Abstract

The mechanisms responsible for nonlinear impairments in single-channel phase modulated system employing differential detection are investigated. The role of dispersion precompensation is discussed. It is shown that precompensation may be designed as to minimize the in-phase components of the fluctuations thus reducing nonlinear impairments. In differential-phase-shift-keying the effect of precompensation is stronger than in differential-quadrature-phase-shift-keying. The results of an analytic theory are compared with split-step based computer simulations using realistic system parameters.

© 2011 OSA

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References

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  1. P. J. Winzer and R-J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94, 952–985 (2006).
    [Crossref]
  2. P. J. Winzer, S. Chandrasekhar, and H. Kim, “Impact of Filtering on RZ-DPSK Reception,” IEEE Photon. Technol. Lett. 15, 840–842 (2003).
    [Crossref]
  3. A. Mecozzi, “A unified theory of intra-channel nonlinearity in pseudo-linear phase-modulated transmission,” IEEE Photon. J. 2, 728–735 (2010).
    [Crossref]
  4. X. Wei and X. Liu, “Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion,” Opt. Lett. 18, 2300–2302, Dec. 1, 2003.
    [Crossref]
  5. T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
    [Crossref]
  6. X. Wei, X. Liu, S. H. Simon, and C. J. McKinstrie, “Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map,” Opt. Lett. 31, 29–31, 2006.
    [Crossref] [PubMed]
  7. A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Dispersion Management in Phase Modulated Optical Transmission Systems,” Proceedings of the 36th European Conference on Optical Communication, (ECOC 2010, Torino, Italy), Vol. 1, 311–313, September 19–23, 2010.

2010 (1)

A. Mecozzi, “A unified theory of intra-channel nonlinearity in pseudo-linear phase-modulated transmission,” IEEE Photon. J. 2, 728–735 (2010).
[Crossref]

2006 (3)

P. J. Winzer and R-J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94, 952–985 (2006).
[Crossref]

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

X. Wei, X. Liu, S. H. Simon, and C. J. McKinstrie, “Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map,” Opt. Lett. 31, 29–31, 2006.
[Crossref] [PubMed]

2003 (2)

P. J. Winzer, S. Chandrasekhar, and H. Kim, “Impact of Filtering on RZ-DPSK Reception,” IEEE Photon. Technol. Lett. 15, 840–842 (2003).
[Crossref]

X. Wei and X. Liu, “Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion,” Opt. Lett. 18, 2300–2302, Dec. 1, 2003.
[Crossref]

Ania-Castañón, J. D.

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

Chandrasekhar, S.

P. J. Winzer, S. Chandrasekhar, and H. Kim, “Impact of Filtering on RZ-DPSK Reception,” IEEE Photon. Technol. Lett. 15, 840–842 (2003).
[Crossref]

Chen, X.

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

Ellingham, T. J.

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

Essiambre, R-J.

P. J. Winzer and R-J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94, 952–985 (2006).
[Crossref]

Ibbotson, R.

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

Kim, H.

P. J. Winzer, S. Chandrasekhar, and H. Kim, “Impact of Filtering on RZ-DPSK Reception,” IEEE Photon. Technol. Lett. 15, 840–842 (2003).
[Crossref]

Liu, X.

X. Wei, X. Liu, S. H. Simon, and C. J. McKinstrie, “Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map,” Opt. Lett. 31, 29–31, 2006.
[Crossref] [PubMed]

X. Wei and X. Liu, “Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion,” Opt. Lett. 18, 2300–2302, Dec. 1, 2003.
[Crossref]

Matera, F.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Dispersion Management in Phase Modulated Optical Transmission Systems,” Proceedings of the 36th European Conference on Optical Communication, (ECOC 2010, Torino, Italy), Vol. 1, 311–313, September 19–23, 2010.

McKinstrie, C. J.

Mecozzi, A.

A. Mecozzi, “A unified theory of intra-channel nonlinearity in pseudo-linear phase-modulated transmission,” IEEE Photon. J. 2, 728–735 (2010).
[Crossref]

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Dispersion Management in Phase Modulated Optical Transmission Systems,” Proceedings of the 36th European Conference on Optical Communication, (ECOC 2010, Torino, Italy), Vol. 1, 311–313, September 19–23, 2010.

