Abstract

We analyze pulse propagation in an optical fiber employing a periodic dispersion map. Second-order averaging is used to determine a general evolution equation valid for both return-to-zero and non-return-to-zero pulses in dispersion-managed systems. The equation is then applied to the case of solitons, and an analytic expression for the power enhancement arising from the dispersion management is obtained.

© 1997 Optical Society of America

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References

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  1. C. Kurtzke, IEEE Photonics Technol. Lett. 5, 1250 (1993).
    [CrossRef]
  2. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
    [CrossRef]
  3. M. Suzuki, I. Morita, N. Edgawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [CrossRef]
  4. M. Nakazawa and H. Kubota, Jpn. J. Appl. Phys. Lett. 34, L681 (1995).
    [CrossRef]
  5. I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
    [CrossRef]
  6. N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996).
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  9. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  10. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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  14. T. Kano, J. Phys. Soc. Jpn. 58, 4322 (1989).
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1996 (5)

1995 (4)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

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

M. Nakazawa and H. Kubota, Jpn. J. Appl. Phys. Lett. 34, L681 (1995).
[CrossRef]

Y. Kodama, J. Stat. Phys. 39, 597 (1995).
[CrossRef]

1993 (2)

C. Kurtzke, IEEE Photonics Technol. Lett. 5, 1250 (1993).
[CrossRef]

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[CrossRef]

1991 (1)

1989 (1)

T. Kano, J. Phys. Soc. Jpn. 58, 4322 (1989).
[CrossRef]

Akiba, S.

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

Bennion, I.

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

Blow, K. J.

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

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[CrossRef]

Bronski, J. C.

Chraplyvy, A. R.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Cole, J. D.

J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer, New York, 1981).
[CrossRef]

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Doran, N. J.

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

N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996).
[CrossRef] [PubMed]

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

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[CrossRef]

Edgawa, N.

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

Forghieri, F.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Forysiak, W.

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

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[CrossRef]

Gabitov, I. R.

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Hasegawa, A.

Kano, T.

T. Kano, J. Phys. Soc. Jpn. 58, 4322 (1989).
[CrossRef]

Kevorkian, J.

J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer, New York, 1981).
[CrossRef]

Knox, F. M.

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

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

Kodama, Y.

Kubota, H.

M. Nakazawa and H. Kubota, Jpn. J. Appl. Phys. Lett. 34, L681 (1995).
[CrossRef]

Kurtzke, C.

C. Kurtzke, IEEE Photonics Technol. Lett. 5, 1250 (1993).
[CrossRef]

Kutz, J. N.

Morita, I.

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

Nakazawa, M.

M. Nakazawa and H. Kubota, Jpn. J. Appl. Phys. Lett. 34, L681 (1995).
[CrossRef]

Smith, N. J.

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]

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Turitsyn, S. K.

Yamamoto, S.

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

Electron. Lett. (3)

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

W. Forysiak, K. J. Blow, and N. J. Doran, Electron. Lett. 29, 1225 (1993).
[CrossRef]

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

IEEE Photonics Technol. Lett. (1)

C. Kurtzke, IEEE Photonics Technol. Lett. 5, 1250 (1993).
[CrossRef]

J. Lightwave Technol. (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

J. Phys. Soc. Jpn. (1)

T. Kano, J. Phys. Soc. Jpn. 58, 4322 (1989).
[CrossRef]

J. Stat. Phys. (1)

Y. Kodama, J. Stat. Phys. 39, 597 (1995).
[CrossRef]

Jpn. J. Appl. Phys. Lett. (1)

M. Nakazawa and H. Kubota, Jpn. J. Appl. Phys. Lett. 34, L681 (1995).
[CrossRef]

Opt. Lett. (5)

Other (1)

J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer, New York, 1981).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Comparison of pulse shapes obtained with the numerical (solid curve), analytical (dotted curve), and path-averaged nonlinear Schrödinger equation (dashed curve) solutions. Here β¨2-β¨1=1.82 ps2/km-1. For β¨2-β¨1 above 2.9 ps2/km-1, however, the analytical solution develops two peaks.

Fig. 2
Fig. 2

Comparison between the numerical (solid curve) and analytical (dashed curve) results for the soliton power enhancement that is due to a two-step dispersion map. The parameters are as described in the text, and the pulse energy has been normalized by -3.52β¨/γτFWHM.

Equations (16)

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E=-3.52β¨γτFWHM1+0.7×β¨1-β¨l1-β¨2-β¨l2τFWHM22,
iuz-12σz2ut2+u2u=0.
Uz=Uz0+Uz1+2Uz2+.
iu1ζ+iUz0-12σζ2Ut2+U2U=0.
iUz0=12σ2Ut2-U2U,
u1=-i2μ1ζ-μ12Ut2,
u2=-μ2ζ-μ2U2Utt*+2UUt2+Ut2U*-18μ1ζ-μ12-2MUtttt,
iUz2=MU2Utttt*+6UUtUttt*+2U2tUttt+5UUtt2+7Ut2Utt*+10Ut2Utt+52Utt2U*.
iUz-12σUtt+U2U=2MU2Utttt*+6UUtUttt*+2U2tUttt+5UUtt2+7Ut2Utt*+10Ut2Utt+52Utt2U*+.
q=U+2M14Utttt+1σUtU2t+UUUt*t+.
iqz-12σ2qt2+q2q=2Mσ×q2q2t2q2+12q2t2q4+.
R=-σ1/2αsechαt+432Mα4×2sechαt-sech3αt-sech5αt+,
u=expiκz-σ1/2αsechαt+132Mα4×8sechαt+8sech3αt-19sech5αt-2σμ2α44sech3αt-5sech5αt+.
α=1.761+1.29241M-21σμ2+.
-u2dt=-3.52σ×1+273.53M-27.11σμ2+.
E=-3.52β¨γτFWHM1+0.766S2-0.564l1+2l2τFWHM2β¨S+,

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