Abstract

The nonlinear dynamics of a high-power femtosecond singular pulse in Kerr media are analyzed numerically upon optically induced ionization. We examine the plasma inertia impact to stable propagation of optical vortices. Multifoci behavior of vortices in medium are revealed. Next we numerically demonstrate that inertial character of plasma formation provides a quasi-soliton regime of vortex propagation resistant to symmetry-breaking perturbation.

© 2012 Optical Society of America

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  4. E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Overview of plasma-based accelerator concepts,” IEEE Trans. Plasma Sci. 24, 252–288 (1996).
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  8. A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113(2000).
    [CrossRef]
  9. I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
    [CrossRef]
  10. B. A. Malomed, L.-C. Crasovan, and D. Mihalache, “Stability of vortex solitons in the cubic-quintic model,” Physica D 161, 187–201 (2002).
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  16. D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
    [CrossRef]
  17. S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603-1–7 (2006).
    [CrossRef]
  18. A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, “Infrared femtosecond light filaments in air: simulation and experiment,” J. Opt. Soc. Am. B 19, 1117–1131 (2002).
    [CrossRef]
  19. L. Berge and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7, 210–230 (2000).
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  20. F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
    [CrossRef]
  21. L. Berge and A. Couairon, “Gas-induced solitons,” Phys. Rev Lett. 86, 1003–1006 (2001).
    [CrossRef]
  22. N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
    [CrossRef]
  23. R. A. Vlasov, O. K. Khasanov, and T. V. Smirnova, “Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionization,” Quantum Electron. 35, 947–952 (2005).
    [CrossRef]
  24. V. Skarka, N. B. Aleksic, and V. I. Berezhiani, “Evolution of singular optical pulses towards vortex solitons and filamentation in air,” Phys. Lett. A 319, 317–324 (2003).
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  25. A. Vinçotte and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901-1–14 (2005).
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  26. L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
    [CrossRef]
  27. Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behaviour of a focused femtosecond laser pulse in fused silica,” J. Opt.-Pure Appl. Opt. 5, 102–107 (2003).
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  29. V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
    [CrossRef]

2010 (1)

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

2007 (1)

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

2006 (1)

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603-1–7 (2006).
[CrossRef]

2005 (2)

R. A. Vlasov, O. K. Khasanov, and T. V. Smirnova, “Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionization,” Quantum Electron. 35, 947–952 (2005).
[CrossRef]

A. Vinçotte and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901-1–14 (2005).
[CrossRef]

2004 (3)

Y.-F. Chen, K. Beckwitt, F. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E 70, 046610-1 (2004).

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “Fine structure of singular beams in crystals: colours and polarization,” J. Opt. Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92, 083902-1–4 (2004).
[CrossRef]

2003 (4)

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behaviour of a focused femtosecond laser pulse in fused silica,” J. Opt.-Pure Appl. Opt. 5, 102–107 (2003).
[CrossRef]

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Optics 45, 119–204 (2003).
[CrossRef]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

V. Skarka, N. B. Aleksic, and V. I. Berezhiani, “Evolution of singular optical pulses towards vortex solitons and filamentation in air,” Phys. Lett. A 319, 317–324 (2003).
[CrossRef]

2002 (3)

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

B. A. Malomed, L.-C. Crasovan, and D. Mihalache, “Stability of vortex solitons in the cubic-quintic model,” Physica D 161, 187–201 (2002).
[CrossRef]

A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, “Infrared femtosecond light filaments in air: simulation and experiment,” J. Opt. Soc. Am. B 19, 1117–1131 (2002).
[CrossRef]

2001 (3)

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Optics 42, 219–276 (2001).

L. Berge and A. Couairon, “Gas-induced solitons,” Phys. Rev Lett. 86, 1003–1006 (2001).
[CrossRef]

2000 (3)

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[CrossRef]

A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113(2000).
[CrossRef]

L. Berge and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7, 210–230 (2000).
[CrossRef]

1999 (1)

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Optics 39, 291–372 (1999).
[CrossRef]

1998 (2)

1997 (1)

D. E. Edmundson, “Unstable higher modes of a three-dimensional nonlinear Schrödinger equation,” Phys. Rev. E 55, 7636–7644 (1997).
[CrossRef]

1996 (1)

E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Overview of plasma-based accelerator concepts,” IEEE Trans. Plasma Sci. 24, 252–288 (1996).
[CrossRef]

Aközbek, N.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[CrossRef]

Aleksic, N. B.

V. Skarka, N. B. Aleksic, and V. I. Berezhiani, “Evolution of singular optical pulses towards vortex solitons and filamentation in air,” Phys. Lett. A 319, 317–324 (2003).
[CrossRef]

Alexeyev, C.

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, L. I. Chen, ed. (Nova Science, 2007), 131–223.

Allen, L.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Optics 39, 291–372 (1999).
[CrossRef]

Babiker, M.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Optics 39, 291–372 (1999).
[CrossRef]

Bang, O.

