Abstract

We study interaction-induced timing jitter in single-channel dispersion-managed return-to-zero ttransmission systems operating at high map strengths. An equation for the frequency and timing shifts of two interacting pulses is derived by a variational approach. The interaction can be of either an attractive or a repulsive character, and we show that the resultant timing jitter can be reduced by proper design of the dispersion map.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
    [CrossRef]
  2. P. V. Mamyshev and N. A. Mamysheva, Opt. Lett. 24, 1454 (1999).
    [CrossRef]
  3. P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
    [CrossRef]
  4. T. Yu, E. A. Golovchenko, and C. R. Menyuk, Opt. Lett. 22, 793 (1997).
    [CrossRef] [PubMed]
  5. A. Berntson, J. Mårtensson, and M. Westlund, in Conference on Lasers and Electro-Optics (CLEO 2000), 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), p. 237.
  6. M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
    [CrossRef]
  7. D. J. Kaup, B. A. Malomed, and J. Yang, Opt. Lett. 23, 1600 (1998).
    [CrossRef]
  8. J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, Opt. Lett. 22, 1695 (1997).
    [CrossRef]
  9. D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
    [CrossRef] [PubMed]
  10. S. Kumar, M. Wald, F. Lederer, and A. Hasegawa, Opt. Lett. 23, 1019 (1998).
    [CrossRef]
  11. J. Mårtensson, M. Westlund, and A. Berntson, Electron. Lett. 36, 244 (2000).
    [CrossRef]

2000

J. Mårtensson, M. Westlund, and A. Berntson, Electron. Lett. 36, 244 (2000).
[CrossRef]

1999

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

P. V. Mamyshev and N. A. Mamysheva, Opt. Lett. 24, 1454 (1999).
[CrossRef]

P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

1998

1997

1985

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Alleston, S. B.

P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

Anderson, D.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Bennion, I.

P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

Berntson, A.

J. Mårtensson, M. Westlund, and A. Berntson, Electron. Lett. 36, 244 (2000).
[CrossRef]

A. Berntson, J. Mårtensson, and M. Westlund, in Conference on Lasers and Electro-Optics (CLEO 2000), 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), p. 237.

Devaney, J. F. L.

Doran, N. J.

P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, Opt. Lett. 22, 1695 (1997).
[CrossRef]

Ellis, A. D.

P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

Essiambre, R.-J.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Forysiak, W.

Golovchenko, E. A.

Harper, P.

P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

Hasegawa, A.

Kaup, D. J.

Kumar, S.

Lederer, F.

M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

S. Kumar, M. Wald, F. Lederer, and A. Hasegawa, Opt. Lett. 23, 1019 (1998).
[CrossRef]

Lisak, M.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Malomed, B. A.

M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, Opt. Lett. 23, 1600 (1998).
[CrossRef]

Mamyshev, P. V.

Mamysheva, N. A.

Mårtensson, J.

J. Mårtensson, M. Westlund, and A. Berntson, Electron. Lett. 36, 244 (2000).
[CrossRef]

A. Berntson, J. Mårtensson, and M. Westlund, in Conference on Lasers and Electro-Optics (CLEO 2000), 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), p. 237.

Menyuk, C. R.

Mikkelsen, B.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Niculae, A. M.

Raybon, G.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Wald, M.

M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

S. Kumar, M. Wald, F. Lederer, and A. Hasegawa, Opt. Lett. 23, 1019 (1998).
[CrossRef]

Westlund, M.

J. Mårtensson, M. Westlund, and A. Berntson, Electron. Lett. 36, 244 (2000).
[CrossRef]

A. Berntson, J. Mårtensson, and M. Westlund, in Conference on Lasers and Electro-Optics (CLEO 2000), 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), p. 237.

Yang, J.

Yu, T.

Electron. Lett.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

P. Harper, S. B. Alleston, I. Bennion, A. D. Ellis, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

J. Mårtensson, M. Westlund, and A. Berntson, Electron. Lett. 36, 244 (2000).
[CrossRef]

Opt. Commun.

M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. A

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Other

A. Berntson, J. Mårtensson, and M. Westlund, in Conference on Lasers and Electro-Optics (CLEO 2000), 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), p. 237.

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 (5)

Fig. 1
Fig. 1

Schematic diagram of the dispersion map.

Fig. 2
Fig. 2

Evolution of the frequency shift during one dispersion period for L=50 km in the lossless case: solid curve, variational approximation, X=0; asterisks, numerical simulation, X=0; dashed curve, variational approximation, X=1; open circles, numerical simulation, X=1. The dashed and solid curves almost coincide.

Fig. 3
Fig. 3

Timing shift after 500  km of propagation as a function of map strength in the lossless case: (i) X=0, (ii) X=1. Solid curves, variational approximation; asterisks, numerical simulation.

Fig. 4
Fig. 4

Timing shift after one dispersion period as a function of launch position for L=50 km in the lossless case: solid curve, variational approximation; asterisks, numerical simulation.

Fig. 5
Fig. 5

Timing shift after one dispersion period as a function of launch position for L=50 km including loss: (i) amplifier placed before normal dispersion fiber in dispersion map; (ii) amplifier placed after normal dispersion fiber in dispersion map. Solid curves, variational approximation; asterisks, numerical simulation.

Equations (5)

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

iAz=12β22At2-γA2A-iα2A,
iA1z=12β22A1t2-γA12+2A22A1-iα2A1,iA2z=12β22A2t2-γA22+2A12A2-iα2A2.
d2ΔTdz2=22πβ2γWΔT2exp-ΔT2/2τ02τ0/ΔT3,
d2τ0dz2=β22τ03+122πβ2γWτ02+2πβ2γWτ021-ΔT2τ02×exp-ΔT2/2τ02,
dΔfdz=-1π2πγWΔT2Fτ0/ΔT,Fx=exp-1/2x2x3.

Metrics