Abstract

We present an experimental study of the probabilistic nature of pulsation self-starting in passively mode-locked lasers. It is a Poissonian process that results from a noise-activated switching barrier. The switching rate from cw operation to pulsation when the laser pump level is turned on has an exponential dependence that is inversely proportional to the square of the laser power.

© 2005 Optical Society of America

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  1. H. A. Haus and E. P. Ippen, Opt. Lett. 16, 1331 (1991).
    [CrossRef] [PubMed]
  2. F. Krausz, T. Brabec, and Ch. Spilmann, Opt. Lett. 16, 235 (1991).
    [CrossRef] [PubMed]
  3. J. Herrmann, Opt. Commun. 98, 111 (1993).
    [CrossRef]
  4. A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
    [CrossRef]
  5. A. Gordon and B. Fischer, Opt. Commun. 223, 151 (2003).
    [CrossRef]
  6. A. Gordon and B. Fischer, Opt. Lett. 28, 1326 (2003).
    [CrossRef] [PubMed]
  7. O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
    [CrossRef]
  8. B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
    [CrossRef]
  9. A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, in Conference on Lasers and Electro-Optics (CLEO’05) (Optical Society of America, 2005).
  10. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
    [CrossRef]
  11. H. A. Kramers, Physica (Utrecht) 7, 284 (1940).
    [CrossRef]
  12. M. B. Willemsen, M. U.F. Khalid, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
    [CrossRef]
  13. S. Barbay, G. Giacomelli, and F. Marine, Phys. Rev. E 61, 157 (2000).
    [CrossRef]
  14. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
    [CrossRef]
  15. H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
    [CrossRef]
  16. D. Abraham, R. Nagar, V. Mikhelashvili, and G. Eisenstein, Appl. Phys. Lett. 63, 2857 (1993).
    [CrossRef]

2004 (2)

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

2003 (2)

A. Gordon and B. Fischer, Opt. Commun. 223, 151 (2003).
[CrossRef]

A. Gordon and B. Fischer, Opt. Lett. 28, 1326 (2003).
[CrossRef] [PubMed]

2002 (1)

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

2000 (2)

S. Barbay, G. Giacomelli, and F. Marine, Phys. Rev. E 61, 157 (2000).
[CrossRef]

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

1999 (1)

M. B. Willemsen, M. U.F. Khalid, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
[CrossRef]

1993 (2)

D. Abraham, R. Nagar, V. Mikhelashvili, and G. Eisenstein, Appl. Phys. Lett. 63, 2857 (1993).
[CrossRef]

J. Herrmann, Opt. Commun. 98, 111 (1993).
[CrossRef]

1992 (1)

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

1991 (2)

1990 (1)

P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
[CrossRef]

1940 (1)

H. A. Kramers, Physica (Utrecht) 7, 284 (1940).
[CrossRef]

Abraham, D.

D. Abraham, R. Nagar, V. Mikhelashvili, and G. Eisenstein, Appl. Phys. Lett. 63, 2857 (1993).
[CrossRef]

Barbay, S.

S. Barbay, G. Giacomelli, and F. Marine, Phys. Rev. E 61, 157 (2000).
[CrossRef]

Bekker, A.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

Borkovec, M.

P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
[CrossRef]

Brabec, T.

Eisenstein, G.

D. Abraham, R. Nagar, V. Mikhelashvili, and G. Eisenstein, Appl. Phys. Lett. 63, 2857 (1993).
[CrossRef]

Fischer, B.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

A. Gordon and B. Fischer, Opt. Lett. 28, 1326 (2003).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Opt. Commun. 223, 151 (2003).
[CrossRef]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, in Conference on Lasers and Electro-Optics (CLEO’05) (Optical Society of America, 2005).

Gat, O.

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, in Conference on Lasers and Electro-Optics (CLEO’05) (Optical Society of America, 2005).

Giacomelli, G.