Settembre, M.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Dispersion Management in Phase Modulated Optical Transmission Systems,” Proceedings of the 36th European Conference on Optical Communication, (ECOC 2010, Torino, Italy), Vol. 1, 311–313, September 19–23, 2010.

Simon, S. H.

Tabacchiera, M.

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Dispersion Management in Phase Modulated Optical Transmission Systems,” Proceedings of the 36th European Conference on Optical Communication, (ECOC 2010, Torino, Italy), Vol. 1, 311–313, September 19–23, 2010.

Turitsyn, S. K.

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

Wei, X.

X. Wei, X. Liu, S. H. Simon, and C. J. McKinstrie, “Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map,” Opt. Lett. 31, 29–31, 2006.
[Crossref] [PubMed]

X. Wei and X. Liu, “Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion,” Opt. Lett. 18, 2300–2302, Dec. 1, 2003.
[Crossref]

Winzer, P. J.

P. J. Winzer and R-J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94, 952–985 (2006).
[Crossref]

P. J. Winzer, S. Chandrasekhar, and H. Kim, “Impact of Filtering on RZ-DPSK Reception,” IEEE Photon. Technol. Lett. 15, 840–842 (2003).
[Crossref]

Zhang, L.

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

IEEE Photon. J. (1)

A. Mecozzi, “A unified theory of intra-channel nonlinearity in pseudo-linear phase-modulated transmission,” IEEE Photon. J. 2, 728–735 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (2)

P. J. Winzer, S. Chandrasekhar, and H. Kim, “Impact of Filtering on RZ-DPSK Reception,” IEEE Photon. Technol. Lett. 15, 840–842 (2003).
[Crossref]

T. J. Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-Lossless Optical Links for Broad-Band Transmission and Data Processing,” IEEE Photon. Technol. Lett. 18, 268–230, Jan. 1, 2006.
[Crossref]

Opt. Lett. (2)

X. Wei, X. Liu, S. H. Simon, and C. J. McKinstrie, “Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map,” Opt. Lett. 31, 29–31, 2006.
[Crossref] [PubMed]

X. Wei and X. Liu, “Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion,” Opt. Lett. 18, 2300–2302, Dec. 1, 2003.
[Crossref]

Proc. IEEE (1)

P. J. Winzer and R-J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94, 952–985 (2006).
[Crossref]

Other (1)

A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Dispersion Management in Phase Modulated Optical Transmission Systems,” Proceedings of the 36th European Conference on Optical Communication, (ECOC 2010, Torino, Italy), Vol. 1, 311–313, September 19–23, 2010.

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Figures (2)

Fig. 1
Fig. 1

Q factor in linear scale vs. the precompensation distance z* in the lossless case, with 3 dBm average input power, and the parameters listed in Table 1. a) Solid line and circles, theory and simulations for DBPSK; b) Solid line and circles, theory and simulations for DQPSK.

Fig. 2
Fig. 2

Q factor in linear scale vs. the precompensation distance z* with lumped amplification, 0.25 dB/km of fiber loss, 15 dBm average input power, and the parameters listed in Table 1. a) Solid line and circles, theory and simulations for DBPSK; b) Solid line and circles, theory and simulations for DQPSK. Insets: Q vs. input power when ASE noise is included for zero precompensation (see text).

Tables (1)

Tables Icon

Table 1 Numerical parameters

Equations (6)

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J j , l = i γ 2 π 3 A 4 π 3 z * L z * f ( z + z * ) G ( T j , T l ; z ) d z ,
G ( T j , T l ; z ) = 1 2 π τ 2 ( z / z d ) 2 + 1 exp { T j 2 + T l 2 2 i ( z / z d ) T j T l 2 τ 2 [ ( z / z d ) 2 + 1 ] } .
Δ I mod 2 = e η h ¯ ω 0 ( C mod , FWM + C mod , corr ) ,
C DBPSK , FWM = j , l f j , l [ | J l , j | 2 + Re ( J l , j 2 ) ] ,
C DBPSK , corr = j Re [ q j ( J 1 , j J 1 , j * + J 1 , j J 1 , j ) + s j ( | J j , 1 j | 2 + J j , 1 j 2 ) ] ,
C DQPSK , FWM = j , l f j , l | J l , j | 2 , C DQPSK , corr = j Re ( q j J 1 , j J 1 , j ) .

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