Abstract

We theoretically analyzed the Gordon–Haus timing jitter in a periodically dispersion-compensated optical transmission system as a result of upgrading a preinstalled uniform-dispersion system. We show that the enhanced peak power for a large dispersion difference in the period reduces the frequency shift induced by noise, and a proper setting of the receiver position further reduces the timing jitter.

© 1998 Optical Society of America

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References

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  1. M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995).
    [CrossRef]
  2. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [CrossRef]
  3. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  4. A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
    [CrossRef]
  5. N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
    [CrossRef]
  6. G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, Opt. Lett. 22, 513 (1997).
    [CrossRef] [PubMed]
  7. M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
    [CrossRef]
  8. M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
    [CrossRef]
  9. Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
    [CrossRef]
  10. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  11. S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
    [CrossRef]
  12. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  13. S. Kumar and F. Lederer, Opt. Lett. 22, 1870 (1997).
    [CrossRef]
  14. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
    [CrossRef] [PubMed]
  15. N. J. Doran, N. J. Smith, W. Forysiak, and F. M. Knox, in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–14.
    [CrossRef]

1997

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, Opt. Lett. 22, 513 (1997).
[CrossRef] [PubMed]

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[CrossRef]

Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
[CrossRef]

S. Kumar and F. Lederer, Opt. Lett. 22, 1870 (1997).
[CrossRef]

1996

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[CrossRef]

1995

M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995).
[CrossRef]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

1986

1983

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Aceves, A. B.

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

Akiba, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Carter, G. M.

Cole, M. J.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[CrossRef]

Doran, N. J.

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

N. J. Doran, N. J. Smith, W. Forysiak, and F. M. Knox, in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–14.
[CrossRef]

Durkin, M.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[CrossRef]

Edagawa, N.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Forysiak, W.

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

N. J. Doran, N. J. Smith, W. Forysiak, and F. M. Knox, in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–14.
[CrossRef]

Golovchenko, E. A.

Gordon, J. P.

Hasegawa, A.

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Haus, H. A.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

Ibsen, M.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[CrossRef]

Jacob, J. M.

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

N. J. Doran, N. J. Smith, W. Forysiak, and F. M. Knox, in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–14.
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
[CrossRef]

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

Kubota, H.

M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995).
[CrossRef]

Kumar, S.

Laming, R. I.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[CrossRef]

Lederer, F.

Maruta, A.

Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
[CrossRef]

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Matsumoto, M.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

Menyuk, C. R.

Morita, I.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Nakazawa, M.

M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995).
[CrossRef]

Pilipetskii, A. N.

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

N. J. Doran, N. J. Smith, W. Forysiak, and F. M. Knox, in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–14.
[CrossRef]

Suzuki, M.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Taga, H.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Wabnitz, S.

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

Yamamoto, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Electron. Lett.

M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995).
[CrossRef]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[CrossRef]

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

Opt. Fiber Technol.

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. A

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Other

N. J. Doran, N. J. Smith, W. Forysiak, and F. M. Knox, in Physics and Applications of Optical Solitons in Fibres ’95, A. Hasegawa, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–14.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Upgraded models of preinstalled systems.

Fig. 2
Fig. 2

Mean square of the timing jitter obtained by use of Eqs.  (16) and (17) (top) and by use of the numerical simulation (bottom).

Equations (17)

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

iqZ+DZ2qTT+q2q=iGZq+iR
DZ=Dx+αˆxn=1MδZ-2n-1Za, GZ=-Γ+Gan=1NδZ-nZa.
iuZ+DZ2uTT+AZu2u=iRAZ,
uZ, T=aZexp-τ2Z, T+iφZ, T,
dadZ=-12DaC+2πA-ReRe-iφ×3-4τ2e-τ2dτ,
dpdZ=-DpC+pa2/πA-ReRe-iφ×1-4τ2e-τ2dτ,
dCdZ=D4p4-C2-2Aa2p2-4p2a2/πA×-ImRe-iφ1-4τ2e-τ2dτ,
dκdZ=2ap2/πA-C ReRe-iφ+2p2 ImRe-iφ×τe-τ2dτ,
dT0dZ=Dκ+2ap2/πA-ReRe-iφτe-τ2dτ,
dθdZ=D2κ2-2p2+52Aa28+ap2πA×-4κ ReRe-iφτ+p ImRe-iφ×3-4τ2e-τ2dτ.
R=ra expiκZT-T0Z+iθZδZ-nZa,
dκdZ=2ap2/πAδZ-nZa-CrR+2p2rI×cosCτ22p2+CrI-2p2rRsinCτ22p2τe-τ2dτ,
dT0dZ=Dκ.
rirj=n0δijδT-T,  i, j=R or I,
n0=2π2c2hnspnNLts1.763d¯λ4AeffG0-1.
κ2nZa=2π4p4nZa+C2nZaa2nZapnZan0SG0,
t02=1.763λ22πcts2n=1Nκ2nzanzaNzadzdz2.

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