OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 12 — Jun. 12, 2006
  • pp: 5468–5475

Collapse dynamics of super-Gaussian beams

Taylor D. Grow, Amiel A. Ishaaya, Luat T. Vuong, Alexander L. Gaeta, Nir Gavish, and Gadi Fibich  »View Author Affiliations

Optics Express, Vol. 14, Issue 12, pp. 5468-5475 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (1908 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We investigate the self-focusing dynamics of super-Gaussian optical beams in a Kerr medium. We find that up to several times the critical power for self-focusing, super-Gaussian beams evolve towards a Townes profile. At higher powers the super-Gaussian beams form rings which break into filaments as a result of noise. Our results are consistent with the observed self-focusing dynamics of femtosecond laser pulses in air [1] in which filaments are formed along a ring about the axis of the initial beam where the initial beam did not form a ring.

© 2006 Optical Society of America

OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

Original Manuscript: April 20, 2006
Revised Manuscript: June 1, 2006
Manuscript Accepted: June 2, 2006
Published: June 12, 2006

Taylor D. Grow, Amiel A. Ishaaya, Luat T. Vuong, Alexander L. Gaeta, Nir Gavish, and Gadi Fibich, "Collapse dynamics of super-Gaussian Beams," Opt. Express 14, 5468-5475 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, "White-light filaments for atmospheric analysis," Science 301,61-64 (2003). [CrossRef] [PubMed]
  2. P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965). [CrossRef]
  3. B. W. Zeff, B. Kleber, J. Fineberg, and D. P. Lathrop, "Singularity dynamics in curvature collapse and jet eruption on a fluid surface," Nature (London) 403, 401-404 (2000). [CrossRef]
  4. P. A. Robinson, "Nonlinear wave collapse and strong turbulence," Rev. Mod. Phys. 69, 507-573 (1997). [CrossRef]
  5. C. A. Sackett, J. M. Gerton, M. Welling, and R. G. Hulet, "Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions," Phys. Rev. Lett. 82, 876-879 (1999). [CrossRef]
  6. L. Berg´e, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, "Multiple filamentation of terawatt laser pulses in air," Phys. Rev. Lett. 92, 225002 1-4 (2004). [CrossRef]
  7. G. Fibich and A. L. Gaeta, "On the critical power for self-focusing in bulk media and hollow waveguides," Opt. Lett. 25, 335-337 (2000). [CrossRef]
  8. G. Fraiman, "Asymptotic stability of manifold of self-similar solutions in self-focusing," Sov. Phys. JETP 61, 228-233 (1985).
  9. M. Landman, G. Papanicolaou, C. Sulem, and P. Sulem, "Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension," Phys. Rev. A 38, 3837-3843 (1988). [CrossRef] [PubMed]
  10. B. LeMesurier, P. Papanicolaou, C. Sulem, and P. Sulem, "Local structure of the self-focusing singularity of the nonlinear Schr¨odinger equation," Physica D 32, 210-226 (1988). [CrossRef]
  11. F. Merle, and P. Raphael, "Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation," Geom. Funct. Anal. 13, 591-642 (2003). [CrossRef]
  12. K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: observation of the Townes profile," Phys. Rev. Lett. 90, 203902 1-4 (2003). [CrossRef]
  13. G. Fibich, N. Gavish, and X.-P. Wang, "New singular solutions of the nonlinear Schrödinger equation," [CrossRef]
  14. PhysicaD 211, 193-220 (2005). [CrossRef]
  15. D. V. Skryabin and W. J. Firth, "Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media," Phys. Rev. E 58, 3916-3930 (1998). [CrossRef]
  16. L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 1-4 (2006).
  17. A. J. Campillo, S. L. Shapiro and B. R. Suydam, "Periodic breakup of optical beams due to self-focusing," Appl. Phys. B 23, 628-630 (1973). [CrossRef] [PubMed]
  18. J. M. Soto-Crespo, D. R. Heatley, and E. M. Wright, "Stability of the higher-bound states in a saturable selffocusing medium," Phys. Rev. A 44, 636-644 (1991). [CrossRef]
  19. M. D. Feit and J. A. Fleck, Jr., "Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams," J. Opt. Soc. Am. B 5, 633-640 (1988). [CrossRef] [PubMed]
  20. J. M. Soto-Crespo, E. M. Wright and N. N. Akhmediev, "Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium," Phys. Rev. A 45, 3168-3174 (1992).
  21. V. I. Bespalov and V. I. Talanov, "Filamentary structure of light beams in non-linear liquids," JETP Lett. 3,307-310 (1966). [CrossRef]
  22. A. J. Campillo, S. L. Shapiro, B. R. Suydam, "Relationship of self-focusing to spatial instability modes," Appl. Phys. Lett. 24, 178-180 (1974). [CrossRef] [PubMed]
  23. G. Fibich, S. Eisenmann, B. Ilan, Y. Erlich, M. Fraenkel, Z. Henis, A. L. Gaeta, and A. Zigler, "Self-focusing distances of very high power laser pulses," Opt. Express 13, 5897-5903 (2005). [CrossRef]
  24. S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, "Filamentation of femtosecond light pulses in the air: Turbulent cells versus long-range clusters," Phys. Rev. E 70, 046602 1-15 (2004). [CrossRef]
  25. R. Y. Chiao, E. Garmire, and C. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479-482 (1964). 25. L. Berg´e, C. Gou´edard, J. Schjodt-Eriksen, and H. Ward, "Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states," Physica D 176, 181-211 (2003). [CrossRef]
  26. A. Dubietis, E. Gaižauskas, G. Tamǒsauskas, and P. D. Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 1-4 (2004). [CrossRef]
  27. A. L. Gaeta, "Catastrophic collapse of ultrashort pulses," Phys. Rev. Lett. 84, 3582-3585 (2000). [CrossRef] [PubMed]
  28. G. M´echain, A. Couairon, Y.-B. Andé, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, and A. Mysyrowicz, R. Sauerbrey, "Long-range self-channeling of infrared laser pulses in air: a new propagation regime without ionization," Appl. Phys. B 79, 379-382 (2004). [CrossRef]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited