Abstract

Limitations in the performance of coherent transmission systems employing digital back-propagation due to four-wave mixing impairments are reported for the first time. A significant performance constraint is identified, originating from four-wave mixing between signals and amplified spontaneous emission noise which induces a linear increase in the standard deviation of the received field with signal power, and linear dependence on transmission distance.

© 2011 OSA

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References

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  2. D. Rafique, M. Forzati, and J. Mårtensson, “Impact of Nonlinear Fibre Impairments in 112 Gb/s PM-QPSK Transmission with 43 Gb/s and 10.7 Gb/s Neighbours,” in Proc. ICTON 2010, paper We.D1.6 (2010).
  3. C. Weber, C.-A. Bunge, and K. Petermann, “Fiber Nonlinearities in Systems Using Electronic Predistortion of Dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. 27(16), 3654–3661 (2009).
    [CrossRef]
  4. F. Yaman and G. Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photonics Technol. Lett. 1, 144–152 (2009).
  5. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
    [CrossRef]
  6. D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010).
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. 9(10), 1330–1334 (1991).
    [CrossRef]
  11. J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, pp1104 (2000).
  12. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16(2), 73–85 (2010).
    [CrossRef]
  13. J. Cai, Y. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “Transmission of 96x100G Pre‐Filtered PDM‐RZ‐QPSK Channels with 300% Spectral Efficiency over 10,608km and 400% Spectral Efficiency over 4,368km,” in Proc. OFC 2010, PDPB10 (2010).
  14. A. D. Ellis, and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in Non-Linear Effects in Fibre Communications, IEE Colloquium on, 6/1–6/4, (1990).
  15. K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).
    [CrossRef]
  16. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010).
    [CrossRef] [PubMed]
  17. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
    [CrossRef]
  18. 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]

2010

D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010).

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16(2), 73–85 (2010).
[CrossRef]

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
[CrossRef]

X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010).
[CrossRef] [PubMed]

2009

C. Weber, C.-A. Bunge, and K. Petermann, “Fiber Nonlinearities in Systems Using Electronic Predistortion of Dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. 27(16), 3654–3661 (2009).
[CrossRef]

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

2008

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]

2000

J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, pp1104 (2000).

1997

R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. 15(7), 1071–1082 (1997).
[CrossRef]

1995

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).
[CrossRef]

1991

D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. 9(10), 1330–1334 (1991).
[CrossRef]

1990

1986

Bononi, A.

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16(2), 73–85 (2010).
[CrossRef]

Bunge, C.-A.

Chen, X.

Cotter, D.

Ellis, A. D.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
[CrossRef]

D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010).

Gordon, J. P.

Haus, H. A.

Hui, R.

R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. 15(7), 1071–1082 (1997).
[CrossRef]

Inoue, K.

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).
[CrossRef]

Ip, E.

Kahn, J. M.

Li, G.

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

Marcuse, D.

D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. 9(10), 1330–1334 (1991).
[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]

Mollenauer, L. F.

O’Sullivan, M.

R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. 15(7), 1071–1082 (1997).
[CrossRef]

Petermann, K.

Rafique, D.

D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010).

Robinson, A.

R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. 15(7), 1071–1082 (1997).
[CrossRef]

Rossi, N.

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16(2), 73–85 (2010).
[CrossRef]

Serena, P.

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16(2), 73–85 (2010).
[CrossRef]

Shieh, W.

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]

Tang, J.

J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, pp1104 (2000).

Taylor, M.

R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. 15(7), 1071–1082 (1997).
[CrossRef]

Toba, H.

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).
[CrossRef]

Weber, C.

Yaman, F.

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

Zhao, J.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
[CrossRef]

D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010).

IEEE Photonics Technol. Lett.

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

J. Lightwave Technol.

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).
[CrossRef]

R. Hui, M. O’Sullivan, A. Robinson, and M. Taylor, “Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments,” J. Lightwave Technol. 15(7), 1071–1082 (1997).
[CrossRef]

D. Marcuse, “Bit-error rate of lightwave systems at the zero dispersion wavelength,” J. Lightwave Technol. 9(10), 1330–1334 (1991).
[CrossRef]

J. Tang, “The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, pp1104 (2000).

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

C. Weber, C.-A. Bunge, and K. Petermann, “Fiber Nonlinearities in Systems Using Electronic Predistortion of Dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. 27(16), 3654–3661 (2009).
[CrossRef]

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
[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]

OECC’2010

D. Rafique, J. Zhao, and A. D. Ellis, “Impact of Dispersion Map Management on the Performance of Back-Propagation for Nonlinear WDM Transmissions,” OECC’2010 , 00107 (2010).

Opt. Express

Opt. Fiber Technol.

A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. 16(2), 73–85 (2010).
[CrossRef]

Opt. Lett.

Other

J. Cai, Y. Cai, C. Davidson, D. Foursa, A. Lucero, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “Transmission of 96x100G Pre‐Filtered PDM‐RZ‐QPSK Channels with 300% Spectral Efficiency over 10,608km and 400% Spectral Efficiency over 4,368km,” in Proc. OFC 2010, PDPB10 (2010).

A. D. Ellis, and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in Non-Linear Effects in Fibre Communications, IEE Colloquium on, 6/1–6/4, (1990).

S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proc. ECOC 2008, Mo.3.D.1 (2008).

D. Rafique, M. Forzati, and J. Mårtensson, “Impact of Nonlinear Fibre Impairments in 112 Gb/s PM-QPSK Transmission with 43 Gb/s and 10.7 Gb/s Neighbours,” in Proc. ICTON 2010, paper We.D1.6 (2010).

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Figures (4)

Fig. 1
Fig. 1

Simulation model for 112 Gb/s PM-QPSK transmission.

Fig. 2
Fig. 2

(a) BER of a 112 Gb/s PM-QPSK transmission system as a function of launch power per span after 4,800 km for various dispersion maps after DBP, (b) Constellation diagram (x-polarization) at a launch power of 4 dBm for 20 ps/nm/km of dispersion, showing definition of angular and radial noise distributions after DBP. Inset in Fig. 2a shows transmission with (solid) and without (open) noise cases for 5 ps/nm/km, after DBP.

Fig. 3
Fig. 3

Normalized standard deviation of the received field for various dispersion maps after DBP, as a function of launch power per channel per span for 112 Gb/s PM-QPSK transmission after 4,800 km (a) Radial jitter (b) Angular Jitter. Data (symbols), Lines (theory).

Fig. 4
Fig. 4

(a) Normalized standard deviation (Angular Jitter) after DBP as a function of distance transmitted for 20 ps/nm/km dispersion at 5 dBm. Data (green triangles), analytical fit (black line) noise only (blue line), (b) Predicted information spectral density limits per polarization after 12,000 km for linear transmission (magenta curve), for non-linear transmission including; XPM for a WDM system with 101, 50GHz spaced channels (blue curve) and signal-ASE FWM within one channel (red curve) (and all other parameters same as numerical simulations).

Equations (3)

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E F W M = i 2 π w n c D χ 3 E p E q E r × e ( α 2 + i β ) L × 1 e { ( α + i Δ β ) L } α i Δ β ,
                    I S N F W M = I n o i s e . I s i g n a l 2 ( C 1 + C 2 ) , C 1 = N γ 2 ln ( 2 π 2 B 2 | β 2 | / α ) π | β 2 | α , C 2 = γ 2 π α | β 2 | ( N π + 2 α L { N log ( N ) N + 1 } ) ,
I T o t a l 2 = M 2 I n o i s e 2 + N = 1 M ( I S N F W M ) 2 .

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