Abstract

This investigation proposes a novel all-optical phase noise averager to reduce residual phase noise in the differential phase-shift keying (DPSK) transmission system with phase-preserving amplitude regenerators. The proposed phase noise averager is based on a phase-sensitive amplifier but does not require an extra phase-locking optical pump beam. It can increase the correlation between the phase noises of neighboring bits and greatly reduce the differential phase noise in the transmission system. Independently of the cascaded spans, analytical analysis demonstrates that, in the DPSK system with repeated averagers, the total differential phase noise will be less than that before the first averager. Theoretical analysis and numerical simulation are carried out and confirm the significant improvement of DPSK signals using the proposed novel phase noise averagers.

© 2006 Optical Society of America

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  1. A. Gnauck, "40-Gb/s RZ-differential phase shift keyed transmission," Optical Fiber Communication Conference 2003, paper ThE1.
  2. J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, "DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system," IEEE Photonics Technol. Lett. 12, 1627-1629 (2000).
    [CrossRef]
  3. A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
    [CrossRef]
  4. J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communication systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).
    [CrossRef] [PubMed]
  5. C. J. McKinstrie, C. Xie, and C. Xu, "Effects of cross-phase modulation on phase jitter in soliton systems with constant disperision," Opt. Lett. 28, 604-606 (2003).
    [CrossRef] [PubMed]
  6. C. J. MaKinstrie, S. Radic, and C. Xie, "Reduction of soliton phase jitter by in-line phase conjugation," Opt. Lett. 28, 1519-1521 (2003)
    [CrossRef]
  7. <jrn>. S. L. Jansen, D. van den Borne, G. D. Khoe, H. de Waardt, C. C. Monsalve, S. Spalter and P. M. Krummrich, "Reduction of nonlinear phase noise by mid-link spectral inversion in a DPSK based transmission system," Optical Fiber Communications 2005, paper OTh05.</jrn>
  8. X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
    [CrossRef]
  9. C. Xu and X. Liu, "Post-nonlinearity compensation with data-driven phase modulators in phase-shift keying transmission," Opt. Lett. 27, 1619-1621 (2002).
    [CrossRef]
  10. S. A. Derevyanko and S. K. Turitsyn, "Reduction of the phase jitter in differential phase-shift-keying soliton transmission systems by in-line Butterworth filters," Opt. Lett. 29, 35-37 (2004).
    [CrossRef] [PubMed]
  11. D. Boivin, M. Hanna, P.-A. Lacourt, and J.-P. Goedgebuer, "Reduction of phase jitter in dispersion-managed systems by in-line filtering," Opt. Lett. 29, 688-690 (2004).
    [CrossRef] [PubMed]
  12. P. V. Mamyshev, "All-optical data regeneration based on self-phase modulation effect," European Conference on Optical Communication 1998, pp. 475-476.
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    [CrossRef]
  14. S. Mazumder and S. Yamashita, "Optical 2R regeneration of 10Gbps signal using cascaded fiber four wave mixing," European Conference on Optical Communication 2005, pp. 57-58.
  15. K. Croussore, C. Kim, and G. Li, "All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification," Opt. Lett. 29, 2357-2359 (2004).
    [CrossRef] [PubMed]
  16. K. Croussore, I. Kim, C. Kim, Y. Han, and G. Li, "Phase-and-amplitude regeneration of differential phase-shift keyed signals using a phase-sensitive amplifier," Opt. Express 14, 2085-2094 (2006).
    [CrossRef] [PubMed]
  17. M. Shin, P. S. Devgan, V. S. Grigoryan, and P. Kumar, "SNR improvement of DPSK signals in a semiconductor optical regenerative amplifier," IEEE Photonics Technol. Lett. 18, 49-51 (2006).
    [CrossRef]
  18. A. Striegler and B. Schmauss, "All-optical DPSK signal regeneration based on cross-phase modulation," IEEE Photonics Technol. Lett. 16, 1083-1085 (2004).
    [CrossRef]
  19. A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
    [CrossRef]
  20. M. Matsumoto, "Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators," IEEE Photonics Technol. Lett. 17, 1055-1057 (2005).
    [CrossRef]
  21. S. Boscolo, R. Bhamber, and S. K. Turitsyn, "Design of Raman-based NOLM for optical 2R regeneration of RZ-DPSK transmission," Optical Fiber Communication Conference 2006, paper OWJ5.
  22. K.-P. Ho, "Asymptotic probability density of nonlinear phase noise," Opt. Lett. 28, 1350-1352 (2003).
    [CrossRef] [PubMed]
  23. A. Mecozzi, "Probability density functions of the nonlinear phase noise," Opt. Lett. 29, 673-675 (2004).
    [CrossRef] [PubMed]
  24. C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).
    [CrossRef]
  25. X. Zhang, Z. Qu, and G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 258, 177-183 (2006)
    [CrossRef]
  26. X. Wei and X Liu, "Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion," Opt. Lett. 28, 2300-2302 (2003).
    [CrossRef] [PubMed]
  27. L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
    [CrossRef]