S. Barbay, G. Giacomelli, and F. Marine, Phys. Rev. E 61, 157 (2000).
[CrossRef]

Gordon, A.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

A. Gordon and B. Fischer, Opt. Lett. 28, 1326 (2003).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Opt. Commun. 223, 151 (2003).
[CrossRef]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, in Conference on Lasers and Electro-Optics (CLEO’05) (Optical Society of America, 2005).

Hänggi, P.

P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
[CrossRef]

Haus, H. A.

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

H. A. Haus and E. P. Ippen, Opt. Lett. 16, 1331 (1991).
[CrossRef] [PubMed]

Herrmann, J.

J. Herrmann, Opt. Commun. 98, 111 (1993).
[CrossRef]

Ippen, E. P.

Kartner, F. X.

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, in Conference on Lasers and Electro-Optics (CLEO’05) (Optical Society of America, 2005).

Khalid, M. U.F.

M. B. Willemsen, M. U.F. Khalid, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
[CrossRef]

Kramers, H. A.

H. A. Kramers, Physica (Utrecht) 7, 284 (1940).
[CrossRef]

Krausz, F.

Marine, F.

S. Barbay, G. Giacomelli, and F. Marine, Phys. Rev. E 61, 157 (2000).
[CrossRef]

Matsas, V. J.

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

Mikhelashvili, V.

D. Abraham, R. Nagar, V. Mikhelashvili, and G. Eisenstein, Appl. Phys. Lett. 63, 2857 (1993).
[CrossRef]

Nagar, R.

D. Abraham, R. Nagar, V. Mikhelashvili, and G. Eisenstein, Appl. Phys. Lett. 63, 2857 (1993).
[CrossRef]

Newson, T. P.

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

Payne, D. N.

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

Richardson, D. J.

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

Smulakovsky, V.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

Spilmann, Ch.

Talkner, P.

P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
[CrossRef]

van Exter, M. P.

M. B. Willemsen, M. U.F. Khalid, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
[CrossRef]

Vodonos, B.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

Weill, R.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

Willemsen, M. B.

M. B. Willemsen, M. U.F. Khalid, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
[CrossRef]

Woerdman, J. P.

M. B. Willemsen, M. U.F. Khalid, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

D. Abraham, R. Nagar, V. Mikhelashvili, and G. Eisenstein, Appl. Phys. Lett. 63, 2857 (1993).
[CrossRef]

Electron. Lett. (1)

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

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

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

Opt. Commun. (2)

J. Herrmann, Opt. Commun. 98, 111 (1993).
[CrossRef]

A. Gordon and B. Fischer, Opt. Commun. 223, 151 (2003).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. E (2)

S. Barbay, G. Giacomelli, and F. Marine, Phys. Rev. E 61, 157 (2000).
[CrossRef]

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef]

M. B. Willemsen, M. U.F. Khalid, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 82, 4815 (1999).
[CrossRef]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef]

Physica (Utrecht) (1)

H. A. Kramers, Physica (Utrecht) 7, 284 (1940).
[CrossRef]

Rev. Mod. Phys. (1)

P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
[CrossRef]

Other (1)

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, in Conference on Lasers and Electro-Optics (CLEO’05) (Optical Society of America, 2005).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup: A fiber ring laser passively mode locked by nonlinear polarization rotation was switched on and off by modulating the pump current. The self-starting dynamics was measured by photodetector PD and a real-time oscilloscope.[8] WDM, wavelength-division multiplexer; PC1, PC2, polarization controllers.

Fig. 2
Fig. 2

Example of a measured distribution of the startup times for a pumping current of 88 mA presented (a) as a time recording of the experimental data and in the form of a histogram (2000 measured points distributed among 50 bins) on (b) linear and (c) logarithmic scales.

Fig. 3
Fig. 3

Dependence of mean cw lifetime on intracavity power P. The results are for two sets of measurements (circles and triangles). The estimated mean cw lifetime is shown versus 1 P 2 on a logarithmic scale.

Equations (3)

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d x d t = N f ( x ) + g ( x ) η ( t ) ,
P r cw ( t ) = exp ( t τ cw ) ,
log τ cw 1 P 2 .

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