Abstract

A dispersion-managed optical system with stepwise periodic variation of dispersion is studied in the framework of a path-averaged Gabitov–Turitsyn equation. The soliton solution is obtained by means of iterating the path-averaged equation. The dependence of soliton parameters on dispersion map strength is investigated, together with the oscillating tails of the soliton.

© 2000 Optical Society of America

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References

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  1. C. Lin, H. Kogelnik, and L. G. Cohen, Opt. Lett. 5, 476 (1980).
    [CrossRef] [PubMed]
  2. M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995).
    [CrossRef]
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    [CrossRef]
  4. I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996); JETP Lett. 63, 861 (1996).
    [CrossRef]
  5. S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
    [CrossRef] [PubMed]
  6. P. V. Mamyshev and N. A. Mamysheva, Opt. Lett. 24, 1454 (1999).
    [CrossRef]
  7. L. F. Mollenauer, P. V. Mamyshev, J. Gripp, M. J. Neubelt, N. Mamysheva, L. Grüner-Nielsen, and T. Veng, Opt. Lett. 25, 704 (2000).
    [CrossRef]
  8. S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.
  9. M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
    [CrossRef]
  10. S. K. Turitsyn and V. K. Mezentsev, JETP Lett. 67, 640 (1998); S. K. Turitsyn, Phys. Rev. E 58, 1256 (1998).
    [CrossRef]
  11. T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998).
    [CrossRef]
  12. V. K. Mezentsev, Institute of Automation and Electrometry, Russian Academy of Sciences, 630090, Novosibirsk, Russia (personal communication, 1999).
  13. V. E. Zakharov, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 73; V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578 (1999).
    [CrossRef]

2000 (1)

1999 (1)

1998 (3)

M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
[CrossRef]

S. K. Turitsyn and V. K. Mezentsev, JETP Lett. 67, 640 (1998); S. K. Turitsyn, Phys. Rev. E 58, 1256 (1998).
[CrossRef]

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998).
[CrossRef]

1997 (1)

1996 (2)

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

I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996); JETP Lett. 63, 861 (1996).
[CrossRef]

1995 (1)

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

1980 (1)

Ablowitz, M. J.

Bennion, I.

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

Biondini, G.

Blow, K. J.

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

Cohen, L. G.

Doran, N. J.

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

S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.

Forysiak, W.

S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.

Gabitov, I.

Gripp, J.

Grüner-Nielsen, L.

Hasegawa, A.

Kaup, D. J.

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998).
[CrossRef]

Knox, F. M.

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

Kogelnik, H.

Kubota, H.

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

Kumar, S.

Lakoba, T.

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998).
[CrossRef]

Lin, C.

Mamyshev, P. V.

Mamysheva, N.

Mamysheva, N. A.

Mezentsev, V. K.

S. K. Turitsyn and V. K. Mezentsev, JETP Lett. 67, 640 (1998); S. K. Turitsyn, Phys. Rev. E 58, 1256 (1998).
[CrossRef]

S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.

V. K. Mezentsev, Institute of Automation and Electrometry, Russian Academy of Sciences, 630090, Novosibirsk, Russia (personal communication, 1999).

Mollenauer, L. F.

Nakazawa, M.

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

Neubelt, M. J.

Nijhof, J. H. B.

S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.

Schäfer, T.

S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.

Smith, N. J.

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

Turitsyn, S. K.

S. K. Turitsyn and V. K. Mezentsev, JETP Lett. 67, 640 (1998); S. K. Turitsyn, Phys. Rev. E 58, 1256 (1998).
[CrossRef]

I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996); JETP Lett. 63, 861 (1996).
[CrossRef]

S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.

Veng, T.

Zakharov, V. E.

V. E. Zakharov, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 73; V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578 (1999).
[CrossRef]

Electron. Lett. (3)

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

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

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998).
[CrossRef]

JETP Lett. (1)

S. K. Turitsyn and V. K. Mezentsev, JETP Lett. 67, 640 (1998); S. K. Turitsyn, Phys. Rev. E 58, 1256 (1998).
[CrossRef]

Opt. Lett. (6)

Other (3)

V. K. Mezentsev, Institute of Automation and Electrometry, Russian Academy of Sciences, 630090, Novosibirsk, Russia (personal communication, 1999).

V. E. Zakharov, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 73; V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578 (1999).
[CrossRef]

S. K. Turitsyn, N. J. Doran, J. H. B. Nijhof, V. K. Mezentsev, T. Schäfer, and W. Forysiak, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabnitz, eds. (Springer-Verlag, Berlin, 1999), p. 91.

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Figures (2)

Fig. 1
Fig. 1

Time dependence of first, second, third, and fourth iterations (curves 1, 2, 3, and 4, respectively).

Fig. 2
Fig. 2

First iteration A1t (curve 1) versus Eq. (12) (curve 2).

Equations (12)

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

iuz+dzutt+u2u=0,
iψ^zω-ω2dψ^+12π2sin sω1ω2sω1ω2ψ^ω1+ω×ψ^ω2+ωψ^*ω1+ω2+ωdω1dω2=0,
iψz+dψtt-12πsCit1t2sψt1+tψt2+t×ψ*t1+t2+tdt1dt2=0,
AGauss=p exp-β2t2,
-λA+dAtt=12πsCit1t2sAt1+t×At2+tAt1+t2+tdt1dt2.
sin sω1ω2sω1ω2=12s-ssexpisω1ω2ds
A1=p1-s˜s˜exp-β/23i+s/i+3st21-2is+3s2ds, A2=p2-s˜s˜exp-qt2f1f2f3gdsds1ds2ds3, A3=,
p1=3parcsinh3s˜-i2+c.c., Att1|t=0=-p12β32s˜+i3s˜-i+36arcsinh3s˜-i2+c.c.,
s˜=βs=2.393
λ=p2×0.482....
A1expβt22p1-8.211×10-2t˜4-2.654×10-2t˜6-4.383×10-3t˜8-3.946×10-4t˜10+.
A|t=p116β2t2exp-β23i+s˜i+3s˜t23s˜+is˜-i3/2×-4is˜-i+3s˜-5i3s˜+it2+c.c.+O1t6.

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