Abstract

The effect of beam spatial profile on self-focusing has been investigated. A circular aperture is used to create a Fresnel diffraction pattern. It is shown that self-focusing (a pre-requisite for filament formation) occurs in the presence of the aperture but that no formation is observed when the aperture is removed, even though the beam has higher power well above the threshold for critical power. An analytical solution to the Huygens-Fresnel diffraction integral shows that the axial intensity oscillates between maxima and minima as the distance from the aperture increases and that filament formation coincides with the presence of an axial maximum.

© 2005 Optical Society of America

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References

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  1. R. R. Alfano and S. L. Shapiro, "Emission in the region 4000 to 7000 �? via four-photon coupling in glass," Phys. Rev. Lett. 24, 584-587 (1970).
    [CrossRef]
  2. M. Wittmann and A. Penzkofer, "Spectral broadening of femtosecond laser pulses," Opt. Commun. 126, 308-317 (1996).
    [CrossRef]
  3. A. Gaeta, "Catastrophic collapse of ultrashort pulses," Phys. Rev. Lett. 84, 3582-3585 (2000).
    [CrossRef] [PubMed]
  4. A. Brodeur, F. A. Ilkov and S. L. Chin, "Beam filamentation and the white-light continuum divergence," Opt. Commun. 129, 193-198 (1996).
    [CrossRef]
  5. H. Wille, M. Rodriguez, J. Kasparian, D. Mondelain, J. Yu, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf and L. Wöste, "Teramobile: A mobile femtosecond-terawatt laser and detection system," Eur. Phys. J. AP. 20, 183-190 (2002).
    [CrossRef]
  6. C. V. Shank, R. K. Fork, R. F. Leheny and J. Shah, "Dynamics of photoexcited GaAs band-edge absorption with subpicosecond resolution," Phys. Rev. Lett. 42, 112-115 (1979).
    [CrossRef]
  7. P. B. Corkum, C. Rolland, T. Srinivasan-Rao, "Supercontinuum generation in gases," Phys. Rev. Lett. 57, 2268-2271 (1986).
    [CrossRef] [PubMed]
  8. G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon and J-P. Wolf, "Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system," Appl. Phys. B. 78, 535-537 (2004).
    [CrossRef]
  9. G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
    [CrossRef] [PubMed]
  10. H. Schroeder, J. Liu and S. L. Chin, "From random to controlled small-scale filamentation in water," Opt. Express. 12, 4768-4774 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768</a>
    [CrossRef] [PubMed]
  11. G. Fibich, S. Eisenmann, B. Ilan and A. Zigler, "Control of multiple filamentation in air," Optics Letters, 29, 1772-1774 (2004).
    [CrossRef] [PubMed]
  12. A. D. Dubietis, G. Tamošauskas, G. Fibich and B. Ilan, "Multiple filamentation induced by beam ellipticity," Optics Letters, 29, 1126-1128 (2004).
    [CrossRef] [PubMed]
  13. E. Siegman, Lasers, University Science Books, Sausalito, pp632 (1986).
  14. R. A. Lamb, K. J. Cook and A K. Kar, "Phase stability and diffraction effects in self-focused white-light filaments in water and glass," Proc. SPIE. 5620, 218-227 (2004).
    [CrossRef]
  15. K. Cook, R. A. Lamb, A. K. Kar, �??White-light supercontinuum interference of self-focused filaments in water,�??Appl. Phys. Lett. 83, 3861-3863 (2003).
    [CrossRef]
  16. W. Liu, S. L. Chin, O. Kosareva, I. S. Golubtsov and V. P. Kandidov, Opt. Commun. 225, 193 (2003).
    [CrossRef]
  17. Y. R. Shen, Principles of Non-linear Optics, John Wiley & Sons, New York, pp312 (1984).
  18. A. Brodeur and S. L. Chin, "Ultrafast white-light continuum generation and self-focsuing in condensed media," J. Opt. Soc. Am. B. 16, 637-650 (1999).

Appl. Phys. B

G. Méjean, J. Kasparian, J. Yu, S. Frey, E. Salmon and J-P. Wolf, "Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system," Appl. Phys. B. 78, 535-537 (2004).
[CrossRef]

Appl. Phys. Lett.

