Abstract

Optical phase jitter limits the performance of amplified differential-phase-shift-keyed optical communication systems. We propose an approach to evaluate the phase jitter for arbitrary pulses in dispersion-managed links based on the moment method. This calculation requires only the knowledge of the unperturbed optical signal, therefore avoiding computationally intensive Monte Carlo simulations. We apply this method to a dispersion-managed soliton system and a quasi-linear dispersion-compensated channel and demonstrate its validity by comparing the obtained results with Monte Carlo simulations.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. C. Xu and X. Liu, “Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. 27, 1619–1621 (2002).
    [CrossRef]
  3. A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, “2.5 Tb/s (64× 42.7 Gb/s) transmission over 40×100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in Optical Fiber Communications Conference, Vol. 70 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.
  4. J. Leibrich, C. Wree, and W. Rosenkranz, “CF-RZ-DPSK for suppression of XPM on dispersion-managed long-haul optical WDM transmission on standard single-mode fiber,” IEEE Photon. Technol. Lett. 14, 155–157 (2002).
    [CrossRef]
  5. C. Xu, X. Liu, and X. Wei, “Ultra-long haul DWDM transmission with differential phase-shift keying dispersion-managed soliton,” in 28th European Conference on Optical Communications 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), paper 1.1.5.
  6. G. P. Agrawal, “Coherent lightwave systems,” in Fiber-Optic Communication Systems, K. Chang, ed. (Wiley, New York, 2002), p. 478.
  7. M. Forzati, J. Martensson, A. Berntson, and A. Djupsjobacka, “Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format,” IEEE Photon. Technol. Lett. 14, 1285–1287 (2002).
    [CrossRef]
  8. H. Kim and A. Gnauck, “Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise,” IEEE Photon. Technol. Lett. 15, 320–322 (2003).
    [CrossRef]
  9. M. Hanna, H. Porte, W. T. Rhodes, and J.-P. Goedgebuer, “Soliton optical phase control by use of in-line filters,” Opt. Lett. 24, 732–735 (1999).
    [CrossRef]
  10. C. J. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 616–625 (2002).
    [CrossRef]
  11. C. J. McKinstrie, C. Xie, and T. I. Lakoba, “Efficient modeling of phase jitter in dispersion-managed soliton systems,” Opt. Lett. 27, 1887–1889 (2002).
    [CrossRef]
  12. V. S. Grigoryan, C. R. Menyuk, and R. M. Mu, “Calculation of timing and amplitude jitter in dispersion-managed optical fiber communications using linearization,” J. Lightwave Technol. 17, 1347–1356 (1999).
    [CrossRef]
  13. C. J. McKinstrie, “Effects of filtering on Gordon–Haus timing jitter in dispersion-managed systems,” J. Opt. Soc. Am. B 19, 1275–1285 (2002).
    [CrossRef]
  14. S. K. Turitsyn, T. Schäfer, and V. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
    [CrossRef]
  15. C. J. McKinstrie, C. Xie, and C. Xu, “Effects of cross-phase modulation on phase jitter in soliton systems with constant dispersion,” Opt. Lett. 28, 604–606 (2003).
    [CrossRef] [PubMed]

2003 (2)

H. Kim and A. Gnauck, “Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise,” IEEE Photon. Technol. Lett. 15, 320–322 (2003).
[CrossRef]

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

2002 (7)

J. Leibrich, C. Wree, and W. Rosenkranz, “CF-RZ-DPSK for suppression of XPM on dispersion-managed long-haul optical WDM transmission on standard single-mode fiber,” IEEE Photon. Technol. Lett. 14, 155–157 (2002).
[CrossRef]

M. Forzati, J. Martensson, A. Berntson, and A. Djupsjobacka, “Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format,” IEEE Photon. Technol. Lett. 14, 1285–1287 (2002).
[CrossRef]

C. J. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 616–625 (2002).
[CrossRef]

C. J. McKinstrie, “Effects of filtering on Gordon–Haus timing jitter in dispersion-managed systems,” J. Opt. Soc. Am. B 19, 1275–1285 (2002).
[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, “Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. 27, 1619–1621 (2002).
[CrossRef]

C. J. McKinstrie, C. Xie, and T. I. Lakoba, “Efficient modeling of phase jitter in dispersion-managed soliton systems,” Opt. Lett. 27, 1887–1889 (2002).
[CrossRef]

1999 (3)

Berntson, A.

M. Forzati, J. Martensson, A. Berntson, and A. Djupsjobacka, “Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format,” IEEE Photon. Technol. Lett. 14, 1285–1287 (2002).
[CrossRef]

Djupsjobacka, A.

M. Forzati, J. Martensson, A. Berntson, and A. Djupsjobacka, “Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format,” IEEE Photon. Technol. Lett. 14, 1285–1287 (2002).
[CrossRef]

Forzati, M.

M. Forzati, J. Martensson, A. Berntson, and A. Djupsjobacka, “Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format,” IEEE Photon. Technol. Lett. 14, 1285–1287 (2002).
[CrossRef]

Gnauck, A.

H. Kim and A. Gnauck, “Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise,” IEEE Photon. Technol. Lett. 15, 320–322 (2003).
[CrossRef]

Goedgebuer, J.-P.

Grigoryan, V. S.

Hanna, M.

Kim, H.

H. Kim and A. Gnauck, “Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise,” IEEE Photon. Technol. Lett. 15, 320–322 (2003).
[CrossRef]

Lakoba, T. I.

Leibrich, J.

J. Leibrich, C. Wree, and W. Rosenkranz, “CF-RZ-DPSK for suppression of XPM on dispersion-managed long-haul optical WDM transmission on standard single-mode fiber,” IEEE Photon. Technol. Lett. 14, 155–157 (2002).
[CrossRef]

Liu, X.

