Abstract

We present an analytic description of dispersion-managed soliton propagation based on split-step and variational models. Using these models, we derive the threshold map strength for the existence of dispersion-managed solitons in the normal dispersion regime and obtain a bound on the maximum normal average dispersion.

© 1998 Optical Society of America

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  1. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
    [CrossRef]
  2. F. Favre, D. L. Guen, and T. Georges, Electron. Lett. 34, 201 (1998).
    [CrossRef]
  3. N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.
  4. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
    [CrossRef]
  5. J. N. Kutz and J. S. G. Evangelides, Opt. Lett. 23, 685 (1998).
    [CrossRef]
  6. S. K. Turitsyn and E. G. Shapiro, Opt. Lett. 23, 682 (1998).
    [CrossRef]
  7. V. S. Grigoryan and C. R. Menyuk, Opt. Lett. 23, 609 (1998).
    [CrossRef]
  8. T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
    [CrossRef]
  9. M. J. Potasek, G. P. Agrawal, and S. C. Pinault, J. Opt. Soc. Am. B 3, 205 (1986).
    [CrossRef]
  10. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Sec. 2.4.1.
  11. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  12. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
    [CrossRef]
  13. B. A. Malomed, Opt. Commun. 136, 313 (1997).
    [CrossRef]
  14. A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
    [CrossRef]
  15. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
    [CrossRef] [PubMed]
  16. M. Matsumoto, Opt. Lett. 22, 1238 (1997).
    [CrossRef] [PubMed]

1998

F. Favre, D. L. Guen, and T. Georges, Electron. Lett. 34, 201 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

J. N. Kutz and J. S. G. Evangelides, Opt. Lett. 23, 685 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, Opt. Lett. 23, 682 (1998).
[CrossRef]

V. S. Grigoryan and C. R. Menyuk, Opt. Lett. 23, 609 (1998).
[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
[CrossRef]

1997

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

B. A. Malomed, Opt. Commun. 136, 313 (1997).
[CrossRef]

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

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

1996

1986

1983

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

Agrawal, G. P.

M. J. Potasek, G. P. Agrawal, and S. C. Pinault, J. Opt. Soc. Am. B 3, 205 (1986).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Sec. 2.4.1.

Anderson, D.

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

Berntson, A.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
[CrossRef]

Bonato, L.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Cavaciuti, A.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Corsini, R.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Davis, G.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
[CrossRef]

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]

Evangelides, J. S. G.

Favre, F.

F. Favre, D. L. Guen, and T. Georges, Electron. Lett. 34, 201 (1998).
[CrossRef]

Fee, J.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
[CrossRef]

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]

Franco, P.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Gabitov, I.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

Georges, T.

F. Favre, D. L. Guen, and T. Georges, Electron. Lett. 34, 201 (1998).
[CrossRef]

Grasso, G.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Grigoryan, V. S.

Guen, D. L.

F. Favre, D. L. Guen, and T. Georges, Electron. Lett. 34, 201 (1998).
[CrossRef]

Kaup, D. J.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[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]

Kutz, J. N.

Lakoba, T. I.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Macchi, M.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Malomed, B. A.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

B. A. Malomed, Opt. Commun. 136, 313 (1997).
[CrossRef]

Matsumoto, M.

Menyuk, C. R.

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
[CrossRef]

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

Pinault, S. C.

Potasek, M. J.

Robinson, N.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Schiffini, A.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Shapiro, E. G.

S. K. Turitsyn and E. G. Shapiro, Opt. Lett. 23, 682 (1998).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

Smith, N. J.

Turitsyn, S. K.

S. K. Turitsyn and E. G. Shapiro, Opt. Lett. 23, 682 (1998).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

Yang, J.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Zuccala, A.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

Electron. Lett.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

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

F. Favre, D. L. Guen, and T. Georges, Electron. Lett. 34, 201 (1998).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

B. A. Malomed, Opt. Commun. 136, 313 (1997).
[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. E

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Sec. 2.4.1.

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, in Optical Fiber Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD-19.

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Figures (2)

Fig. 1
Fig. 1

Evolution over two periods of the map for zero average dispersion. Solid curve, pulse width; dashed curve, square of the bandwidth.

Fig. 2
Fig. 2

Square of the bandwidth in the midpoints of the fibers versus the peak power for net zero dispersion. +,×, numerical data from Ref. 1; dashed lines, Eq. (17).

Equations (17)

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

ut=P exp-1+iχt2/2T2+iϕ,
χ1=0+βa,nla,nΩa,n2/4,
Ωa,n2TNL2=1+χ12,
χ2=χ1+Ela,n/2TNL,
Ωb2TNL2=1+χ22,
χa,n=χ2+βa,nla,nΩb2/4,
ca,n=βa,nla,nΩb2/4,
Ωa,n=Ωb-γEla,nΩb2ca,n1+ca,n2-3/2
χa,n=2ca,n-12γEla,nΩb1-ca,n21+ca,n2-3/2.
dχ/dz=βΩ2+γE/T,
dT/dz=βχ/T,
dΩ/dz=γEΩ2χ/1+χ23/2.
Ωa,n=Ωb1-γEΩbla,n4ca,n×1-11+4ca,n21/2,
χa,n=2ca,n+γEΩbla,n1-11+4ca,n21/2-arsinh 2ca,n4ca,n.
β=γEΩbarcsinh 2c2c-21+4c21/2.
βeff=βΩ2Ω2β-2γE3Ωb1-1+4c2-1/2,
lβωrms,a,n2=lβω021±γPa,nl/ϕ0,

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