Abstract

We demonstrate electronic post-compensation for nonlinear phase fluctuation in a 1000-km 20-Gbit/s optical quadrature phase-shift keying (QPSK) transmission system, where group-velocity dispersion is well managed. The inter-symbol interference (ISI) at the transmitter induces the nonlinear phase fluctuation through self-phase modulation (SPM) of the signal transmitted through a fiber. However, when the optimized phase shift proportional to the intensity fluctuation is given to the complex amplitude of the signal electric field by using a digital coherent receiver, the nonlinear phase fluctuation can be reduced effectively.

© 2008 Optical Society of America

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References

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  1. C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Select. Topics Quantum Electron. 10, 281-293 (2004).
    [CrossRef]
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    [CrossRef]
  3. T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, "A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise," J. Lightwave Technol. 21, 1933-1943 (2003).
    [CrossRef]
  4. J.P. Gordon and L.F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).
    [CrossRef] [PubMed]
  5. X. Liu, X. Wei, R. 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]
  6. C. Xu and X. Liu, "Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission," Opt. Lett. 27, 1619-1621 (2002)
    [CrossRef]
  7. K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," IEEE J. Selected Topics on Quantum Electron. 12, 563-570 (2006).
    [CrossRef]
  8. K.-P. Ho and J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightwave Technol. 22, 779-783 (2004).
    [CrossRef]
  9. D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006).
    [CrossRef]
  10. G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed. (Academic, New York, 2001).
  11. C. Lorattanasane and K. Kikuchi, "Design theory of long-distance optical transmission systems using midway optical phase conjugation," IEEE J. Lightwave Technol. 15, 948-955 (1997).
    [CrossRef]
  12. X. Wang, K. Kikuchi, and Y. Takushima, "Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion," IEICE Trans. on Electron.E 82-C, 1407-1413 (1999).
  13. S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
    [CrossRef]

2006 (2)

K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," IEEE J. Selected Topics on Quantum Electron. 12, 563-570 (2006).
[CrossRef]

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006).
[CrossRef]

2005 (1)

2004 (2)

K.-P. Ho and J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightwave Technol. 22, 779-783 (2004).
[CrossRef]

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

2003 (1)

2002 (2)

2001 (1)

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

1999 (1)

X. Wang, K. Kikuchi, and Y. Takushima, "Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion," IEICE Trans. on Electron.E 82-C, 1407-1413 (1999).

1997 (1)

C. Lorattanasane and K. Kikuchi, "Design theory of long-distance optical transmission systems using midway optical phase conjugation," IEEE J. Lightwave Technol. 15, 948-955 (1997).
[CrossRef]

1990 (1)

Abe, J.

Gnauck, A. H.

Gordon, J.P.

Ho, K.-P.

Ishida, K.

Izutsu, M.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

Kahn, J. M.

Kasahara, K.

Katoh, K.

Kawanishi, T.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

Kikuchi, K.

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006).
[CrossRef]

K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," IEEE J. Selected Topics on Quantum Electron. 12, 563-570 (2006).
[CrossRef]

X. Wang, K. Kikuchi, and Y. Takushima, "Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion," IEICE Trans. on Electron.E 82-C, 1407-1413 (1999).

C. Lorattanasane and K. Kikuchi, "Design theory of long-distance optical transmission systems using midway optical phase conjugation," IEEE J. Lightwave Technol. 15, 948-955 (1997).
[CrossRef]

Kinjo, K.

Kobayashi, T.

Kubodera, K.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

Liu, X.

Lorattanasane, C.

C. Lorattanasane and K. Kikuchi, "Design theory of long-distance optical transmission systems using midway optical phase conjugation," IEEE J. Lightwave Technol. 15, 948-955 (1997).
[CrossRef]

Ly-Gagnon, D.-S.

McKinstrie, C.J.

Mitsugi, N.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

Mizuochi, T.

Mollenauer, L.F.

Motoshima, K.