Martensson, J.

M. Forzati, J. Martensson, A. Berntson, and A. Djupsjobacka, “Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format,” IEEE Photon. Technol. Lett. 14, 1285–1287 (2002).
[CrossRef]

McKinstrie, C. J.

Menyuk, C. R.

Mezentsev, V.

S. K. Turitsyn, T. Schäfer, and V. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

Mu, R. M.

Porte, H.

Rhodes, W. T.

Rosenkranz, W.

J. Leibrich, C. Wree, and W. Rosenkranz, “CF-RZ-DPSK for suppression of XPM on dispersion-managed long-haul optical WDM transmission on standard single-mode fiber,” IEEE Photon. Technol. Lett. 14, 155–157 (2002).
[CrossRef]

Schäfer, T.

S. K. Turitsyn, T. Schäfer, and V. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

Slusher, R. E.

Turitsyn, S. K.

S. K. Turitsyn, T. Schäfer, and V. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

Wei, X.

Wree, C.

J. Leibrich, C. Wree, and W. Rosenkranz, “CF-RZ-DPSK for suppression of XPM on dispersion-managed long-haul optical WDM transmission on standard single-mode fiber,” IEEE Photon. Technol. Lett. 14, 155–157 (2002).
[CrossRef]

Xie, C.

Xu, C.

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

C. J. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 616–625 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

S. K. Turitsyn, T. Schäfer, and V. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

J. Leibrich, C. Wree, and W. Rosenkranz, “CF-RZ-DPSK for suppression of XPM on dispersion-managed long-haul optical WDM transmission on standard single-mode fiber,” IEEE Photon. Technol. Lett. 14, 155–157 (2002).
[CrossRef]

M. Forzati, J. Martensson, A. Berntson, and A. Djupsjobacka, “Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format,” IEEE Photon. Technol. Lett. 14, 1285–1287 (2002).
[CrossRef]

H. Kim and A. Gnauck, “Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise,” IEEE Photon. Technol. Lett. 15, 320–322 (2003).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Opt. Lett. (5)

Other (3)

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, “2.5 Tb/s (64× 42.7 Gb/s) transmission over 40×100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in Optical Fiber Communications Conference, Vol. 70 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

C. Xu, X. Liu, and X. Wei, “Ultra-long haul DWDM transmission with differential phase-shift keying dispersion-managed soliton,” in 28th European Conference on Optical Communications 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), paper 1.1.5.

G. P. Agrawal, “Coherent lightwave systems,” in Fiber-Optic Communication Systems, K. Chang, ed. (Wiley, New York, 2002), p. 478.

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

Standard deviation of the phase as a function of distance over 1 Mm. Quasi-linear system: Monte Carlo (solid curve) and moment method (dashed curve). DM soliton system: Monte Carlo (dashed–dotted curve) and moment method (crosses).

Fig. 2
Fig. 2

Standard deviation of the phase as a function of distance over 5 Mm. Quasi-linear system: Monte Carlo (solid curve) and moment method (dashed curve). DM soliton system: Monte Carlo (dashed–dotted curve) and moment method (crosses).

Fig. 3
Fig. 3

Standard deviation of the phase as a function of distance over 5 Mm for the multipulse simulation. Quasi-linear system: Monte Carlo (solid curve) and moment method (dashed curve). DM soliton system: Monte Carlo (dashed–dotted curve) and moment method (crosses).

Equations (26)

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

i uz-β2(z)2 2ut2+γ(z)|u|2u=ig(z)u+Fˆ(z, t),
Fˆ(z, t)Fˆ*(z, t)=2g0ω0nsp(z)δ(z-z)δ(t-t),
E=-+|u|2dt,
P=1E -+|u|4dt,
Φ=1E -+|u|2 arg(u)dt,
Ω2=-12E -+ (uut*)2+(u*ut)2|u|2 dt,
dΦdz=γP-β22Ω2+iE -+[arg(u)-Φ]×(uFˆ*-u*Fˆ)dt-12E -+u*Fˆ+uFˆ*dt,
dPdz=2gP+β2E -+|u|4[arg(u)]ttdt+iE -+(2|u|2-P)(uFˆ*-u*Fˆ)dt.
dΦdz=-β2ϕ2Φ+γP+iE -+[arg(u)-Φ]×(uFˆ*-u*Fˆ)dt-12E -+u*Fˆ+uFˆ*dt,
dPdz=2(g+β2ϕ2)P+iE -+(2|u|2-P)×(uFˆ*-u*Fˆ)dt.
P=P0+i0z1EA1 -+[(2|u|2-P)]×(uFˆ*-u*Fˆ)dtdz1A1,
A1(z)=exp0z2(g+β2ϕ2)dz1.
Φ=Φ1+Φ2+Φ3,
Φ1=A20z γPA2 dz1,
Φ2=iA20z1EA2 -+[arg(u)-Φ]×(uFˆ*-u*Fˆ)dtdz1,
Φ3=-A22 0z1EA2 -+u*Fˆ+uFˆ*dtdz1,
A2=exp-0zβ2ϕ2dz1.
σΦ2=Φ2-Φ2=Φ12+Φ22+Φ32+2Φ1Φ2,
(δqi, δqj)=-+δqiδqj*+δqi*δqjdt
δq1=2ignspω0 2|u|2-PEA1u,
δq2=2ignspω0 arg(u)-ΦEA2u,
δq3=2gnspω0 uEA2,
Φ12=A220z γA1A2 0z1 γA1A2×0z2(δq1, δq1)dz3dz2dz1,
Φ22=A222 0z(δq2, δq2)dz1,
Φ32=A228 0z(δq3, δq3)dz1,
2Φ1Φ2=A220zγA10z1(δq1, δq2)dz2dz1.

Metrics