2006 (3)

M. Shin, P. S. Devgan, V. S. Grigoryan, and P. Kumar, "SNR improvement of DPSK signals in a semiconductor optical regenerative amplifier," IEEE Photonics Technol. Lett. 18, 49-51 (2006).
[CrossRef]

X. Zhang, Z. Qu, and G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 258, 177-183 (2006)
[CrossRef]

K. Croussore, I. Kim, C. Kim, Y. Han, and G. Li, "Phase-and-amplitude regeneration of differential phase-shift keyed signals using a phase-sensitive amplifier," Opt. Express 14, 2085-2094 (2006).
[CrossRef] [PubMed]

2005 (2)

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

M. Matsumoto, "Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators," IEEE Photonics Technol. Lett. 17, 1055-1057 (2005).
[CrossRef]

2004 (8)

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

A. Striegler and B. Schmauss, "All-optical DPSK signal regeneration based on cross-phase modulation," IEEE Photonics Technol. Lett. 16, 1083-1085 (2004).
[CrossRef]

A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
[CrossRef]

S. A. Derevyanko and S. K. Turitsyn, "Reduction of the phase jitter in differential phase-shift-keying soliton transmission systems by in-line Butterworth filters," Opt. Lett. 29, 35-37 (2004).
[CrossRef] [PubMed]

A. Mecozzi, "Probability density functions of the nonlinear phase noise," Opt. Lett. 29, 673-675 (2004).
[CrossRef] [PubMed]

D. Boivin, M. Hanna, P.-A. Lacourt, and J.-P. Goedgebuer, "Reduction of phase jitter in dispersion-managed systems by in-line filtering," Opt. Lett. 29, 688-690 (2004).
[CrossRef] [PubMed]

K. Croussore, C. Kim, and G. Li, "All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification," Opt. Lett. 29, 2357-2359 (2004).
[CrossRef] [PubMed]

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).
[CrossRef]

2003 (4)

2002 (2)

2000 (2)

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, "DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system," IEEE Photonics Technol. Lett. 12, 1627-1629 (2000).
[CrossRef]

E. Ciaramella and S. Trillo, "All-optical signal reshaping via four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 12, 849-851 (2000).
[CrossRef]

1990 (1)

Boivin, D.

Burrows, E. C.

A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
[CrossRef]

Cheng, K. S.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, "DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system," IEEE Photonics Technol. Lett. 12, 1627-1629 (2000).
[CrossRef]

Chowdhury, D.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, "DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system," IEEE Photonics Technol. Lett. 12, 1627-1629 (2000).
[CrossRef]

Chraplyvy, A. R.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Ciaramella, E.

E. Ciaramella and S. Trillo, "All-optical signal reshaping via four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 12, 849-851 (2000).
[CrossRef]

Croussore, K.

Cvecek, K.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

Derevyanko, S. A.

