Abstract

We derive an expression for the timing jitter of a soliton owing to amplifier noise in dispersion-managed fiber systems. We show that the timing jitter is a function of the pulse width as well as of the chirp at the amplifier location and that it can be minimized by a proper choice of the amplifier position relative to the dispersion map.

© 1997 Optical Society of America

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References

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  1. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [Crossref] [PubMed]
  2. W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
    [Crossref]
  3. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [Crossref]
  4. M. Nakazawa, H. Kubota, and K. Tamura, IEEE Photon. Technol. Lett. 8, 452 (1996).
    [Crossref]
  5. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [Crossref]
  6. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
    [Crossref]
  7. I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 863 (1996); Opt. Lett. 21, 327 (1996).
    [Crossref]
  8. T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (1997).
    [Crossref]
  9. G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, Opt. Lett. 22, 513 (1997).
    [Crossref] [PubMed]
  10. N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
    [Crossref]
  11. S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
    [Crossref] [PubMed]
  12. Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
    [Crossref]
  13. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, New York, 1995), p. 117.
  14. D. Marcuse, IEEE J. Lightwave Technol. 10, 273 (1992).
    [Crossref]

1997 (4)

1996 (4)

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

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 863 (1996); Opt. Lett. 21, 327 (1996).
[Crossref]

M. Nakazawa, H. Kubota, and K. Tamura, IEEE Photon. Technol. Lett. 8, 452 (1996).
[Crossref]

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

1995 (2)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[Crossref]

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

1993 (1)

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[Crossref]

1992 (1)

D. Marcuse, IEEE J. Lightwave Technol. 10, 273 (1992).
[Crossref]

1986 (1)

Akiba, S.

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

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[Crossref]

Carter, G. M.

Charbonnier, B.

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (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]

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[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]

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[Crossref]

Gabitov, I.

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 863 (1996); Opt. Lett. 21, 327 (1996).
[Crossref]

Georges, T.

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (1997).
[Crossref]

Golovchenko, E. A.

Gordon, J. P.

Hasegawa, A.

S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
[Crossref] [PubMed]

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, New York, 1995), p. 117.

Haus, H. A.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[Crossref]

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

Ippen, E. P.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[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]

Kodama, Y.

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

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, New York, 1995), p. 117.

Kubota, H.

M. Nakazawa, H. Kubota, and K. Tamura, IEEE Photon. Technol. Lett. 8, 452 (1996).
[Crossref]

Kumar, S.

Marcuse, D.

D. Marcuse, IEEE J. Lightwave Technol. 10, 273 (1992).
[Crossref]

Maruta, A.

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, H. Kubota, and K. Tamura, IEEE Photon. Technol. Lett. 8, 452 (1996).
[Crossref]

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[Crossref]

Pilipetskii, A. N.

Smith, 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]

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]

Tamura, K.

M. Nakazawa, H. Kubota, and K. Tamura, IEEE Photon. Technol. Lett. 8, 452 (1996).
[Crossref]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[Crossref]

Turitsyn, S. K.

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 863 (1996); Opt. Lett. 21, 327 (1996).
[Crossref]

Yamamoto, S.

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

Electron. Lett. (4)

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[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]

IEEE J. Lightwave Technol. (1)

D. Marcuse, IEEE J. Lightwave Technol. 10, 273 (1992).
[Crossref]

IEEE J. Quantum Electron. (1)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[Crossref]

IEEE Photon. Technol. Lett. (2)

M. Nakazawa, H. Kubota, and K. Tamura, IEEE Photon. Technol. Lett. 8, 452 (1996).
[Crossref]

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (1997).
[Crossref]

JETP Lett. (1)

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 863 (1996); Opt. Lett. 21, 327 (1996).
[Crossref]

Opt. Lett. (4)

Other (1)

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, New York, 1995), p. 117.

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Figures (2)

Fig. 1
Fig. 1

Mean-square frequency shift times A2 as a function of amplifier location in units of Zd. Dashed curve, d1=30 (-3 ps2/km); d2=-28 (2.8 ps2/km); peak power, 5.76 (1.08 mW); solid curve, d1=40 (-4 ps2/km), d2=-38 (3.8 ps2/km); peak power, 8.76 (1.64 mW). Zd=0.069 72 km. An unchirped Gaussian pulse is assumed to be the initial condition.

Fig. 2
Fig. 2

Variance in pulse arrival time versus distance. Solid curves, theoretical result; dashed curves, numerical simulation of Eq.  (1). The top curves correspond to the case of sech solitons; the lower curves, to the case of the dispersion-managed soliton. For the case of the dispersion-managed soliton d1=30, d2=-28, Zd=0.069.

Equations (19)

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iqZ+dZ22qT2+q2q=iRT, Z.
dZ=d1 for Zd/4Z3Zd/4=d2 elsewhere in 0, Zd,
q=pZνpZT-T0Z, Zexp-iΩT+iCZ×T-T0Z2/2.
dT0/dZ=-dZΩ.
iνZ+dZp222ντ2+pν2-KZ2τ2ν=Ω2d2ν,
iVZ+D022Vτ2+D1V2-D2τ2V=D3V.
Vsτ, Z=AfτexpiλZ
ddZq2dT=2 ReRq*dT, ddZImqqT*dT=2 ImRqT*dT.
dAdZ=1pg0ReRfτexpiθdτ,
dΩdZ=2pg0AImRdfτdτexpiθdτ-Cp2ReRfττ expiθdτ,
δΩ=2prg0AImΔqdfτdτexpiθexpiΩrτ/prdτ-Crpr2ReΔqτfτexpiθiΩrτ/prdτ,
δΩ=4πprg0AImg1ω-ωprηωdω-Crpr2Reg2ω-ωprηωdω,
ηωηω=0, ηωη*ωSηδω-ω.
δΩ2=4πpr2NspG-1N0g02A2g1ω2dω+Cr2pr4g2ω2dω-2Crpr2Img1ωg2*ωdω.
δΩ2=NspG-12πN0 A24pr2+Cr2pr2.
δΩ2=2Nsppr2G-1Ω¯2N0E,
Ω¯2=2π/g0Ω2 f˜Ω2dΩ,
δT02=nδΩn2[nZaLdZdZ]2.
δC=-2prAg0ImΔqdfτdTTexp-iθdT+ReΔqΩr-CrT-TorT+Crfτexp-iθdT.

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