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603-1–7 (2006).
[CrossRef]

Beckwitt, K.

Y.-F. Chen, K. Beckwitt, F. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E 70, 046610-1 (2004).

Berezhiani, V. I.

V. Skarka, N. B. Aleksic, and V. I. Berezhiani, “Evolution of singular optical pulses towards vortex solitons and filamentation in air,” Phys. Lett. A 319, 317–324 (2003).
[CrossRef]

Berge, L.

L. Berge and A. Couairon, “Gas-induced solitons,” Phys. Rev Lett. 86, 1003–1006 (2001).
[CrossRef]

L. Berge and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7, 210–230 (2000).
[CrossRef]

Bergé, L.

Bigelow, M. S.

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92, 083902-1–4 (2004).
[CrossRef]

Boutou, V.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

Bowden, C. M.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[CrossRef]

Boyd, R. W.

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92, 083902-1–4 (2004).
[CrossRef]

Buccoliero, D.

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

Buryak, A. V.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

Chen, Y.-F.

Y.-F. Chen, K. Beckwitt, F. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E 70, 046610-1 (2004).

Chin, S. L.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[CrossRef]

Cojocaru, C.

Couairon, A.

A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, “Infrared femtosecond light filaments in air: simulation and experiment,” J. Opt. Soc. Am. B 19, 1117–1131 (2002).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

L. Berge and A. Couairon, “Gas-induced solitons,” Phys. Rev Lett. 86, 1003–1006 (2001).
[CrossRef]

L. Berge and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7, 210–230 (2000).
[CrossRef]

Courvoisier, F.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

Crasovan, L. C.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

Crasovan, L.-C.

B. A. Malomed, L.-C. Crasovan, and D. Mihalache, “Stability of vortex solitons in the cubic-quintic model,” Physica D 161, 187–201 (2002).
[CrossRef]

Desyatnikov, A.

A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113(2000).
[CrossRef]

Desyatnikov, A. S.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

Edmundson, D.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603-1–7 (2006).
[CrossRef]

Edmundson, D. E.

D. E. Edmundson, “Unstable higher modes of a three-dimensional nonlinear Schrödinger equation,” Phys. Rev. E 55, 7636–7644 (1997).
[CrossRef]

Egorov, Y. A.

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “Fine structure of singular beams in crystals: colours and polarization,” J. Opt. Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

Esarey, E.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Overview of plasma-based accelerator concepts,” IEEE Trans. Plasma Sci. 24, 252–288 (1996).
[CrossRef]

Fadeyeva, T. A.

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “Fine structure of singular beams in crystals: colours and polarization,” J. Opt. Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

Firth, W. J.

D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
[CrossRef]

Franco, M.

A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, “Infrared femtosecond light filaments in air: simulation and experiment,” J. Opt. Soc. Am. B 19, 1117–1131 (2002).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

Gao, W.

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Optics 45, 119–204 (2003).
[CrossRef]

Gong, Q.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behaviour of a focused femtosecond laser pulse in fused silica,” J. Opt.-Pure Appl. Opt. 5, 102–107 (2003).
[CrossRef]

Izdebskaya, Y. V.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Jiang, H.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behaviour of a focused femtosecond laser pulse in fused silica,” J. Opt.-Pure Appl. Opt. 5, 102–107 (2003).
[CrossRef]

Kasparian, J.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

Khasanov, O. K.

R. A. Vlasov, O. K. Khasanov, and T. V. Smirnova, “Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionization,” Quantum Electron. 35, 947–952 (2005).
[CrossRef]

Kivshar, Y. S.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

Krall, J.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Overview of plasma-based accelerator concepts,” IEEE Trans. Plasma Sci. 24, 252–288 (1996).
[CrossRef]

Krolikowski, W.

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603-1–7 (2006).
[CrossRef]

Krolikowski, W. Z.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Lamouroux, B.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

Lopez-Aguayo, S.

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

Maimistov, A.

A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113(2000).
[CrossRef]

Malomed, B.

A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113(2000).
[CrossRef]

Malomed, B. A.

Y.-F. Chen, K. Beckwitt, F. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E 70, 046610-1 (2004).

B. A. Malomed, L.-C. Crasovan, and D. Mihalache, “Stability of vortex solitons in the cubic-quintic model,” Physica D 161, 187–201 (2002).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

Martorell, J.

Méjean, G.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

Mihalache, D.

B. A. Malomed, L.-C. Crasovan, and D. Mihalache, “Stability of vortex solitons in the cubic-quintic model,” Physica D 161, 187–201 (2002).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

Mysyrowicz, A.

Mysyrowitcz, A.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

Padgett, M.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Optics 39, 291–372 (1999).
[CrossRef]

Petrov, D. V.

Prade, B.

A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, “Infrared femtosecond light filaments in air: simulation and experiment,” J. Opt. Soc. Am. B 19, 1117–1131 (2002).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

Rode, A. V.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Salmon, E.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

Samarskii, A. A.

