Abstract

We extend the theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fiber lasers. Dissipative structures exist at high map strengths, leading to the generation of stable, short pulses with high energy. Two types of intramap pulse evolution are observed depending on the net cavity dispersion. These are characterized by a reduced model, and semianalytical solutions are obtained.

© 2009 Optical Society of America

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References

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  1. H. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
    [CrossRef]
  2. S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
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    [CrossRef] [PubMed]
  5. M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
    [CrossRef]
  6. Y. Chen, F. X. Kärtner, U. Morgner, S. H. Cho, H. A. Haus, E. P. Ippen, and J. G. Fujimoto, J. Opt. Soc. Am. B 16, 1999 (1999).
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    [CrossRef]

2008 (1)

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

2004 (1)

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

2003 (1)

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
[CrossRef]

2000 (1)

H. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

1999 (1)

1998 (1)

1996 (1)

1993 (1)

1979 (1)

A. Bondeson, M. Lisak, and D. Anderson, Phys. Scr. 20, 479 (1979).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

Anderson, D.

A. Bondeson, M. Lisak, and D. Anderson, Phys. Scr. 20, 479 (1979).
[CrossRef]

Bondeson, A.

A. Bondeson, M. Lisak, and D. Anderson, Phys. Scr. 20, 479 (1979).
[CrossRef]

Buckley, J. R.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Chen, Y.

Cho, S. H.

Clark, W. G.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Doran, N. J.

Egangelides, S. G.

Fedoruk, M. P.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
[CrossRef]

Forysiak, W.

Fujimoto, J. G.

Haus, H.

H. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

Haus, H. A.

Horikis, T. P.

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

Ilan, B.

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

Ilday, F. O.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Ippen, E. P.

Kärtner, F. X.

Knox, F. M.

Kutz, J. N.

Lisak, M.

A. Bondeson, M. Lisak, and D. Anderson, Phys. Scr. 20, 479 (1979).
[CrossRef]

Medvedev, S. B.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
[CrossRef]

Mezentsev, V. K.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
[CrossRef]

Morgner, U.

Nelson, L. E.

Shapiro, E. G.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
[CrossRef]

Smith, N. J.

Tamura, K.

Turitsyn, S. K.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
[CrossRef]

Wise, F.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

C. R. Phys. (1)

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, C. R. Phys. 4, 145 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. A (1)

M. J. Ablowitz, T. P. Horikis, and B. Ilan, Phys. Rev. A 77, 033814 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Phys. Scr. (1)

A. Bondeson, M. Lisak, and D. Anderson, Phys. Scr. 20, 479 (1979).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Dependence of maximum pulse energy on map strength for a range of average cavity dispersion values Δ = d ¯ d . Each point represents a stationary solution of Eq. (1) with a two-step map for L = 1 . Dissipative parameters are g 0 = 2 , e 0 = 1 , l 0 = 1 , and p s = 3 .

Fig. 2
Fig. 2

Trends of the pulse amplitude (solid) and duration (dashed) along two distinct branches (insets) for (a) Δ = 0.05 , (b) Δ = 0.01 .

Fig. 3
Fig. 3

Evolution of pulse parameters for typical SP (black) and PCP (gray) solutions from both reduced model (3) (dashed) and full model (1) (solid). Also included is analytic solution (5) (gray dots). Dissipative parameters are the same as in Fig. 1, and map parameters are d = 1 , d ¯ = 0.01 (SP), and d = 0.3 , d ¯ = 0.015 (PCP). Shaded regions correspond to the anomalous GVD segment.

Equations (9)

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i u z + d ( z ) 2 u t t + γ | u | 2 u = i [ g 0 1 + u 2 e 0 l 0 1 + | u | 2 p s ] u ,
u ( t , z ) = η ( z ) exp [ ( t τ ( z ) ) 2 + i C ( z ) t 2 + i φ ( z ) ] .
η z = 2 d ( z ) C η + [ 2 g 0 e 0 c 1 e 0 + η τ l 0 ( 3 F 0 4 F 2 ) ] c 1 η ,
τ z = 2 d ( z ) C τ l 0 ( 4 F 2 F 0 ) c 1 τ ,
C z = 2 d ( z ) [ 1 τ 4 C 2 ] 2 2 γ η τ 2 ,
0 z C ( s ) d s < log ( τ 0 4 C 2 ) 8 d ( 1 + Δ )
η ( z ) = η 0 1 + 2 d ( ± 1 + Δ ) C 0 z ,
τ ( z ) = τ 0 ( 1 + 2 d ( ± 1 + Δ ) C 0 z ) ,
C ( z ) = C 0 1 + 2 d ( ± 1 + Δ ) C 0 z ,

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