Abstract

A dispersion-managed optical system with stepwise periodic variation of dispersion is studied in a strong dispersion map limit in the framework of the path-averaged Gabitov–Turitsyn equation. The soliton solution is obtained by analytical and numerical iteration of the path-averaged equation. An efficient numerical algorithm for finding a DM soliton shape is developed. The envelope of soliton oscillating tails is found to decay exponentially in time, and the oscillations are described by a quadratic law.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]
  3. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  4. I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
    [CrossRef]
  5. S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
    [CrossRef] [PubMed]
  6. T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998).
    [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, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
    [CrossRef]
  9. M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
    [CrossRef]
  10. P. M. Lushnikov, Opt. Lett. 25, 1144 (2000).
    [CrossRef]
  11. D. E. Pelinovsky, Phys. Rev. E 62, 4283 (2000).
    [CrossRef]
  12. V. I. Petviashvili and O. A. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere (Gordon & Breach, Philadelphia, Pa., 1992), p. 248.
  13. V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
    [CrossRef]
  14. V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, Physica D 152, 794 (2001).
    [CrossRef]
  15. P. M. Lushnikov, JETP Lett. 72, 111 (2000).
    [CrossRef]

2001 (1)

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, Physica D 152, 794 (2001).
[CrossRef]

2000 (5)

P. M. Lushnikov, JETP Lett. 72, 111 (2000).
[CrossRef]

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]

D. E. Pelinovsky, Phys. Rev. E 62, 4283 (2000).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
[CrossRef]

P. M. Lushnikov, Opt. Lett. 25, 1144 (2000).
[CrossRef]

1999 (1)

S. K. Turitsyn, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
[CrossRef]

1998 (2)

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

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

1997 (1)

1996 (2)

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

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (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.

S. K. Turitsyn, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
[CrossRef]

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

Gabitov, I.

Grenier, E.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, Physica D 152, 794 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
[CrossRef]

Gripp, J.

Grüner-Nielsen, L.

Hasegawa, A.

Hesthaven, J. S.

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
[CrossRef]

Jones, C. K. R. T.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, Physica D 152, 794 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
[CrossRef]

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.

Lushnikov, P. M.

P. M. Lushnikov, JETP Lett. 72, 111 (2000).
[CrossRef]

P. M. Lushnikov, Opt. Lett. 25, 1144 (2000).
[CrossRef]

Mamyshev, P. V.

Mamysheva, N.

Mezentsev, V. K.

S. K. Turitsyn, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
[CrossRef]

Mollenauer, L. F.

Nakazawa, M.

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

Neubelt, M. J.

Pelinovsky, D. E.

D. E. Pelinovsky, Phys. Rev. E 62, 4283 (2000).
[CrossRef]

Petviashvili, V. I.

V. I. Petviashvili and O. A. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere (Gordon & Breach, Philadelphia, Pa., 1992), p. 248.

Pokhotelov, O. A.

V. I. Petviashvili and O. A. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere (Gordon & Breach, Philadelphia, Pa., 1992), p. 248.

Schäfer, T.

S. K. Turitsyn, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
[CrossRef]

Smith, N. J.

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

Spatschek, K. H.

S. K. Turitsyn, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
[CrossRef]

Turitsyn, S. K.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, Physica D 152, 794 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
[CrossRef]

S. K. Turitsyn, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
[CrossRef]

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

Veng, T.

Zharnitsky, V.

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, Physica D 152, 794 (2001).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
[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)

P. M. Lushnikov, JETP Lett. 72, 111 (2000).
[CrossRef]

Opt. Commun. (1)

S. K. Turitsyn, T. Schäfer, N. J. Doran, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. E (2)

D. E. Pelinovsky, Phys. Rev. E 62, 4283 (2000).
[CrossRef]

V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, Phys. Rev. E 62, 7358 (2000).
[CrossRef]

Physica D (1)

V. Zharnitsky, E. Grenier, C. K. R. T. Jones, and S. K. Turitsyn, Physica D 152, 794 (2001).
[CrossRef]

Other (1)

V. I. Petviashvili and O. A. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere (Gordon & Breach, Philadelphia, Pa., 1992), p. 248.

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 (2)

Fig. 1
Fig. 1

TRMS for (a) s=1, d=0.01 and (b) d=-0.01. Branches I and II for d=-0.01 correspond to two branches of the analytical solution.

Fig. 2
Fig. 2

DM soliton shape (curve  1) versus Eq.  (11) (curve  2) for d=0, s=1, and λ=1. At is an even function.

Equations (13)

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

iuz+dzutt+u2u=0,
iψ^zω-ω2dψ^+Rψ^,ω=0,
Rψ^,ω=12π2sinsΔ/2sΔ/2ψ^ω1ψ^ω2×ψ^*ω3δω1+ω2-ω3-ωdω1dω2dω3,
-λA+dAtt=12πsCit1t2/sAt1+t×At2+tAt1+t2+tdt1dt2,
AGauss=pexp-β2t2,
-λAGauss+dAGausstt+p32s˜-s˜s˜exp-β23i+si+3st21-2is+3s21/2ds=Acorr,
λ=-βd+p223s̃arcsinh3s̃-i2+c.c.,λ=-3βd+2p23s̃s̃+i3s̃-i1/2+312arcsinh3s̃-i2+c.c.,
A^n+1ω=Qn3/2RA^n,ω+d-dω2A^nωλ+dω2,
Qn=F^-1λ+dω2λ+dω2A^nωF^-1RA^,ωλ+dω2|t=0,
sinsΔ/2sΔ/2=1s-s/2s/2expisΔds,
RA^,ω=1s2π2-s/2s/2dsexp-isω2A^sω1×A^sω2A^s*ω3δω1+ω2-ω3-ωdω1dω2dω3,
F^-1RA^,ω=1s-s/2s/2dsGsΨst,
Aasympt=ftcost2a0+atexp-bt,

Metrics