti, G.

Bertolini, M.

Bertran-Pardo, O.

Bigo, S.

Binh, L. N.

Bononi, A.

Brandt-Pearce, M.

B. Xu and M. Brandt-Pearce, “Comparison of FWM- and XPM-Induced Crosstalk Using Volterra Series Transfer Function Method,” J. Lightwave Technol. 21(1), 40–53 (2003).
[CrossRef]

B. Xu and M. Brandt-Pearce, “Modified Volterra Series Transfer Function,” IEEE Photon. Technol. Lett. 14(1), 47–49 (2002).
[CrossRef]

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Approach for Optimizing Fiber-Optic Communications Systems Design,” J. Lightwave Technol. 16(11), 2046–2055 (1998).
[CrossRef]

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Transfer Function of Single-Mode Fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997).
[CrossRef]

Charlet, G.

Chen, S.

Clausen, C. B.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(12), 1633–1635 (2000).
[CrossRef]

Igarashi, K.

Ishihara, K.

Katoh, K.

Kikuchi, K.

Kobayashi, T.

Kudo, R.

Kumar, S.

Liu, L.

Ma, Y.

Magill, P. D.

Mardoyan, H.

Masuda, H.

Mecozzi, A.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(12), 1633–1635 (2000).
[CrossRef]

Miyamoto, Y.

Mori, Y.

Peddanarappagari, K. V.

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Approach for Optimizing Fiber-Optic Communications Systems Design,” J. Lightwave Technol. 16(11), 2046–2055 (1998).
[CrossRef]

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Transfer Function of Single-Mode Fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997).
[CrossRef]

Qian, D.

Renaudier, J.

Rosenkranz, W.

Salsi, M.

Sano, A.

Serena, P.

Shieh, W.

Shtaif, M.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(12), 1633–1635 (2000).
[CrossRef]

Takatori, Y.

Tang, J.

Tang, Y.

Tran, P.

Wang, T.

Xia, C.

Xu, B.

B. Xu and M. Brandt-Pearce, “Comparison of FWM- and XPM-Induced Crosstalk Using Volterra Series Transfer Function Method,” J. Lightwave Technol. 21(1), 40–53 (2003).
[CrossRef]

B. Xu and M. Brandt-Pearce, “Modified Volterra Series Transfer Function,” IEEE Photon. Technol. Lett. 14(1), 47–49 (2002).
[CrossRef]

Yamada, E.

Yamazaki, E.

Yang, D.

Yang, Q.

Yoshida, E.

Yu, J.

Zhang, C.

Zhang, G.

Zhou, X.

IEEE Photon. Technol. Lett. (3)

O. B-Pardo, “D. Mongardien, P. Bousselet, P. Tran, H. Mardoyan, I. Brylski, J. Renaudier, H. Bissesur, “Transmission of 2.6 Tb/s Using 100-Gb/s PDM-QPSK Paired With a Coherent Receiver Over a 401-km Unrepeatered Link,” IEEE Photon. Technol. Lett. 21(23), 1767–1769 (2009).

A. Mecozzi, C. B. Clausen, and M. Shtaif, “System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(12), 1633–1635 (2000).
[CrossRef]

B. Xu and M. Brandt-Pearce, “Modified Volterra Series Transfer Function,” IEEE Photon. Technol. Lett. 14(1), 47–49 (2002).
[CrossRef]

J. Lightwave Technol. (10)

B. Xu and M. Brandt-Pearce, “Comparison of FWM- and XPM-Induced Crosstalk Using Volterra Series Transfer Function Method,” J. Lightwave Technol. 21(1), 40–53 (2003).
[CrossRef]

S. Kumar and D. Yang, “Second-Order Theory for Self-Phase Modulation and Cross-Phase Modulation in Optical Fibers,” J. Lightwave Technol. 23(6), 2073–2080 (2005).
[CrossRef]

J. Tang, “The Channel Capacity of a Multispan DWDM System Employing Dispersive Nonlinear Optical Fibers and an Ideal Coherent Optical Receiver,” J. Lightwave Technol. 20(7), 1095–1101 (2002).
[CrossRef]

A. Bononi, M. Bertolini, P. Serena, and G. Bellotti, “Cross-Phase Modulation Induced by OOK Channels on Higher-Rate DQPSK and Coherent QPSK Channels,” J. Lightwave Technol. 27(18), 3974–3983 (2009).
[CrossRef]

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Transfer Function of Single-Mode Fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997).
[CrossRef]

K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra Series Approach for Optimizing Fiber-Optic Communications Systems Design,” J. Lightwave Technol. 16(11), 2046–2055 (1998).
[CrossRef]

C. Xia and W. Rosenkranz, “Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering,” J. Lightwave Technol. 25(4), 996–1001 (2007).
[CrossRef]

X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, and P. D. Magill, “High-Spectral-Efficiency 114-Gb/s Transmission Using PolMux-RZ-8PSK Modulation Format and Single-Ended Digital Coherent Detection Technique,” J. Lightwave Technol. 27(3), 146–152 (2009).
[CrossRef]

Y. Tang and W. Shieh, “Coherent Optical OFDM Transmission Up to 1Tb/s per Channel,” J. Lightwave Technol. 27(16), 3511–3517 (2009).
[CrossRef]

A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-Guard-Interval Coherent Optical OFDM for 100Gb/s Long-Haul WDM Transmission,” J. Lightwave Technol. 27(16), 3705–3713 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (4)

Other (7)

Q. Zhang, “Performance analysis and design of WDM based optical communications systems using a Volterra series method”, Ph.D dissertation, University of Virginia, 2001.

