Abstract

Using the equations of motion of pulse width and chirp, we present an analytical method for designing dispersion-managed (DM) fiber systems without optical losses. We show that the initial Gaussian pulse considered for the analytical design of periodically amplified DM fiber systems with losses will propagate as a proximity fixed point. Then averaging the DM soliton fields obtained from the slow dynamics of the proximity fixed point will yield the exact fixed point.

© 2001 Optical Society of America

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References

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  1. V. E. Zakharov and S. Wabnitz, Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1998).
  2. V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, Opt. Lett. 22, 1609 (1997).
    [Crossref]
  3. Y. Chen and H. A. Haus, J. Opt. Soc. Am. B 16, 24 (1999).
    [Crossref]
  4. P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, J. Phys. A 34, L103 (2001).
    [Crossref]
  5. T. S. Yang, W. L. Kath, and S. K. Turitsyn, Opt. Lett. 23, 597 (1998).
    [Crossref]
  6. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
    [Crossref]

2001 (1)

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, J. Phys. A 34, L103 (2001).
[Crossref]

1999 (1)

1998 (1)

1997 (2)

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

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

Chen, Y.

Doran, N. J.

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

Forysiak, W.

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

Golovchenko, E. A.

Grigoryan, V. S.

Haus, H. A.

Kath, W. L.

Knox, F. M.

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

Menyuk, C. R.

Moubissi, A. B.

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, J. Phys. A 34, L103 (2001).
[Crossref]

Nakkeeran, K.

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, J. Phys. A 34, L103 (2001).
[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.

Tchofo Dinda, P.

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, J. Phys. A 34, L103 (2001).
[Crossref]

Turitsyn, S. K.

Wabnitz, S.

V. E. Zakharov and S. Wabnitz, Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1998).

Yang, T. S.

Yu, T.

Zakharov, V. E.

V. E. Zakharov and S. Wabnitz, Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1998).

Electron. Lett. (1)

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

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, J. Phys. A 34, L103 (2001).
[Crossref]

Opt. Lett. (2)

Other (1)

V. E. Zakharov and S. Wabnitz, Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1998).

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Figures (3)

Fig. 1
Fig. 1

Pulse width versus chirp obtained from the propagation of an initially assumed Gaussian pulse in the analytically design map without losses.

Fig. 2
Fig. 2

Schematic representation of the analytically designed dispersion map with losses and gain.

Fig. 3
Fig. 3

Evolution of the proximity DM soliton field and the averaged DM soliton field plotted after each amplification period for propagation in the analytically designed map with losses and gain. β±=±6.8 ps2/km, γ=0.0014 mW-1, and α=0.2 dB/km.

Equations (10)

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ψz+iβz2ψtt-iγψ2ψ=0,
ψg=x1exp-ξ2/x32+ix4ξ2/2+ix5ξ+ix6,
x·3=-βzx3x4,
x·4=βzx42-4x3-4-2γE0x3-3.
x¨3=4βz2x3-3+2βzγE0x3-2.
x·32/2=-2βz2x3-2-2βzγE0x3-1+c.
c±=2β±2x3±-2+2β±γE0x3±-1.
x·3-β-x3-x3m=x·3+β+x3+x3m.
x3m=2γE0β+β-β--β+/c+β-2-c-β+2.
L±2=fβ±,c±,x3m-γβ±E02c±c±ln4c±x3±-22γβ±E0,

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