Devgan, P. S.

M. Shin, P. S. Devgan, V. S. Grigoryan, and P. Kumar, "SNR improvement of DPSK signals in a semiconductor optical regenerative amplifier," IEEE Photonics Technol. Lett. 18, 49-51 (2006).
[CrossRef]

Essiambre, R.-J.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Gill, D. M.

A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
[CrossRef]

Gliese, U.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, "DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system," IEEE Photonics Technol. Lett. 12, 1627-1629 (2000).
[CrossRef]

Gnauck, A. H.

A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
[CrossRef]

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Goedgebuer, J.-P.

Gordon, J. P.

Grigoryan, V. S.

M. Shin, P. S. Devgan, V. S. Grigoryan, and P. Kumar, "SNR improvement of DPSK signals in a semiconductor optical regenerative amplifier," IEEE Photonics Technol. Lett. 18, 49-51 (2006).
[CrossRef]

Han, Y.

Hanna, M.

Ho, K.-P.

Kim, C.

Kim, I.

Kumar, P.

M. Shin, P. S. Devgan, V. S. Grigoryan, and P. Kumar, "SNR improvement of DPSK signals in a semiconductor optical regenerative amplifier," IEEE Photonics Technol. Lett. 18, 49-51 (2006).
[CrossRef]

Lacourt, P.-A.

Leuchs, G.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

Li, G.

Liu, X

Liu, X.

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).
[CrossRef]

A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
[CrossRef]

X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
[CrossRef]

C. Xu and X. Liu, "Post-nonlinearity compensation with data-driven phase modulators in phase-shift keying transmission," Opt. Lett. 27, 1619-1621 (2002).
[CrossRef]

Matsumoto, M.

M. Matsumoto, "Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators," IEEE Photonics Technol. Lett. 17, 1055-1057 (2005).
[CrossRef]

McKinstrie, C. J.

Mecozzi, A.

Meissner, M.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

Mollenauer, L. F.

Qu, Z.

X. Zhang, Z. Qu, and G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 258, 177-183 (2006)
[CrossRef]

Rhee, J. K.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, "DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system," IEEE Photonics Technol. Lett. 12, 1627-1629 (2000).
[CrossRef]

Schmauss, B.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

A. Striegler and B. Schmauss, "All-optical DPSK signal regeneration based on cross-phase modulation," IEEE Photonics Technol. Lett. 16, 1083-1085 (2004).
[CrossRef]

Shin, M.

M. Shin, P. S. Devgan, V. S. Grigoryan, and P. Kumar, "SNR improvement of DPSK signals in a semiconductor optical regenerative amplifier," IEEE Photonics Technol. Lett. 18, 49-51 (2006).
[CrossRef]

Slusher, R. E.

Sponsel, K.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

Striegler, A.

A. Striegler and B. Schmauss, "All-optical DPSK signal regeneration based on cross-phase modulation," IEEE Photonics Technol. Lett. 16, 1083-1085 (2004).
[CrossRef]

Striegler, A. G.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

Trillo, S.

E. Ciaramella and S. Trillo, "All-optical signal reshaping via four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 12, 849-851 (2000).
[CrossRef]

Turitsyn, S. K.

Wei, X.

A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
[CrossRef]

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).
[CrossRef]

X. Wei and X Liu, "Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion," Opt. Lett. 28, 2300-2302 (2003).
[CrossRef] [PubMed]

X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
[CrossRef]

Wickham, L. K.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Winzer, P. J.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Xie, C.

Xu, C.

Yang, G.

X. Zhang, Z. Qu, and G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 258, 177-183 (2006)
[CrossRef]

Zhang, X.

