Abstract

Self-phase modulation and intrachannel cross-phase-modulation– (IXPM) induced nonlinear phase noise is investigated by the variational method. IXPM can cause a considerable increase of phase noise. We show, however, that IXPM leads to a partial correlation between the phase noises of adjacent pulses, which tends to reduce the influence of nonlinear phase noise in return-to-zero differential phase-shift keying transmission. In highly dispersive transmission systems, intrachannel four-wave mixing-induced differential phase fluctuations are typically larger than differential nonlinear phase noise. The analysis is validated by Monte Carlo simulation.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Xu, X. Liu, and X. Wei, IEEE J. Sel. Top. Quantum Electron. 10, 281 (2004), and reference therein.
    [CrossRef]
  2. J. P. Gordon and L. F. Mollenauer, Opt. Lett. 15, 1351 (1990).
    [CrossRef] [PubMed]
  3. X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
    [CrossRef]
  4. Y. Yadin, M. Shtaif, and M. Orenstein, IEEE Photonics Technol. Lett. 16, 1307 (2004).
    [CrossRef]
  5. S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
    [CrossRef]
  6. X. Wei and X. Liu, Opt. Lett. 28, 2300 (2003).
    [CrossRef] [PubMed]
  7. K.-P. Ho and H.-C. Wang, IEEE Photon. Technol. Lett. 17, 1426 (2005).
    [CrossRef]
  8. C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
    [CrossRef]

2005 (1)

K.-P. Ho and H.-C. Wang, IEEE Photon. Technol. Lett. 17, 1426 (2005).
[CrossRef]

2004 (2)

Y. Yadin, M. Shtaif, and M. Orenstein, IEEE Photonics Technol. Lett. 16, 1307 (2004).
[CrossRef]

C. Xu, X. Liu, and X. Wei, IEEE J. Sel. Top. Quantum Electron. 10, 281 (2004), and reference therein.
[CrossRef]

2003 (2)

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

X. Wei and X. Liu, Opt. Lett. 28, 2300 (2003).
[CrossRef] [PubMed]

2002 (2)

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

1990 (1)

Chowdhury, D. Q.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

Gordon, J. P.

Ho, K.-P.

K.-P. Ho and H.-C. Wang, IEEE Photon. Technol. Lett. 17, 1426 (2005).
[CrossRef]

Kumar, S.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

Liu, X.

C. Xu, X. Liu, and X. Wei, IEEE J. Sel. Top. Quantum Electron. 10, 281 (2004), and reference therein.
[CrossRef]

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

X. Wei and X. Liu, Opt. Lett. 28, 2300 (2003).
[CrossRef] [PubMed]

Mauro, J. C.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

McKinstrie, C. J.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

Mollenauer, L. F.

Orenstein, M.

Y. Yadin, M. Shtaif, and M. Orenstein, IEEE Photonics Technol. Lett. 16, 1307 (2004).
[CrossRef]

Raghavan, S.

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

Shtaif, M.

Y. Yadin, M. Shtaif, and M. Orenstein, IEEE Photonics Technol. Lett. 16, 1307 (2004).
[CrossRef]

Wang, H.-C.

K.-P. Ho and H.-C. Wang, IEEE Photon. Technol. Lett. 17, 1426 (2005).
[CrossRef]

Wei, X.

C. Xu, X. Liu, and X. Wei, IEEE J. Sel. Top. Quantum Electron. 10, 281 (2004), and reference therein.
[CrossRef]

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

X. Wei and X. Liu, Opt. Lett. 28, 2300 (2003).
[CrossRef] [PubMed]

Xie, C.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

Xu, C.

C. Xu, X. Liu, and X. Wei, IEEE J. Sel. Top. Quantum Electron. 10, 281 (2004), and reference therein.
[CrossRef]

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

Yadin, Y.

