OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 23 — Nov. 13, 2006
  • pp: 11142–11154

Self-starting of passive mode locking

Ariel Gordon, Omri Gat, Baruch Fischer, and Franz X. Kärtner  »View Author Affiliations

Optics Express, Vol. 14, Issue 23, pp. 11142-11154 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (227 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It has been recently understood that mode locking of lasers has the signification of a thermodynamic phase transition in a system of many interacting light modes subject to noise. In the same framework, self starting of passive mode locking has the thermodynamic significance of a noise-activated escape process across an entropic barrier. Here we present the first dynamical study of the light mode system. While accordant with the predictions of some earlier theories, it is the first to give precise quantitative predictions for the distribution of self-start times, in closed form expressions, resolving the long standing self starting problem. Numerical simulations corroborate these results, which are also in good agreement with experiments.

© 2006 Optical Society of America

OCIS Codes
(140.3430) Lasers and laser optics : Laser theory
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Lasers and Laser Optics

Original Manuscript: April 11, 2006
Revised Manuscript: September 20, 2006
Manuscript Accepted: September 21, 2006
Published: November 13, 2006

Ariel Gordon, Omri Gat, Baruch Fischer, and Franz X. Kärtner, "Self-starting of passive mode locking," Opt. Express 14, 11142-11154 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. P. Ippen, L. Y. Liu, and H. A. Haus, "Self-starting condition for additive-pulse mode-locked lasers", Opt. Lett. 15, 183 (1990). [CrossRef] [PubMed]
  2. C. J. Chen, P. K. A. Wai and C. R. Menyuk, "Self-starting of passively mode-locked lasers with fast saturable absorbers", Opt. Lett. 20, 350 (1995) [CrossRef] [PubMed]
  3. H. A. Haus and E. P. Ippen, "Self-starting of passively mode-locked lasers", Opt. Lett. 16, 1331 (1991) [CrossRef] [PubMed]
  4. F. Krausz, T. Brabec and Ch. Spielmann, "Self-starting passive mode locking", Opt. Lett. 16, 235 (1991) [CrossRef] [PubMed]
  5. K. Tamura, J. Jacobson, E. P. Ippen, H. A. Haus, and J. G. Fujimoto, "Unidirectional ring resonators for selfstarting passively mode-locked lasers", Opt. Lett. 18, 220 (1993) [CrossRef] [PubMed]
  6. Y.-F. Chou, J. Wang, H.-H. Liu, and N.-P. Kuo, "Measurements of the self-starting threshold of Kerr-lens modelocking lasers", Opt. Lett. 19, 566 (1994) [CrossRef] [PubMed]
  7. Ch. Spielman, F. Krausz, T. Brabec, E. Wintner and A. J. Schmidt, "Experimental study of additive-pulse mode locking in an Nd:Glass laser", IEEE J. Quantum Electron. 27, 1207 (1991) [CrossRef]
  8. F. Krausz and T. Brabec, "Passive mode locking in standing-wave laser resonators", Opt. Lett. 18, 888 (1993) [CrossRef] [PubMed]
  9. Y.-F. Chou, J. Wang, H.-H. Liu, and N.-P. Kuo, "Measurements of the self-starting threshold of Kerr-lens modelocking lasers", Opt. Lett. 19, 566 (1994) [CrossRef] [PubMed]
  10. J. Hermann, "Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled-cavity or Kerr-lens mode locked solid-state lasers", Opt. Comm. 98, 111 (1993). [CrossRef]
  11. A. K. Komarov, K. P. Komarov and F. M. Mitschke, "Phase-modulation bistability and threshold self-start of laser passive mode locking", Phys. Rev. A. 65, 053803
  12. J. M. Soto-Crespo, N. Akhmediev and G. Town, "Continuous-wave versus pulse regime in a passively modelocked laser with a fast saturable absorber", J. Opt. Soc. Am. B 19, 234 (2002) [CrossRef]
  13. H. A. Haus, "Theory of mode locking with a fast saturable absorber", J. Appl. Phys.,  46, 3049 (1975). [CrossRef]
  14. H. A. Haus, "Mode-Locking of Lasers", IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000) [CrossRef]
  15. A. Gordon and B. Fischer, "Phase Transition Theory of Many-Mode Ordering and Pulse Formation in Lasers", Phys. Rev. Lett. 89, 103901, (2002) [CrossRef] [PubMed]
  16. A. Gordon and B. Fischer, Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and Kerr nonlinearity" Opt. Commun. 223, 151 (2003). [CrossRef]
  17. A. Gordon and B. Fischer, "Inhibition of modulation instability in lasers by noise", Opt. Lett 18, 1326 (2003). [CrossRef]
  18. O. Gat, A. Gordon and B. Fischer, "Light-mode locking - A new class of solvable statistical physics systems", New J. Phys. 7, 151 (2005) [CrossRef]
  19. R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, "Critical Behavior of Light in Mode-Locked Lasers," Phys. Rev. Lett. 95, 013903 (2005). [CrossRef] [PubMed]
  20. O. Gat, A. Gordon and B. Fischer, "Solution of a statistical mechanics model for pulse formation in lasers", Phys. Rev. E. 70, 046108 (2004) [CrossRef]
  21. H. A. Kramers, "Brownian motion in a field of fource and the diffusion model of chemical reactions", Physica (Utrecht) 7, 284 (1940). [CrossRef]
  22. P.  Hänggi, P.  Talkner and M.  Borkovec, "Reaction-rate theory: fifty years after Kramers," Rev. Mod. Phys. 62, 251 (1990). [CrossRef]
  23. B. Vodonos, A. Bekker, V. Smulakovsky, A. Gordon, O. Gat, N. K. Berger and B. Fischer "Experimental study of the stochastic nature of the pulsation self-starting process in passive mode-locking," Opt. Lett. 30, 2787 (2005). [CrossRef] [PubMed]
  24. M. Katz, A. Gordon, O. Gat, and B. Fischer, "Non-Gibbsian Stochastic Light-Mode Dynamics of Passive Mode Locking", Phys. Rev. Lett. 97, 113902 (2006) [CrossRef] [PubMed]
  25. R. L. Stratonovich, "Some Markov methods in the theory of stochastic processes in nonlinear dynamical systems", in "Noise in nonlinear dynamical systems, Vol. 1, edited by F. Moss and P. V. E. McClintock, Cambridge University Press (1989)
  26. B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat and Baruch Fischer "Formation and Annihilation of Laser Pulse Quanta in a Thermodynamic-like Pathway", Phys. Rev. Lett. 93,153901 (2004). [CrossRef] [PubMed]
  27. H. H. Risken, "The Fokker-Planck Equation", Second edition, Springler-Verlag (1989, 1996).
  28. C. W. GardinerHandbook of Stochastic Methods, 3rd ed., Springer, New York (2004).
  29. P. E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Springer New York (2000).
  30. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes in C: The Art of Scientific Computing, p. 281., 2nd edition, Cambridge University Press, New York (1992).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material

» Media 1: AVI (2038 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited