Abstract

It is shown how a straightforward regular perturbative analysis can be used to derive an integral equation for the spectral shape of a dispersion-managed soliton that takes fiber loss and amplification into account without resorting to averaging. Using functional analysis, one can then find an accurate approximate Gaussian solution that should prove useful for the design of a dispersion-managed transmission link.

© 2000 Optical Society of America

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References

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  1. N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 15, 1808 (1997), and references therein.
    [CrossRef]
  2. M. Suzuki, I. Morita, N. Edgawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [CrossRef]
  3. S. K. Turitsyn and E. G. Shapiro, Opt. Fiber Technol. 4, 151 (1998); T. Georges, J. Opt. Soc. Am. B 15, 1553 (1998); S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999); M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
    [CrossRef]
  4. T. Lakoba and D. J. Kaup, Phys. Rev. E 58, 6728 (1998); S. K. Turitsyn and E. G. Shapiro, J. Opt. Soc. Am. B 16, 1321 (1999); H. A. Haus and Y. Chen, J. Opt. Soc. Am. B 16, 889 (1999).
    [CrossRef]
  5. P.-A. Bélanger and C. Paré, J. Lightwave Technol. 17, 445 (1999).
    [CrossRef]
  6. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
    [CrossRef]
  7. M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
    [CrossRef]
  8. C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, Phys. Rev. E 60, 4836 (1999).
    [CrossRef]
  9. S. K. Turitsyn, J. H. B. Nijhof, V. K. Mezentsev, and N. J. Doran, Opt. Lett. 24, 1871 (1999).
    [CrossRef]
  10. T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 597 (1997); P. Harper, S. B. Alleston, I. Ennion, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
    [CrossRef]
  11. A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).
  12. In Ref. 6 a similar principle comes out of an averaged Hamiltonian analysis but is not used for deriving approximate analytical solutions of the underlying IE.

1999

1998

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

S. K. Turitsyn and E. G. Shapiro, Opt. Fiber Technol. 4, 151 (1998); T. Georges, J. Opt. Soc. Am. B 15, 1553 (1998); S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999); M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

T. Lakoba and D. J. Kaup, Phys. Rev. E 58, 6728 (1998); S. K. Turitsyn and E. G. Shapiro, J. Opt. Soc. Am. B 16, 1321 (1999); H. A. Haus and Y. Chen, J. Opt. Soc. Am. B 16, 889 (1999).
[CrossRef]

1997

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

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 15, 1808 (1997), and references therein.
[CrossRef]

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 597 (1997); P. Harper, S. B. Alleston, I. Ennion, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

1995

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

Ablowitz, M. J.

Akiba, S.

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

Bélanger, P.-A.

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, Phys. Rev. E 60, 4836 (1999).
[CrossRef]

P.-A. Bélanger and C. Paré, J. Lightwave Technol. 17, 445 (1999).
[CrossRef]

Biondini, G.

Charbonnier, B.

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 597 (1997); P. Harper, S. B. Alleston, I. Ennion, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

Doran, N. J.

S. K. Turitsyn, J. H. B. Nijhof, V. K. Mezentsev, and N. J. Doran, Opt. Lett. 24, 1871 (1999).
[CrossRef]

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 15, 1808 (1997), and references therein.
[CrossRef]

Edgawa, N.

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

Forysiak, W.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 15, 1808 (1997), and references therein.
[CrossRef]

Gabitov, I.

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

Georges, T.

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 597 (1997); P. Harper, S. B. Alleston, I. Ennion, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

Kaup, D. J.

T. Lakoba and D. J. Kaup, Phys. Rev. E 58, 6728 (1998); S. K. Turitsyn and E. G. Shapiro, J. Opt. Soc. Am. B 16, 1321 (1999); H. A. Haus and Y. Chen, J. Opt. Soc. Am. B 16, 889 (1999).
[CrossRef]

Knox, F. M.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 15, 1808 (1997), and references therein.
[CrossRef]

Lakoba, T.

T. Lakoba and D. J. Kaup, Phys. Rev. E 58, 6728 (1998); S. K. Turitsyn and E. G. Shapiro, J. Opt. Soc. Am. B 16, 1321 (1999); H. A. Haus and Y. Chen, J. Opt. Soc. Am. B 16, 889 (1999).
[CrossRef]

Lesage, F.

