Abstract

We report experimental and theoretical evidence of the existence of extreme value events in the form of scarce and randomly emerging giant pulses in the femtosecond (self-pulsing or Kerr-lens mode-locked) Ti:sapphire laser. This laser displays complex dynamical behavior, including deterministic chaos, in two different regimes. The extreme value pulses are observed in the chaotic state of only one of these two regimes. The observations agree with the predictions of a well-tested theoretical model that does not include noise or self-Q-switching into its framework. This implies that, in this laser, the extreme effects have a nontrivial dynamical origin. The Ti:sapphire laser is hence revealed as a new and convenient system for the study of these effects.

© 2011 Optical Society of America

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  1. C. Kharif, E. Pelinovsky, and A. Slunyaev, Extreme Events in the Ocean (Springer-Verlag, 2009).
  2. A. Osborne, M. Onorato, and M. Serio, Phys. Lett. A 275, 386 (2000).
    [Crossref]
  3. K. Trulsen, I. Kliakhandler, K. Dysthe, and M. Velarde, Phys. Fluids 24, 32 (2000).
    [Crossref]
  4. Z. Yan, V. Konotop, and N. Akhmediev, Phys. Rev. E 82, 036610 (2010).
    [Crossref]
  5. D. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
    [Crossref] [PubMed]
  6. C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
    [Crossref]
  7. N. Akhmediev, J. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
    [Crossref]
  8. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
    [Crossref]
  9. J. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
    [Crossref] [PubMed]
  10. A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2011 (3)

F. T. Arecchi, U. Bortolozzo, A. Montina, and S. Residori, Phys. Rev. Lett. 106, 153901 (2011).
[Crossref] [PubMed]

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

J. Soto-Crespo, P. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[Crossref]

2010 (3)

Z. Yan, V. Konotop, and N. Akhmediev, Phys. Rev. E 82, 036610 (2010).
[Crossref]

C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

2009 (3)

A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009).
[Crossref] [PubMed]

N. Akhmediev, J. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[Crossref]

J. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

2008 (2)

A. Hnilo and M. Kovalsky, Int. J. Bif. Chaos 18, 1719 (2008).
[Crossref]

N. Akhmediev, J. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[Crossref]

2007 (1)

D. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[Crossref] [PubMed]

2004 (1)

M. Kovalsky and A. Hnilo, Phys. Rev. A 70, 043813 (2004).
[Crossref]

2000 (3)

M. Kovalsky and A. Hnilo, Opt. Commun. 186, 155 (2000).
[Crossref]

A. Osborne, M. Onorato, and M. Serio, Phys. Lett. A 275, 386 (2000).
[Crossref]

K. Trulsen, I. Kliakhandler, K. Dysthe, and M. Velarde, Phys. Fluids 24, 32 (2000).
[Crossref]

1986 (1)

L. Narducci, J. Tredicce, L. Lugiato, N. Abraham, and D. Bandy, Phys. Rev. A 33, 1842 (1986).
[Crossref] [PubMed]

1985 (1)

Abraham, N.

L. Narducci, J. Tredicce, L. Lugiato, N. Abraham, and D. Bandy, Phys. Rev. A 33, 1842 (1986).
[Crossref] [PubMed]

Akhmediev, N.

J. Soto-Crespo, P. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[Crossref]

Z. Yan, V. Konotop, and N. Akhmediev, Phys. Rev. E 82, 036610 (2010).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

N. Akhmediev, J. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[Crossref]

J. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

N. Akhmediev, J. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[Crossref]

Ankiewicz, A.

N. Akhmediev, J. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[Crossref]

Arecchi, F. T.

F. T. Arecchi, U. Bortolozzo, A. Montina, and S. Residori, Phys. Rev. Lett. 106, 153901 (2011).
[Crossref] [PubMed]

A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009).
[Crossref] [PubMed]

Bandy, D.

L. Narducci, J. Tredicce, L. Lugiato, N. Abraham, and D. Bandy, Phys. Rev. A 33, 1842 (1986).
[Crossref] [PubMed]

Barland, S.

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Bonatto, C.

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Bortolozzo, U.

F. T. Arecchi, U. Bortolozzo, A. Montina, and S. Residori, Phys. Rev. Lett. 106, 153901 (2011).
[Crossref] [PubMed]

A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009).
[Crossref] [PubMed]

Dias, F.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

J. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

Dudley, J.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
[Crossref]

J. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

Dysthe, K.