X. Zhang, Z. Qu, and G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 258, 177-183 (2006)
[CrossRef]

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

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281-293 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E. Ciaramella and S. Trillo, "All-optical signal reshaping via four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 12, 849-851 (2000).
[CrossRef]

IEEE Photonics Technol. Lett. (7)

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, "DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system," IEEE Photonics Technol. Lett. 12, 1627-1629 (2000).
[CrossRef]

A. H. Gnauck, X. Liu, X. Wei, D. M. Gill, and E. C. Burrows, "Comparison of modulation formats for 42.7-Gb/s single-channel transmission through 1980 km of SSMF," IEEE Photonics Technol. Lett. 16, 909-911 (2004).
[CrossRef]

M. Shin, P. S. Devgan, V. S. Grigoryan, and P. Kumar, "SNR improvement of DPSK signals in a semiconductor optical regenerative amplifier," IEEE Photonics Technol. Lett. 18, 49-51 (2006).
[CrossRef]

A. Striegler and B. Schmauss, "All-optical DPSK signal regeneration based on cross-phase modulation," IEEE Photonics Technol. Lett. 16, 1083-1085 (2004).
[CrossRef]

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, "NOLM-based RZ-DPSK signal regeneration," IEEE Photonics Technol. Lett. 17, 639-641 (2005).
[CrossRef]

M. Matsumoto, "Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators," IEEE Photonics Technol. Lett. 17, 1055-1057 (2005).
[CrossRef]

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, "Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photonics Technol. Lett. 16, 1591-1593 (2004).
[CrossRef]

Opt. Commun. (1)

X. Zhang, Z. Qu, and G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 258, 177-183 (2006)
[CrossRef]

Opt. Express (1)

Opt. Lett. (11)

J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communication systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).
[CrossRef] [PubMed]

X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
[CrossRef]

C. Xu and X. Liu, "Post-nonlinearity compensation with data-driven phase modulators in phase-shift keying transmission," Opt. Lett. 27, 1619-1621 (2002).
[CrossRef]

C. J. McKinstrie, C. Xie, and C. Xu, "Effects of cross-phase modulation on phase jitter in soliton systems with constant disperision," Opt. Lett. 28, 604-606 (2003).
[CrossRef] [PubMed]

K.-P. Ho, "Asymptotic probability density of nonlinear phase noise," Opt. Lett. 28, 1350-1352 (2003).
[CrossRef] [PubMed]

C. J. MaKinstrie, S. Radic, and C. Xie, "Reduction of soliton phase jitter by in-line phase conjugation," Opt. Lett. 28, 1519-1521 (2003)
[CrossRef]

X. Wei and X Liu, "Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion," Opt. Lett. 28, 2300-2302 (2003).
[CrossRef] [PubMed]

S. A. Derevyanko and S. K. Turitsyn, "Reduction of the phase jitter in differential phase-shift-keying soliton transmission systems by in-line Butterworth filters," Opt. Lett. 29, 35-37 (2004).
[CrossRef] [PubMed]

A. Mecozzi, "Probability density functions of the nonlinear phase noise," Opt. Lett. 29, 673-675 (2004).
[CrossRef] [PubMed]

D. Boivin, M. Hanna, P.-A. Lacourt, and J.-P. Goedgebuer, "Reduction of phase jitter in dispersion-managed systems by in-line filtering," Opt. Lett. 29, 688-690 (2004).
[CrossRef] [PubMed]

K. Croussore, C. Kim, and G. Li, "All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification," Opt. Lett. 29, 2357-2359 (2004).
[CrossRef] [PubMed]

Other (5)

S. Boscolo, R. Bhamber, and S. K. Turitsyn, "Design of Raman-based NOLM for optical 2R regeneration of RZ-DPSK transmission," Optical Fiber Communication Conference 2006, paper OWJ5.

<jrn>. S. L. Jansen, D. van den Borne, G. D. Khoe, H. de Waardt, C. C. Monsalve, S. Spalter and P. M. Krummrich, "Reduction of nonlinear phase noise by mid-link spectral inversion in a DPSK based transmission system," Optical Fiber Communications 2005, paper OTh05.</jrn>

P. V. Mamyshev, "All-optical data regeneration based on self-phase modulation effect," European Conference on Optical Communication 1998, pp. 475-476.

