Abstract

We investigate the effects of beam ellipticity on the dynamics of multiple filamentation. We find that increasing the ellipticity of the initial beam decreases the power required for multiple filamentation. At lower input ellipticities, the beam breaks into filaments along its widest dimension, whereas for higher ellipticities the pulse breaks into bands and then into filaments as the power is increased. The breakup patterns of the beam along the wider dimension are consistent with the modulational instability, and these patterns are independent of polarization and noise. Numerical simulations are in qualitative agreement with these features of multiple filamentation breakup.

© 2005 Optical Society of America

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References

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  1. J. Kasparian, M. Rodriguez, G. Mjean, J.Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. Andr, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, �??White-light filaments for atmospheric analysis,�?? Science 301, 61 (2003).
    [CrossRef] [PubMed]
  2. K. D. Moll, A. L. Gaeta, and G. Fibich, �??Self-similar optical wave collapse: observation of the Townes profile,�?? Phys. Rev. Lett. 90, 203902 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  4. V. I. Bespalov and V. I. Talanov, �??Filamentary structure of light beams in non-linear liquids,�?? JETP Lett. 3, 307-310 (1966).
  5. J. W. Grantham, H. M. Gibbs, G. Khitrova, J. F. Valley, and Xu Jiajin, �??Kaleidoscopic spatial instability: bifurcations of optical transverse solitary waves,�?? Phys. Rev. Lett. 66, 1422 (1991).
    [CrossRef] [PubMed]
  6. G. Fibich, and B. Ilan, �??Self-focusing of circularly polarized beams,�?? Phys. Rev. E 67, 036622 (2003).
    [CrossRef]
  7. S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, M. Katz, and D. Eger, �??Observation of multiple soliton generation mediated by amplification of asymmetries,�?? Phys. Rev. E 67, 046616 (2003).
    [CrossRef]
  8. A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, �??Multiple filamentation induced by input-beam ellipticity,�?? Opt. Lett. 29, 1126 (2004).
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  9. G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, �??Control of multiple filamentation in air,�?? Opt. Lett. 29, 1772 (2004).
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  10. G. Fibich, and B. Ilan, �??Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation,�?? J. Opt. Soc. Am. B 17, 1749 (2000).
    [CrossRef]
  11. G. Fibich and B. Ilan, �??Deterministic vectorial effects lead to multiple filamentation,�?? Opt. Lett. 26, 840 (2001).
    [CrossRef]
  12. G. Fibich and B. Ilan, �??Vectorial and random effects in self-focusing and in multiple filamentation,�?? Physica D 157, 112 (2001).
    [CrossRef]
  13. R. W. Boyd, Nonlinear Optics (Academic, San Diego, 2003)

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

JETP Lett. (1)

V. I. Bespalov and V. I. Talanov, �??Filamentary structure of light beams in non-linear liquids,�?? JETP Lett. 3, 307-310 (1966).

Opt. Lett. (3)

Phys. Rev. E (2)

G. Fibich, and B. Ilan, �??Self-focusing of circularly polarized beams,�?? Phys. Rev. E 67, 036622 (2003).
[CrossRef]

S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, M. Katz, and D. Eger, �??Observation of multiple soliton generation mediated by amplification of asymmetries,�?? Phys. Rev. E 67, 046616 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

J. W. Grantham, H. M. Gibbs, G. Khitrova, J. F. Valley, and Xu Jiajin, �??Kaleidoscopic spatial instability: bifurcations of optical transverse solitary waves,�?? Phys. Rev. Lett. 66, 1422 (1991).
[CrossRef] [PubMed]

K. D. Moll, A. L. Gaeta, and G. Fibich, �??Self-similar optical wave collapse: observation of the Townes profile,�?? Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

Physica D (2)

L. Bergé, C. Gouédard, J. Schjødt-Eriksen, and H. Ward, �??Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,�?? Physica D 176, 181 (2003).
[CrossRef]

G. Fibich and B. Ilan, �??Vectorial and random effects in self-focusing and in multiple filamentation,�?? Physica D 157, 112 (2001).
[CrossRef]

Science (1)

J. Kasparian, M. Rodriguez, G. Mjean, J.Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. Andr, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, �??White-light filaments for atmospheric analysis,�?? Science 301, 61 (2003).
[CrossRef] [PubMed]

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, San Diego, 2003)

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup and input profiles for various ellipticites e

Fig. 2.
Fig. 2.

CCD camera images of output face of the glass for various input pulse powers. Image area is 2 mm X 1.2 mm. (a) e=2.1 and z=0.34Ldf (b) e=4.1 and z=0.7Ldf (c) e=5.75 and z=0.94Ldf , where Ldf is defined by Eq. 1.

Fig. 3.
Fig. 3.

Lineouts from data displayed in Fig. 2. (a) e=2.1, E=63 µJ, (b) e=5.75, E=27 µJ.

Fig. 4.
Fig. 4.

Simulated output profiles for various input powers P. (a) e=2, z=0.34Ldf , (b) e=6, z=0.94Ldf

Equations (3)

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L df = kab 2 ,
L nl 1 = 6 π ω 2 A 0 2 χ ( 3 ) kc 2 ,
u z = i 4 2 u + i L df L nl u 2 u i N sat u 4 u ,

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