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, Phys. Rev. E 60, 4836 (1999).
[CrossRef]

Mathieu, P.

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, Phys. Rev. E 60, 4836 (1999).
[CrossRef]

Mezentsev, V. K.

Morita, I.

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

Nayfeh, A. H.

A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).

Nijhof, J. H. B.

Paré, C.

P.-A. Bélanger and C. Paré, J. Lightwave Technol. 17, 445 (1999).
[CrossRef]

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, Phys. Rev. E 60, 4836 (1999).
[CrossRef]

Roy, V.

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, Phys. Rev. E 60, 4836 (1999).
[CrossRef]

Shapiro, E. G.

S. K. Turitsyn and E. G. Shapiro, Opt. Fiber Technol. 4, 151 (1998); T. Georges, J. Opt. Soc. Am. B 15, 1553 (1998); S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999); M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

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

Smith, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 15, 1808 (1997), and references therein.
[CrossRef]

Suzuki, M.

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

Taga, H.

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

Turitsyn, S. K.

S. K. Turitsyn, J. H. B. Nijhof, V. K. Mezentsev, and N. J. Doran, Opt. Lett. 24, 1871 (1999).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, Opt. Fiber Technol. 4, 151 (1998); T. Georges, J. Opt. Soc. Am. B 15, 1553 (1998); S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999); M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

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

Yamamoto, S.

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

Electron. Lett.

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

IEEE Photon. Technol. Lett.

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 597 (1997); P. Harper, S. B. Alleston, I. Ennion, and N. J. Doran, Electron. Lett. 35, 2128 (1999).
[CrossRef]

J. Lightwave Technol.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, J. Lightwave Technol. 15, 1808 (1997), and references therein.
[CrossRef]

P.-A. Bélanger and C. Paré, J. Lightwave Technol. 17, 445 (1999).
[CrossRef]

Opt. Fiber Technol.

S. K. Turitsyn and E. G. Shapiro, Opt. Fiber Technol. 4, 151 (1998); T. Georges, J. Opt. Soc. Am. B 15, 1553 (1998); S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999); M. Wald, B. A. Malomed, and F. Lederer, Opt. Commun. 172, 31 (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. E

T. Lakoba and D. J. Kaup, Phys. Rev. E 58, 6728 (1998); S. K. Turitsyn and E. G. Shapiro, J. Opt. Soc. Am. B 16, 1321 (1999); H. A. Haus and Y. Chen, J. Opt. Soc. Am. B 16, 889 (1999).
[CrossRef]

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

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, Phys. Rev. E 60, 4836 (1999).
[CrossRef]

Other

A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).

In Ref. 6 a similar principle comes out of an averaged Hamiltonian analysis but is not used for deriving approximate analytical solutions of the underlying IE.

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Figures (2)

Fig. 1
Fig. 1

Comparison of the launched (solid curve) predicted DM soliton pulse shape (normalized) and the final profile (dashed curve) after 100 periods. Inset, rms pulse-width evolution over one period of the map. See text for details.

Fig. 2
Fig. 2

Comparison of the predicted temporal DM soliton pulse shape (normalized) at the fiber junction according to IE Eq. (5) (solid curves) and the Gaussian approximation given by Eq. (8) (dashed curves). See text for details.

Equations (9)

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

iuz-12ηuττ+σGzu2u=0,
iu0z-12ηu0ττ=0,
iu1z-12ηu1ττ=-σGzu02u0.
u˜n+1fexpiκfu˜nf+idf1df2Rf1,f2,fu˜nf1+f×u˜nf2+fu˜n*f1+f2+f,
Rf1,f2,f=σ1l1expδ1-1δ1+σ2l2 expδ1expδ2-1δ2,
θ-2π2η1l1+η2l2f2W˜f=df1df2Nf1,f2,fW˜f1+fW˜f2+f×W˜*f1+f2+f,
Nf1,f2,f=σ1l1sinhδ1/2δ1/2+σ2l2 expδ1+δ22sinhδ2/2δ2/2.
JU=θU2df-GU2df-12U*dfNUUU*df1df2.
A2.3l1σ1l1+σ2l2θ1/2, a0.30π2l1.

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