Abstract

We report experiments on self-focusing of femtosecond diffraction-resistant vortex beams in water. These beams are higher-order Bessel beams with weak azimuthal modulation of the transverse intensity patterns. The modulation overrides the self-focusing dynamics and results in the formation of regular bottlelike filament distributions. The peak-power thresholds for filamentation, at a particular distance, are relatively accurately estimated by the adaptation of the Marburger formula derived earlier for Gaussian beams. The nonlinear conversion of the incident conical waves into the localized spatial wave packets propagating near the beam axis is observed.

© 2011 Optical Society of America

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  1. A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
    [CrossRef]
  2. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
    [CrossRef]
  3. S. L. Chin, Femtosecond Laser Filamentation (Springer, 2010).
    [CrossRef]
  4. A. Dubietis, P. Polesana, G. Valiulis, A. Stabinis, P. Di Trapani, and A. Piskarkas, Opt. Express 15, 4168 (2007).
    [CrossRef] [PubMed]
  5. P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, Opt. Express 16, 15733 (2008).
    [CrossRef] [PubMed]
  6. M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
    [CrossRef] [PubMed]
  7. A. Vinçotte and L. Bergé, Phys. Rev. Lett. 95, 193901 (2005).
    [CrossRef] [PubMed]
  8. L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
    [CrossRef] [PubMed]
  9. T. D. Grow, A. I. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
    [CrossRef] [PubMed]
  10. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef] [PubMed]
  11. P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. J. H. Marburger, Prog. Quant. Electr. 4, 35 (1975).
    [CrossRef]
  14. Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
    [CrossRef]
  15. R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
    [CrossRef]

2009 (3)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

2008 (1)

2007 (4)

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

A. Dubietis, P. Polesana, G. Valiulis, A. Stabinis, P. Di Trapani, and A. Piskarkas, Opt. Express 15, 4168 (2007).
[CrossRef] [PubMed]

T. D. Grow, A. I. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

2006 (1)

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

2005 (1)

A. Vinçotte and L. Bergé, Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

2004 (1)

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

2001 (1)

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

1996 (1)

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

1975 (1)

J. H. Marburger, Prog. Quant. Electr. 4, 35 (1975).
[CrossRef]

’t Hooft, G. W.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

Atabinis, A.

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

A. Vinçotte and L. Bergé, Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

Bigelow, M. S.

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Chen, Y.-H.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Chin, S. L.

S. L. Chin, Femtosecond Laser Filamentation (Springer, 2010).
[CrossRef]

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Couairon, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Di Trapani, P.

Dubietis, A.

Eliel, E. R.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

Faccio, D.

Fibich, G.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

Gadonas, R.

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

Gaeta, A. L.

T. D. Grow, A. I. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

Grow, T. D.

T. D. Grow, A. I. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

Ishaaya, A.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

Ishaaya, A. I.

T. D. Grow, A. I. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

Jarutis, V.

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

Jones, T. G.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Kasparian, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, Opt. Express 16, 15733 (2008).
[CrossRef] [PubMed]

Marburger, J. H.

J. H. Marburger, Prog. Quant. Electr. 4, 35 (1975).
[CrossRef]

Milchberg, H. M.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Moloney, J.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Paškauskas, R.

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

Paterson, C.

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

Piskarkas, A.

Polesana, P.

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, Opt. Express 16, 15733 (2008).
[CrossRef] [PubMed]

Roberts, A.

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Smilgevicius, V.

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

Smith, R.

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

Stabinis, A.

Thing, A.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Vaicaitis, V.

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

Valiulis, G.

Varma, S.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Vinçotte, A.

A. Vinçotte and L. Bergé, Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

Vuong, L. T.

T. D. Grow, A. I. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

Wilkes, Z. W.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Wolf, J.-P.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Zerom, P.

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Thing, Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Opt. Commun. (2)

R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Atabinis, and V. Vaičaitis, Opt. Commun. 196, 309 (2001).
[CrossRef]

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

Opt. Express (2)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Phys. Rev. Lett. (5)

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

A. Vinçotte and L. Bergé, Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901(2006).
[CrossRef] [PubMed]

T. D. Grow, A. I. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

Prog. Quant. Electr. (1)

J. H. Marburger, Prog. Quant. Electr. 4, 35 (1975).
[CrossRef]

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Other (1)

S. L. Chin, Femtosecond Laser Filamentation (Springer, 2010).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup. The inset shows the word “Tucson” that was printed on the surface of the prism and imaged onto the camera. From this image, the imaging depth is estimated at about 1 mm .

Fig. 2
Fig. 2

Examples of the experimentally gener ated beams in the linear propagation regime (at low intensity).

Fig. 3
Fig. 3

Top row: Images of the white-light emission at the pulse-energy levels corresponding to the onset of filamentation at 5 mm from the entrance to the water cuvette, for selected beam orders. Bottom row: Same as above, at the energy levels corresponding to the onset of filamentation in the secondary ring intensity features.

Fig. 4
Fig. 4

Critical power for filamentation for the diffraction- resistant vortex beams. Experimental data points are shown with circles. The solid line is the result of the calculation based on the adaptation of the Marburger formula.

Fig. 5
Fig. 5

Beams of order 8 (top row) and 12 (bottom row) imaged at 50 mm from the entrance to the water cuvette, at various pulse energies.

Equations (2)

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T n ( r , θ ) = exp ( i n θ ) exp ( 2 π i r r 0 ) .
L c = 0.367 π n 0 w 0 2 λ 0 [ ( P th / P cr ) 1 / 2 0.852 ] 2 0.0219 ,

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