M. Seimetz, “High-Order Modulation for Optical Fiber Transmission,” in Optical Sciences, W.T. Rhodes, ed. (Springer, Atlanta, GA., 2009).

X. Zhu, S. Kumar, S. Raghavan, Y. Mauro, and S. Lobanov, “Nonlinear Electronic Dispersion Compensation Techniques for Fiber-Optic Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWA56.

R. Weidenfeld, M. Nazarathy, R. Noe, and I. Shpatzer, “Volterra Nonlinear Compensation of 112Gb/s Ultra-long-haul Coherent Optical OFDM based on Frequency-Shaped Decision Feedback,” in ECOC’09, paper 2.3.3 (2009).

R. Freund, D. Groß, M. Seimetz, L. Molle, and C. Caspar, “30 Gbit/s RZ-8-PSK Transmission over 2800 km Standard Single Mode Fibre without Inline Dispersion Compensation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMI5.

A. Carena, V. Curri, P. Poggiolini, and F. Forguieri, “Guard-Band for 111Gbit/s coherent PM-QPSK channels on legacy fiber link carrying 10 Gbit/s IMDD channels,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OThR7.

R. Hassun, M. Flaherty, R. Matreci, and M. Taylor, “Effective evaluation of link quality using error vector magnitude techniques,” in Proceedings of IEEE Wireless Communications Conference (Institute of Electrical and Electronics Engineers, Boulder-CO, USA, 1997), pp 89–94.

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Figures (6)

Fig. 1
Fig. 1

Coherent Optical WDM scenario. (A) QPSK transmitter; (B) 8PSK transmitter; (C) Square 16QAM transmitter.

Fig. 2
Fig. 2

EVM (B2B = 1%) of VSTF and SSF after 100km-SSMF. (A) 16x50Gb/s-QPSK transmission. (B) 16x75Gb/s-8PSK transmission. (C) 16x100Gb/s-16QAM transmission.

Fig. 3
Fig. 3

EVM (B2B = 1%) of VSTF and SSF after 100km-NZDSF. (A) 16x50Gb/s-QPSK transmission. (B) 16x75Gb/s-8PSK transmission. (C) 16x100Gb/s-16QAM transmission.

Fig. 4
Fig. 4

EVM (B2B = 1%) as a function of the number of IMDD channels. (A) 4 IMDD channels; (B) 8 IMDD channels; (C) 12 IMDD channels.

Fig. 5
Fig. 5

EVM (B2B = 1%) as a function of the number of IMDD channels. (A) 4 IMDD channels; (B) 8 IMDD channels; (C) 12 IMDD channels.

Fig. 6
Fig. 6

EVM (B2B = 1%) as a function of the number of IMDD channels. (A) 4 IMDD channels; (B) 8 IMDD channels; (C) 12 IMDD channels.

Tables (1)

Tables Icon

Table 1 Optical fiber parameters.

Equations (10)

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

A ( ω , z ) H 1 ( ω , z ) A ( ω ) + 1 4 π 2 H 3 ( ω 1 , ω 2 , ω ω 1 + ω 2 , z ) A ( ω 1 )                     A * ( ω 2 ) A ( ω ω 1 + ω 2 ) d ω 1 d ω 2
H 1 ( ω , z ) = e G 1 ( ω 1 )
H 3 ( ω 1 , ω 2 , ω 3 , z ) = G 3 ( ω 1 , ω 2 , ω 3 ) e ( G 1 ( ω 1 ) + G 1 ( ω 2 ) + G 1 ( ω 3 ) ) z e ( G 1 ( ω 1 ω 2 + ω 3 ) z ) G 1 ( ω 1 ) + G 1 ( ω 2 ) + G 1 ( ω 3 ) G 1 ( ω 1 ω 2 + ω 3 )
G 1 ( ω ) = α 2 j β 2 ω 2 2 j β 3 ω 3 6
G 3 ( ω 1 , ω 2 , ω 3 ) = j ( γ + a 1 ( ω 1 ω 2 + ω 3 ) ) a 2 ( ω 1 ω 2 )
A i S P M ( ω , z ) = 1 4 π 2 H 3 ( ω 1 , ω 2 , ω ω 1 + ω 2 , z ) A i ( ω 1 ) A i * ( ω 2 ) A i ( ω ω 1 + ω 2 ) d ω 1 d ω 2
A i X P M ( ω , z ) = 1 4 π 2 H 3 ( ω 1 , ω 2 , ω ω 1 + ω 2 , z ) { A i ( ω 1 ) [ j i A j * ( ω 2 ) A j ( ω ω 1 + ω 2 ) ] + A i ( ω ω 1 + ω 2 ) [ j i A j ( ω 1 ) A j * ( ω 2 ) ] } d ω 1 d ω 2
A i j + k F W M ( ω , z ) = 1 4 π 2 H 3 ( ω 1 , ω 2 , ω ω 1 + ω 2 , z ) A i ( ω 1 ) A j * ( ω 2 ) A k ( ω ω 1 + ω 2 ) d ω 1 d ω 2
A N L [ n ] z = 1 4 π 2 i j H 3 [ ω i , ω j , ω n i + j ] z A [ i ] A * [ j ] A [ n i + j ]
N c h N F F T + 2 3 Δ f T s N F F T

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