K. Trulsen, I. Kliakhandler, K. Dysthe, and M. Velarde, Phys. Fluids 24, 32 (2000).
[Crossref]

Egorov, O.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, “Extreme events in a mode-locked fiber laser,” presented at the Conference on Lasers and Electro-Optics/EUROPE/European Quantum Electronics Conference 2011, Munich, Germany, May 22–26, 2011.

Fatome, J.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
[Crossref]

Feyereisen, M.

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Finot, C.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
[Crossref]

Fork, R.

Genty, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

J. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

Giudici, M.

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Gordon, J.

Grelu, P.

J. Soto-Crespo, P. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[Crossref]

Grelu, Ph.

N. Akhmediev, J. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[Crossref]

Hammami, K.

C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
[Crossref]

Hnilo, A.

A. Hnilo and M. Kovalsky, Int. J. Bif. Chaos 18, 1719 (2008).
[Crossref]

M. Kovalsky and A. Hnilo, Phys. Rev. A 70, 043813 (2004).
[Crossref]

M. Kovalsky and A. Hnilo, Opt. Commun. 186, 155 (2000).
[Crossref]

Iliew, R.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, “Extreme events in a mode-locked fiber laser,” presented at the Conference on Lasers and Electro-Optics/EUROPE/European Quantum Electronics Conference 2011, Munich, Germany, May 22–26, 2011.

Jalali, B.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[Crossref] [PubMed]

Kharif, C.

C. Kharif, E. Pelinovsky, and A. Slunyaev, Extreme Events in the Ocean (Springer-Verlag, 2009).

Kibler, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

J. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[Crossref] [PubMed]

Kliakhandler, I.

K. Trulsen, I. Kliakhandler, K. Dysthe, and M. Velarde, Phys. Fluids 24, 32 (2000).
[Crossref]

Konotop, V.

Z. Yan, V. Konotop, and N. Akhmediev, Phys. Rev. E 82, 036610 (2010).
[Crossref]

Koonath, P.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[Crossref] [PubMed]

Kovalsky, M.

A. Hnilo and M. Kovalsky, Int. J. Bif. Chaos 18, 1719 (2008).
[Crossref]

M. Kovalsky and A. Hnilo, Phys. Rev. A 70, 043813 (2004).
[Crossref]

M. Kovalsky and A. Hnilo, Opt. Commun. 186, 155 (2000).
[Crossref]

Lederer, F.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, “Extreme events in a mode-locked fiber laser,” presented at the Conference on Lasers and Electro-Optics/EUROPE/European Quantum Electronics Conference 2011, Munich, Germany, May 22–26, 2011.

Leite, J. Ríos

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Lugiato, L.

L. Narducci, J. Tredicce, L. Lugiato, N. Abraham, and D. Bandy, Phys. Rev. A 33, 1842 (1986).
[Crossref] [PubMed]

Martínez, O.

Masoller, C.

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Millot, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
[Crossref]

Montina, A.

F. T. Arecchi, U. Bortolozzo, A. Montina, and S. Residori, Phys. Rev. Lett. 106, 153901 (2011).
[Crossref] [PubMed]

A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009).
[Crossref] [PubMed]

Narducci, L.

L. Narducci, J. Tredicce, L. Lugiato, N. Abraham, and D. Bandy, Phys. Rev. A 33, 1842 (1986).
[Crossref] [PubMed]

Onorato, M.

A. Osborne, M. Onorato, and M. Serio, Phys. Lett. A 275, 386 (2000).
[Crossref]

Osborne, A.

A. Osborne, M. Onorato, and M. Serio, Phys. Lett. A 275, 386 (2000).
[Crossref]

Pelinovsky, E.

C. Kharif, E. Pelinovsky, and A. Slunyaev, Extreme Events in the Ocean (Springer-Verlag, 2009).

Residori, S.

F. T. Arecchi, U. Bortolozzo, A. Montina, and S. Residori, Phys. Rev. Lett. 106, 153901 (2011).
[Crossref] [PubMed]

A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009).
[Crossref] [PubMed]

Ropers, C.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[Crossref] [PubMed]

Serio, M.

A. Osborne, M. Onorato, and M. Serio, Phys. Lett. A 275, 386 (2000).
[Crossref]

Slunyaev, A.

C. Kharif, E. Pelinovsky, and A. Slunyaev, Extreme Events in the Ocean (Springer-Verlag, 2009).

Solli, D.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[Crossref] [PubMed]

Soto-Crespo, J.

