Abstract

We determine the power dependence of dispersion-managed solitons on map strength and average dispersion, using a combination of numerical simulations and the variational approach. In particular, we investigate the behavior near zero dispersion and identify the region of existence of dispersion-managed solitons in the average normal-dispersion regime.

© 1998 Optical Society of America

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References

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  1. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
    [CrossRef] [PubMed]
  2. M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
    [CrossRef]
  3. A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
    [CrossRef]
  4. N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
    [CrossRef]
  5. T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 22, 793 (1997).
    [CrossRef] [PubMed]
  6. J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
    [CrossRef]
  7. D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.
  8. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
    [CrossRef]
  9. V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, Opt. Lett. 22, 1609 (1997).
    [CrossRef]
  10. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  11. Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
    [CrossRef]
  12. E. G. Shapiro and S. K. Turitsyn, Opt. Lett. 22, 1544 (1997).
    [CrossRef]
  13. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
    [CrossRef]
  14. M. Matsumoto, Opt. Lett. 22, 1238 (1997).
    [CrossRef] [PubMed]

1997 (9)

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

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 22, 793 (1997).
[CrossRef] [PubMed]

M. Matsumoto, Opt. Lett. 22, 1238 (1997).
[CrossRef] [PubMed]

E. G. Shapiro and S. K. Turitsyn, Opt. Lett. 22, 1544 (1997).
[CrossRef]

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, Opt. Lett. 22, 1609 (1997).
[CrossRef]

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

1996 (3)

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

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

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

1983 (1)

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

Anderson, D.

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

Carter, G. M.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

Devaux, F.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[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]

Favre, F.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[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]

Gabitov, I.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Georges, T.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.

Golovchenko, E. A.

Grigoryan, V. S.

Hasegawa, A.

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

Henry, M.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.

Jacob, J. M.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

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

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]

Kubota, H.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

Kumar, S.

Le Guen, D.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.

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.

Menyuk, C. R.

Moulinard, M. L.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.

Nakazawa, M.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Pilipetskii, A. N.

Sahara, A.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

Shapiro, E. G.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

E. G. Shapiro and S. K. Turitsyn, Opt. Lett. 22, 1544 (1997).
[CrossRef]

Smith, N. J.

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

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

Tamura, K.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

Turitsyn, S. K.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

E. G. Shapiro and S. K. Turitsyn, Opt. Lett. 22, 1544 (1997).
[CrossRef]

Yu, T.

Electron. Lett. (2)

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

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Menyuk, IEEE Photon. Technol. Lett. 9, 130 (1997).
[CrossRef]

M. Nakazawa, H. Kubota, A. Sahara, and K. Tamura, IEEE Photon. Technol. Lett. 8, 1088 (1996).
[CrossRef]

Opt. Commun. (1)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Opt. Fiber Technol. (1)

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

Opt. Lett. (6)

Phys. Rev. A (1)

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

Other (1)

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, F. Devaux, and T. Georges, in Eleventh International Conference on Optics and Optical Fibre Communication (100C/ECOC ’97) (Institution of Electrical Engineers, London, 1997), p. 25.

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Figures (2)

Fig. 1
Fig. 1

Contour plot of β¯ as a function of map strength and peak power. (a) Variational result with lines for β¯=0.01, 0.05, 0.1, 0.2, 0.3, 0.5 (anomalous average dispersion, thinner solid curves), β¯=0 (thicker solid curves), and β¯=-0.001,-0.005,-0.01,-0.02 (normal average dispersion, dashed curves). Dotted curve, example of constant energy. (b) Results from numerical solutions of the full nonlinear Schrödinger equation. Each point represents a calculated stationary solution; the curves join sets of solutions for the same β¯. Shown are β¯=0.2, 0.1, 0.01, β¯=0, and β¯=-0.01,-0.02.

Fig. 2
Fig. 2

Same data as in Fig.  1 but presented differently. (a) The required β¯ as a function of map strength for three different powers. (b) Lines that show how the normalized peak power depends on β¯, where the curves represent constant map strength; right to left, S=0, 2, 4, 6, 8  20, 25.

Equations (8)

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iuz=β2uττ-γu2u,
iUζ=sgnβ2Uττ-γPcTc2βU2U,
δLdτdz=0,
L=iuu*z-u*uz+β2ut2-γu4,
u=Azexp-τ21-ibz2az2+iΦz,
d2ydζ2=1y3+NVA221y2,
z=fyz-f1,
fy=1CCy2-2NVA2y-11/2+NVA2C×lny-NVA2C+Cy2-2NVA2y-11/2,

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