Abstract

We show from an elementary symmetry analysis that, in dispersion-compensated systems for which a lossless model is valid, nonlinearity requires a chirp-free point at the center of symmetry (if such exists) of the map for any kind of unique periodic solution. We also present an example of a more-complex map when the periodic solution is not unique.

© 1999 Optical Society of America

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  1. N. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
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  3. S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, Opt. Fiber Technol. 4, 384 (1998).
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  5. T. S. Yang, W. L. Kath, and S. K. Turitsyn, Opt. Lett. 23, 597 (1998).
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  6. I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996); JETP Lett. 63, 862 (1996).
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  7. E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 22, 793 (1997); V. S. Grigoryan and C. R. Menyuk, Opt. Lett. 23, 685 (1998).
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    [CrossRef]
  9. A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
    [CrossRef]
  10. J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
    [CrossRef]
  11. P. Holmes and J. N. Kutz, SIAM J. Appl. Math. 59, 1288 (1999).
    [CrossRef]
  12. T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998); T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
    [CrossRef]
  13. L. F. Mollenauer and P. V. Mamyushev, IEEE J. Quantum Electron. 34, 2089 (1998).
    [CrossRef]

1999

P. Holmes and J. N. Kutz, SIAM J. Appl. Math. 59, 1288 (1999).
[CrossRef]

1998

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998); T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

L. F. Mollenauer and P. V. Mamyushev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
[CrossRef]

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, Opt. Fiber Technol. 4, 384 (1998).
[CrossRef]

T. S. Yang, W. L. Kath, and S. K. Turitsyn, Opt. Lett. 23, 597 (1998).
[CrossRef]

1997

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 22, 793 (1997); V. S. Grigoryan and C. R. Menyuk, Opt. Lett. 23, 685 (1998).
[CrossRef]

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

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

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (1997).
[CrossRef]

1996

Bennion, I.

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

Blow, K. J.

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

Charbonnier, B.

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (1997).
[CrossRef]

Doran, N. J.

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

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 26, 1981 (1996).
[CrossRef]

Evangelides, S. G.

Forysiak, W.

Gabitov, I.

Georges, T.

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (1997).
[CrossRef]

Golovchenko, E. A.

Gordon, J. P.

Hasegawa, A.

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

Haus, H. A.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

Holmes, P.

Kath, W. L.

Kaup, D. J.

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998); T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Knox, F. M.

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 26, 1981 (1996).
[CrossRef]

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

Kodama, Y.

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

Kutz, J. N.

Lakoba, T.

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998); T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Mamyushev, P. V.

L. F. Mollenauer and P. V. Mamyushev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

Maruta, A.

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

Matsumoto, M.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

Menyuk, C. R.

Mezentsev, V. K.

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, Opt. Fiber Technol. 4, 384 (1998).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer and P. V. Mamyushev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

Pilipetskii, A. N.

Shapiro, E. G.

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, Opt. Fiber Technol. 4, 384 (1998).
[CrossRef]

Smith, N.

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

Smith, N. J.

Turitsyn, S. K.

Yang, T. S.

Electron. Lett.

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

T. Lakoba and D. J. Kaup, Electron. Lett. 34, 1124 (1998); T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

IEEE J. Quantum Electron.

L. F. Mollenauer and P. V. Mamyushev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

T. Georges and B. Charbonnier, IEEE Photon. Technol. Lett. 9, 127 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Fiber Technol.

S. K. Turitsyn, E. G. Shapiro, and V. K. Mezentsev, Opt. Fiber Technol. 4, 384 (1998).
[CrossRef]

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

Opt. Lett.

SIAM J. Appl. Math.

P. Holmes and J. N. Kutz, SIAM J. Appl. Math. 59, 1288 (1999).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Two stable periodic solutions do exist in the dispersion map shown by dashed lines. Bottom, pulse width evolution (solid lines) over one period. Top, three-dimensional stroboscopic evolution (at the ends of the section), demonstrating the stability of both solutions. In this case CFP’s that correspond to the minima of the pulse width are not in the centers of the symmetry. Distance is normalized by L.

Fig. 2
Fig. 2

Slow (stroboscopic) evolution of two input Gaussian pulses (with parameters found from the ODE model) launched at CFP’s (solid curves) and at the junction between fibers (dashed curves). Left, evolution of the pulse peak power (top) and rms pulse width (bottom) of the Gaussian pulses with parameters found from the ODE model. Right, the slow (stroboscopic) dynamics appears as mapping in the plane (rms pulse width, rms chirp).

Equations (2)

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

iAz+dz2At2+σA2A=0,
iFz-kF+dz2Ft2+σF2F=0.

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