J. Soto-Crespo, P. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[Crossref]

N. Akhmediev, J. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[Crossref]

N. Akhmediev, J. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[Crossref]

Tredicce, J.

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

L. Narducci, J. Tredicce, L. Lugiato, N. Abraham, and D. Bandy, Phys. Rev. A 33, 1842 (1986).
[Crossref] [PubMed]

Trulsen, K.

K. Trulsen, I. Kliakhandler, K. Dysthe, and M. Velarde, Phys. Fluids 24, 32 (2000).
[Crossref]

Velarde, M.

K. Trulsen, I. Kliakhandler, K. Dysthe, and M. Velarde, Phys. Fluids 24, 32 (2000).
[Crossref]

Yan, Z.

Z. Yan, V. Konotop, and N. Akhmediev, Phys. Rev. E 82, 036610 (2010).
[Crossref]

Zaviyalov, A.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, “Extreme events in a mode-locked fiber laser,” presented at the Conference on Lasers and Electro-Optics/EUROPE/European Quantum Electronics Conference 2011, Munich, Germany, May 22–26, 2011.

IEEE J. Quantum Electron. (1)

C. Finot, K. Hammami, J. Fatome, J. Dudley, and G. Millot, IEEE J. Quantum Electron. 46, 205 (2010).
[Crossref]

Int. J. Bif. Chaos (1)

A. Hnilo and M. Kovalsky, Int. J. Bif. Chaos 18, 1719 (2008).
[Crossref]

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

Nat. Phys. (1)

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. Dudley, Nat. Phys. 6, 790 (2010).
[Crossref]

Nature (1)

D. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Kovalsky and A. Hnilo, Opt. Commun. 186, 155 (2000).
[Crossref]

Opt. Express (1)

Phys. Fluids (1)

K. Trulsen, I. Kliakhandler, K. Dysthe, and M. Velarde, Phys. Fluids 24, 32 (2000).
[Crossref]

Phys. Lett. A (3)

A. Osborne, M. Onorato, and M. Serio, Phys. Lett. A 275, 386 (2000).
[Crossref]

N. Akhmediev, J. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[Crossref]

N. Akhmediev, J. Soto-Crespo, and Ph. Grelu, Phys. Lett. A 372, 3124 (2008).
[Crossref]

Phys. Rev. A (2)

L. Narducci, J. Tredicce, L. Lugiato, N. Abraham, and D. Bandy, Phys. Rev. A 33, 1842 (1986).
[Crossref] [PubMed]

M. Kovalsky and A. Hnilo, Phys. Rev. A 70, 043813 (2004).
[Crossref]

Phys. Rev. E (2)

J. Soto-Crespo, P. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[Crossref]

Z. Yan, V. Konotop, and N. Akhmediev, Phys. Rev. E 82, 036610 (2010).
[Crossref]

Phys. Rev. Lett. (3)

A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009).
[Crossref] [PubMed]

F. T. Arecchi, U. Bortolozzo, A. Montina, and S. Residori, Phys. Rev. Lett. 106, 153901 (2011).
[Crossref] [PubMed]

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. Ríos Leite, and J. Tredicce, Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Other (2)

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, “Extreme events in a mode-locked fiber laser,” presented at the Conference on Lasers and Electro-Optics/EUROPE/European Quantum Electronics Conference 2011, Munich, Germany, May 22–26, 2011.

C. Kharif, E. Pelinovsky, and A. Slunyaev, Extreme Events in the Ocean (Springer-Verlag, 2009).

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Figures (3)

Fig. 1
Fig. 1

Spectra obtained in the stable state of the two dynamical regimes: (a) P1, transform-limited pulses—extreme events are not observed and (b) P2, chirped pulses—extreme events are observed, note the similarity with the spectrum in microstructured fibers [5, 6]. In the chaotic states of P1 and P2, the spectra are unstable but still clearly distinguishable.

Fig. 2
Fig. 2

Distributions of the pulse energies in the chaotic states, experimental results: (a) regime P2—the dotted line indicates the standard boundary values for extreme events and (b) regime P1—the boundary values ( 2 × H s = 178.4 and 4 × σ = 165.7 ) are rightward and out of the figure.

Fig. 3
Fig. 3

Distributions of the pulse energies in the chaotic states, numerical results according to the five-variables map: (a) regime P2—the vertical dotted line indicates the standard boundary values for extreme events and (b) regime P1—the boundary values ( 2 × H s = 187.8 and 4 × σ = 180.4 ) are out of the figure. Therefore, extreme events are predicted to exist in regime P2 only, in agreement with the observations.

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