K. Cook, R. A. Lamb, A. K. Kar, �??White-light supercontinuum interference of self-focused filaments in water,�??Appl. Phys. Lett. 83, 3861-3863 (2003).
[CrossRef]

Eur. Phys. J. AP.

H. Wille, M. Rodriguez, J. Kasparian, D. Mondelain, J. Yu, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf and L. Wöste, "Teramobile: A mobile femtosecond-terawatt laser and detection system," Eur. Phys. J. AP. 20, 183-190 (2002).
[CrossRef]

Opt. Commun.

M. Wittmann and A. Penzkofer, "Spectral broadening of femtosecond laser pulses," Opt. Commun. 126, 308-317 (1996).
[CrossRef]

A. Brodeur, F. A. Ilkov and S. L. Chin, "Beam filamentation and the white-light continuum divergence," Opt. Commun. 129, 193-198 (1996).
[CrossRef]

W. Liu, S. L. Chin, O. Kosareva, I. S. Golubtsov and V. P. Kandidov, Opt. Commun. 225, 193 (2003).
[CrossRef]

Opt. Express.

H. Schroeder, J. Liu and S. L. Chin, "From random to controlled small-scale filamentation in water," Opt. Express. 12, 4768-4774 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768</a>
[CrossRef] [PubMed]

Opt. Soc. Am. B

A. Brodeur and S. L. Chin, "Ultrafast white-light continuum generation and self-focsuing in condensed media," J. Opt. Soc. Am. B. 16, 637-650 (1999).

Optics Letters

G. Fibich, S. Eisenmann, B. Ilan and A. Zigler, "Control of multiple filamentation in air," Optics Letters, 29, 1772-1774 (2004).
[CrossRef] [PubMed]

A. D. Dubietis, G. Tamošauskas, G. Fibich and B. Ilan, "Multiple filamentation induced by beam ellipticity," Optics Letters, 29, 1126-1128 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. R. Alfano and S. L. Shapiro, "Emission in the region 4000 to 7000 �? via four-photon coupling in glass," Phys. Rev. Lett. 24, 584-587 (1970).
[CrossRef]

A. Gaeta, "Catastrophic collapse of ultrashort pulses," Phys. Rev. Lett. 84, 3582-3585 (2000).
[CrossRef] [PubMed]

C. V. Shank, R. K. Fork, R. F. Leheny and J. Shah, "Dynamics of photoexcited GaAs band-edge absorption with subpicosecond resolution," Phys. Rev. Lett. 42, 112-115 (1979).
[CrossRef]

P. B. Corkum, C. Rolland, T. Srinivasan-Rao, "Supercontinuum generation in gases," Phys. Rev. Lett. 57, 2268-2271 (1986).
[CrossRef] [PubMed]

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Proc. SPIE

R. A. Lamb, K. J. Cook and A K. Kar, "Phase stability and diffraction effects in self-focused white-light filaments in water and glass," Proc. SPIE. 5620, 218-227 (2004).
[CrossRef]

Other

Y. R. Shen, Principles of Non-linear Optics, John Wiley & Sons, New York, pp312 (1984).

E. Siegman, Lasers, University Science Books, Sausalito, pp632 (1986).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental set-up for inducing filament formation.

Fig. 2.
Fig. 2.

Theoretical and measured axial intensity of the Fresnel diffraction profile. Inset: Images of transverse profile at various maxima and minima.

Fig. 3.
Fig. 3.

Filament position inside glass block (right Y axis, red and green lines) recorded for various post-aperture pulse energies. The measured axial beam intensity from Fig. 2. is also plotted (left Y axis, blue line).

Fig. 4.
Fig. 4.

Filament position inside glass block for maximum post-aperture energy of 62µJ (right Y axis, red and green lines) recorded for various post-aperture pulse energies. The measured axial beam intensity from Fig. 2. is also plotted (left Y axis, blue line).

Equations (3)

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E ( s , z ) = i λ 0 a 0 2 π E 0 ( s 0 , z 0 ) exp ( i k ρ ) cos ( θ ) ρ d S 0
I ( s , z ) = 2 I 0 ( s 0 ) [ 1 cos ( k a 2 2 z ) ]
z f = 0.367 k b 2 { [ P P crit 0.852 ] 2 0.0219 } 1 2

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