Abstract

We report the observation of bound states of 350 pulses in a ring fiber laser mode locked by nonlinear rotation of the polarization. The phenomenon is described theoretically using a multiscale approach to the gain dynamics; the fast evolution of a small excess of gain is responsible for the stabilization of a periodic pattern, while the slow evolution of the mean value of gain explains the finite length of the quasiperiodic soliton train.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. A. Hideur, B. Ortaç, T. Chartier, M. Brunel, H. Leblond, and F. Sanchez, Opt. Commun. 225, 71 (2003).
    [CrossRef]
  5. H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, J. Opt. A 8, 319 (2006).
    [CrossRef]
  6. B. Ortaç, A. Hideur, T. Chartier, M. Brunel, Ph. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
    [CrossRef]
  7. D. Y. Tang, L. M. Zhao, and B. Zhao, Appl. Phys. B 80, 239 (2005).
    [CrossRef]
  8. E. Fermi, J. Pasta, and H. C. Ulam, Collected Papers of Enrico Fermi, E.Segrè, ed. (University of Chicago, 1965), Vol. 2, p. 977.
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    [CrossRef]
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    [CrossRef]
  15. J. Matsas, T. P. Newton, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
    [CrossRef]
  16. H. Leblond, “The reductive perturbation method and some of its applications,” J. Phys. B (to be published).
  17. H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, Phys. Rev. A 65, 063811 (2002).
    [CrossRef]
  18. A. Komarov, H. Leblond, and F. Sanchez, Opt. Commun. 267, 162 (2006).
    [CrossRef]

2006 (2)

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, J. Opt. A 8, 319 (2006).
[CrossRef]

A. Komarov, H. Leblond, and F. Sanchez, Opt. Commun. 267, 162 (2006).
[CrossRef]

2005 (1)

D. Y. Tang, L. M. Zhao, and B. Zhao, Appl. Phys. B 80, 239 (2005).
[CrossRef]

2004 (1)

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, Ph. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

2003 (1)

A. Hideur, B. Ortaç, T. Chartier, M. Brunel, H. Leblond, and F. Sanchez, Opt. Commun. 225, 71 (2003).
[CrossRef]

2002 (2)

H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, Phys. Rev. A 65, 063811 (2002).
[CrossRef]

C. Cambournac, H. Maillotte, E. Lantz, J. M. Dudley, and M. Chauvet, J. Opt. Soc. Am. B 19, 574 (2002).
[CrossRef]

2001 (1)

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

2000 (1)

S. Rutz and F. Mitschke, J. Opt. B 2, 364366 (2000).
[CrossRef]

1998 (2)

B. A. Malomed, A. Schwache, and F. Mitschke, Fiber Integr. Opt. 17, 267 (1998).
[CrossRef]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
[CrossRef]

1997 (1)

V. V. Afanasjev, B. A. Malomed, and P. L. Chu, Phys. Rev. E 56, 6020 (1997).
[CrossRef]

1992 (1)

J. Matsas, T. P. Newton, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

1989 (1)

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

1985 (1)

N. N. Akhmediev, V. M. Eleonskiĭ, and N. E. Kulagin, Sov. Phys. JETP 62, 894 (1985).

Appl. Phys. B (1)

D. Y. Tang, L. M. Zhao, and B. Zhao, Appl. Phys. B 80, 239 (2005).
[CrossRef]

Electron. Lett. (1)

J. Matsas, T. P. Newton, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

Fiber Integr. Opt. (1)

B. A. Malomed, A. Schwache, and F. Mitschke, Fiber Integr. Opt. 17, 267 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, Ph. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

J. Opt. A (1)

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, J. Opt. A 8, 319 (2006).
[CrossRef]

J. Opt. B (1)

S. Rutz and F. Mitschke, J. Opt. B 2, 364366 (2000).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

H. Leblond, “The reductive perturbation method and some of its applications,” J. Phys. B (to be published).

Opt. Commun. (2)

A. Komarov, H. Leblond, and F. Sanchez, Opt. Commun. 267, 162 (2006).
[CrossRef]

A. Hideur, B. Ortaç, T. Chartier, M. Brunel, H. Leblond, and F. Sanchez, Opt. Commun. 225, 71 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, Phys. Rev. A 65, 063811 (2002).
[CrossRef]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

Phys. Rev. E (1)

V. V. Afanasjev, B. A. Malomed, and P. L. Chu, Phys. Rev. E 56, 6020 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

N. N. Akhmediev, V. M. Eleonskiĭ, and N. E. Kulagin, Sov. Phys. JETP 62, 894 (1985).

Other (1)

E. Fermi, J. Pasta, and H. C. Ulam, Collected Papers of Enrico Fermi, E.Segrè, ed. (University of Chicago, 1965), Vol. 2, p. 977.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. PBS, polarization beam splitter; DSF, dispersion-shifted fiber ( 2.15 m , β 2 = + 0.14 ps 2 m ); SMF 28 , standard single-mode fiber ( 9.6 m , β 2 = 0.0217 ps 2 m ); PC, polarization controller; VSP, V-groove side-pumping; Er Yb DCF, Er Yb doped double-clad fiber ( 9 m , β 2 = 0.015 ps 2 m ).

Fig. 2
Fig. 2

Oscilloscope trace, the repetition of the pulse train at the fundamental frequency of the cavity. The inset presents the global shape of a train.

Fig. 3
Fig. 3

Autocorrelation trace showing the periodic local pattern.

Fig. 4
Fig. 4

Optical spectrum of the pulse train. Left, experimental; right, reconstructed.

Fig. 5
Fig. 5

Evolution of the electric field in the laser cavity, starting from a single pulse, spontaneous arising of a periodic regime.

Fig. 6
Fig. 6

Schema showing the evolution of gain in the cavity, each of the N pulses takes off an amount δ G of gain, and after the train relaxation restores the amount Δ g .

Equations (7)

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f = j = 1 N E e i ( ω ( t j Δ τ ) + j δ φ ) e i C [ ( t j Δ τ ) 2 ] 2 τ 2 cosh ( t j Δ τ τ ) ,
g t = g τ g a g E 2 + Λ ,
g 0 τ = ( 1 τ g a E 2 ) g 0 + Λ .
i E ζ = i g 1 E + ( β 2 2 + i ρ ) 2 E T 2 + ( D r + i D i ) E E 2 i G E T ( E 2 ( T ) E 2 ) d T ,
G = g 0 a exp ( 2 g 0 L ) 1 2 g 0 L ,
δ G = G E 0 2 τ ,
Δ g = g f g i = ( Λ τ g g i ) ( 1 exp ( Δ T τ g ) ) ,

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