Oikawa, S.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

Saitou, T.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

Shimotsu, S.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

Slusher, R.

Takushima, Y.

X. Wang, K. Kikuchi, and Y. Takushima, "Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion," IEICE Trans. on Electron.E 82-C, 1407-1413 (1999).

Tsukamoto, S.

Wang, X.

X. Wang, K. Kikuchi, and Y. Takushima, "Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion," IEICE Trans. on Electron.E 82-C, 1407-1413 (1999).

Wei, X.

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

X. Liu, X. Wei, R. 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]

Winzer, P. J.

Xu, C.

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

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

E (1)

X. Wang, K. Kikuchi, and Y. Takushima, "Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion," IEICE Trans. on Electron.E 82-C, 1407-1413 (1999).

IEEE J. Lightwave Technol. (1)

C. Lorattanasane and K. Kikuchi, "Design theory of long-distance optical transmission systems using midway optical phase conjugation," IEEE J. Lightwave Technol. 15, 948-955 (1997).
[CrossRef]

IEEE J. Select. Topics Quantum Electron. (1)

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

IEEE J. Selected Topics on Quantum Electron. (1)

K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," IEEE J. Selected Topics on Quantum Electron. 12, 563-570 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Lett. (3)

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed. (Academic, New York, 2001).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of the phase diversity homodyne receiver. PBS: polarization beam splitter, HWP: half-wave plate, QWP: quarter-wave plate, HM: half mirror, LO: local oscillator, PD: double-balanced photodiode.

Fig. 2.
Fig. 2.

Digital phase estimation process for M-ary PSK signals.

Fig. 3.
Fig. 3.

Schematic diagram of the RZ QPSK transmission system.

Fig. 4.
Fig. 4.

Comparison of the intensity waveform between the back-to-back RZ QPSK signal (a) and the RZ pulse train after 1000-km transmission.

Fig. 5.
Fig. 5.

Bit-error rate measured as a function of the compensation parameter α.

Fig. 6.
Fig. 6.

Constellation maps of the transmitted RZ QPSK signal at the uncompensated state (A in Fig. 5), the optimally compensated state (B), the overcompensated state (C), and the under-compensated state (D). The upper row shows the measured results and the lower row shows the simulation results.

Equations (12)

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

A z = α p ( z ) 2 A + j 2 β 2 ( z ) 2 A T 2 j γ ( z ) A 2 A .
A * z = + α p ( z ) 2 A * + j 2 β 2 ( z ) 2 A * T 2 j γ ( z ) A 2 A * .
A c ( t ) = A ( L , t ) exp ( jm ( γ ) eff A ( L , t ) 2 ) .
( γ ) eff = 0 γ ( z ) exp ( α p ( z ) ) d z .
A c ( t ) = A ( L , t ) exp ( j α m ( γ ) eff A ( L , t ) 2 ) .
δ I ( t ) = 2 A 0 k = 1 m a k ( t ) ,
δ I 2 ¯ = 4 A 0 2 m a 2 ¯ ,
δ ϕ ( t ) = 2 A 0 ( γ ) eff k = 1 m ka k ( t ) .
δ ϕ 2 ¯ = ( 2 A 0 ( γ ) eff ) 2 a 2 ¯ k = 1 m k 2 ( 2 A 0 ( γ ) eff ) 2 a 2 ¯ m 3 3 = ( ( γ ) eff ) 2 δ I 2 ¯ m 3 3 .
δ ϕ c ( t ) = δ ϕ ( t ) + α m ( γ ) eff δ I ( t ) = 2 A 0 ( γ ) eff k = 1 m ( k m α ) a k ( t ) ,
δ ϕ c 2 ¯ = ( 2 A 0 ( γ ) eff ) 2 a 2 ¯ k = 1 m ( k m α ) 2 ,
δ ϕ c 2 ¯ = ( ( γ ) eff ) 2 δ I 2 ¯ m 3 12 .

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