A. Gnauck, "40-Gb/s RZ-differential phase shift keyed transmission," Optical Fiber Communication Conference 2003, paper ThE1.

S. Mazumder and S. Yamashita, "Optical 2R regeneration of 10Gbps signal using cascaded fiber four wave mixing," European Conference on Optical Communication 2005, pp. 57-58.

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Figures (7)

Fig. 1.
Fig. 1.

Concept of a PNA

Fig. 2.
Fig. 2.

Optical DPSK transmission system with amplitude regenerators and PNAs inserted every K spans.

Fig. 3.
Fig. 3.

The variances of differential PN as functions of the number of PNAs.

Fig. 4.
Fig. 4.

Setup of a PNA

Fig. 5.
Fig. 5.

(a). Normalized output power, (b) output phase and (c) output phase slope of a PNA.

Fig. 6.
Fig. 6.

(a). Normalized IN and (b) differential PN versus transmission distance for 40 Gbps 33% RZ-DPSK

Fig. 7.
Fig. 7.

Differential phasor diagrams for 40 Gbps 33% RZ-DPSK after 2800 km transmission. For (a), FWM-based regenerators are inserted, and for (b), FWM-based regenerators and PSA-based PNA are both inserted every 400 km. (c) and (d) are the differential phase eye-diagrams corresponding to (a) and (b), respectively.

Equations (20)

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E n , avg = 2 s n E 0 cos ( φ n φ n 1 2 ) × e j φ n + φ n 1 2
φ n ( M ) = k = 0 M ( C k M · φ n k ) 2 M
Δ φ n ( M ) = φ n ( M ) φ n 1 ( M ) = φ n + k = 1 M [ ( C k M C k 1 M ) · φ n k ] φ n M 1 2 M
( Δ φ n ( M ) ) 2 = 2 + k = 1 M ( C k M C k 1 M ) 2 2 2 M × σ 2
Δ Φ 2 = N = 1 M ( Δ φ n ( N ) ) 2 = N = 1 M ( 2 + k = 1 N ( C k N C k 1 N ) 2 2 2 N ) × σ 2
E s = e j θ 0 ( E s cos θ nl E p sin θ nl )
E s = e j θ 0 ( e j Δ φ n R tan ϑ nl ) × s n E 0 cos ϑ nl e j φ n 1
E ˜ s = e j Δ φ n Θ R sin ( Δ φ n )
( E ˜ s ) Δ φ n = 1 2 & E ˜ s 2 Δ φ n = 0
C k n + 1 = C k n + C k 1 n
φ n ( 2 ) = 1 2 ( ( C 0 1 · φ n + C 1 1 · φ n 1 ) 2 + ( C 0 1 · φ n 1 + C 1 1 · φ n 2 ) 2 )
= C 0 2 · φ n + C 1 2 · φ n 1 + C 2 2 · φ n 2 2 2
k = 1 n ( C k n C k 1 n ) 2 = 2 × k = 1 n ( C k n ) 2 + 2 × k = 1 n ( C k 1 n ) 2 k = 1 n ( C k n + C k 1 n ) 2
k = 0 n ( C k n ) 2 = C n 2 n
k = 1 n ( C k n C k 1 n ) 2 = 2 × ( C n 2 n C 0 n ) + 2 × ( C n 2 n C n n ) ( C n + 1 2 n + 2 C 0 n + 1 C n + 1 n + 1 )
= 4 × C n 2 n C n + 1 2 n + 2 2 = 2 n + 1 C n 2 n 2
n = C n 2 n n + 1
N = 1 M [ 2 + k = 1 N ( C k N C k 1 N ) 2 2 2 N ] = 2 × N = 1 M ( N 2 2 N )
1 1 4 x 2 x = n = 0 ( n · x n ) = 1 + x + 2 x 2 + 5 x 2 +
lim M 2 × N = 1 M [ N · ( 1 4 ) N ] = 2

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