Y. Yadin, M. Shtaif, and M. Orenstein, IEEE Photonics Technol. Lett. 16, 1307 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

S. Kumar, J. C. Mauro, S. Raghavan, and D. Q. Chowdhury, IEEE J. Sel. Top. Quantum Electron. 8, 626 (2002).
[CrossRef]

C. Xu, X. Liu, and X. Wei, IEEE J. Sel. Top. Quantum Electron. 10, 281 (2004), and reference therein.
[CrossRef]

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

K.-P. Ho and H.-C. Wang, IEEE Photon. Technol. Lett. 17, 1426 (2005).
[CrossRef]

X. Wei, X. Liu, and C. Xu, IEEE Photon. Technol. Lett. 15, 1636 (2003).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

Y. Yadin, M. Shtaif, and M. Orenstein, IEEE Photonics Technol. Lett. 16, 1307 (2004).
[CrossRef]

Opt. Lett. (2)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

STD of the differential nonlinear phase noise and of that which is due to IFWM. The simulation results (curves with symbols) are compared with the analytical values (curves without symbols). The simulated σ SPM agrees with its analytical equivalent very well, and the two lines merge into each other. n s p = 1 .

Fig. 2
Fig. 2

Relative strength of IFWM-induced differential phase fluctuations and differential nonlinear phase noise as a function of OSNR. N = 50 spans.

Fig. 3
Fig. 3

Differential phase noise STD owing to SPM, IXPM, and IFWM as a function of fiber link dispersion. N = 50 spans, ρ s = 50 ( 17 dB ) .

Equations (11)

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

i A k z β 2 2 A k t 2 + γ ¯ A k 2 A k + 2 γ ¯ A 3 k 2 A k = 0 , k = 1 , 2 .
d τ 1 d z = β C 1 τ 1 ,
d C 1 d z = β τ 1 2 ( 1 + C 1 2 ) + γ ¯ E 1 ( 2 π ) 1 2 τ 1 4 γ ¯ E 2 τ 1 2 [ 2 ( T 1 T 2 ) 2 ( τ 1 2 + τ 2 2 ) ] π 1 2 ( τ 1 2 + τ 2 2 ) 5 2 exp [ ( T 1 T 2 ) 2 τ 1 2 + τ 2 2 ] ,
d ϕ 1 d z = β 2 τ 1 2 + 5 γ ¯ E 1 2 5 2 π 1 2 τ 1 + 2 γ ¯ E 2 π 1 2 ( τ 1 2 + τ 2 2 ) 1 2 exp [ ( T 1 T 2 ) 2 τ 1 2 + τ 2 2 ] .
ϕ k , n = f 1 i = 2 n j = 1 i 1 δ τ k j + f 2 i = 2 n j = 1 i 1 δ E k j + f 3 i = 2 n j = 1 i 1 δ τ k j + i = 1 n δ ϕ k i + m k [ f 4 m , k i = 2 n j = 1 i 1 δ E m j + f 5 m , k i = 2 n j = 1 i 1 δ τ k j + f 5 m , k i = 2 n j = 1 i 1 δ τ m j + f 6 m , k i = 2 n j = 1 i 1 δ T m j ] ,
f 1 = 0 l A β τ 3 d z , f 2 = 0 l A 5 γ ¯ 2 5 2 π 1 2 τ d z ,
f 3 = 0 l A 5 γ ¯ E 2 5 2 π 1 2 τ 2 d z ,
f 4 m , k = 0 l A 2 γ ¯ π 1 2 τ exp [ ( m T b k T b ) 2 2 τ 2 ] d z ,
f 5 m , k = 0 l A γ ¯ E [ ( m T b k T b ) 2 τ 2 ] π 1 2 2 τ 4 exp [ ( m T b k T b ) 2 2 τ 2 ] d z ,
f 6 m , k = 0 l A 2 γ ¯ E ( m T b k T b ) π 1 2 τ 3 exp [ ( m T b k T b ) 2 2 τ 2 ] d z ,
( σ diff SPM + IXPM ) 2 ( σ diff Total ) 2 ( σ diff IFWM ) 2 ( σ diff linear ) 2 .

Metrics