A. A. Samarskii, The Theory of Difference Schemes (Marcel Dekker, 2001).

Sammut, R. A.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

Shvedov, V. G.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Skarka, V.

V. Skarka, N. B. Aleksic, and V. I. Berezhiani, “Evolution of singular optical pulses towards vortex solitons and filamentation in air,” Phys. Lett. A 319, 317–324 (2003).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
[CrossRef]

Skupin, S.

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603-1–7 (2006).
[CrossRef]

Smirnova, T. V.

R. A. Vlasov, O. K. Khasanov, and T. V. Smirnova, “Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionization,” Quantum Electron. 35, 947–952 (2005).
[CrossRef]

Soskin, M.

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Optics 42, 219–276 (2001).

Sprangle, P.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Overview of plasma-based accelerator concepts,” IEEE Trans. Plasma Sci. 24, 252–288 (1996).
[CrossRef]

Sudrie, L.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

Talebpour, A.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[CrossRef]

Ting, A.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Overview of plasma-based accelerator concepts,” IEEE Trans. Plasma Sci. 24, 252–288 (1996).
[CrossRef]

Torner, L.

Torres, J. P.

Towers, I.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

Tzortzakis, S.

A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, “Infrared femtosecond light filaments in air: simulation and experiment,” J. Opt. Soc. Am. B 19, 1117–1131 (2002).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

Vasnetsov, M. V.

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Optics 42, 219–276 (2001).

Vilaseca, R.

Vinçotte, A.

A. Vinçotte and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901-1–14 (2005).
[CrossRef]

Vlasov, R. A.

R. A. Vlasov, O. K. Khasanov, and T. V. Smirnova, “Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionization,” Quantum Electron. 35, 947–952 (2005).
[CrossRef]

Volyar, A.

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, L. I. Chen, ed. (Nova Science, 2007), 131–223.

Volyar, A. V.

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “Fine structure of singular beams in crystals: colours and polarization,” J. Opt. Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

Wise, F.

Y.-F. Chen, K. Beckwitt, F. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E 70, 046610-1 (2004).

Wolf, J.-P.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

Wu, Z.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behaviour of a focused femtosecond laser pulse in fused silica,” J. Opt.-Pure Appl. Opt. 5, 102–107 (2003).
[CrossRef]

Yang, H.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behaviour of a focused femtosecond laser pulse in fused silica,” J. Opt.-Pure Appl. Opt. 5, 102–107 (2003).
[CrossRef]

Yavorsky, M.

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, L. I. Chen, ed. (Nova Science, 2007), 131–223.

Yin, J.

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Optics 45, 119–204 (2003).
[CrossRef]

Yu, J.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

Zerom, P.

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92, 083902-1–4 (2004).
[CrossRef]

Zhu, Y.

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Optics 45, 119–204 (2003).
[CrossRef]

Appl. Phys. A (1)

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215(2003).
[CrossRef]

IEEE Trans. Plasma Sci. (1)

E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Overview of plasma-based accelerator concepts,” IEEE Trans. Plasma Sci. 24, 252–288 (1996).
[CrossRef]

J. Opt. Pure Appl. Opt. (1)

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “Fine structure of singular beams in crystals: colours and polarization,” J. Opt. Pure Appl. Opt. 6, S217–S228 (2004).
[CrossRef]

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

J. Opt.-Pure Appl. Opt. (1)

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behaviour of a focused femtosecond laser pulse in fused silica,” J. Opt.-Pure Appl. Opt. 5, 102–107 (2003).
[CrossRef]

Opt. Commun. (1)

D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (2)

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, “Stability of spinning ring solitons in the cubic-quintic nonlinear Schroedinger equation,” Phys. Lett. A 288, 292–298 (2001).
[CrossRef]

V. Skarka, N. B. Aleksic, and V. I. Berezhiani, “Evolution of singular optical pulses towards vortex solitons and filamentation in air,” Phys. Lett. A 319, 317–324 (2003).
[CrossRef]

Phys. Plasmas (1)

L. Berge and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7, 210–230 (2000).
[CrossRef]

Phys. Rev Lett. (1)

L. Berge and A. Couairon, “Gas-induced solitons,” Phys. Rev Lett. 86, 1003–1006 (2001).
[CrossRef]

Phys. Rev. E (5)

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540–4549 (2000).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603-1–7 (2006).
[CrossRef]

D. E. Edmundson, “Unstable higher modes of a three-dimensional nonlinear Schrödinger equation,” Phys. Rev. E 55, 7636–7644 (1997).
[CrossRef]

A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113(2000).
[CrossRef]

Y.-F. Chen, K. Beckwitt, F. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E 70, 046610-1 (2004).

Phys. Rev. Lett. (3)

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92, 083902-1–4 (2004).
[CrossRef]

A. Vinçotte and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901-1–14 (2005).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowitcz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601-1–4 (2002).
[CrossRef]

Physica B (1)

D. Buccoliero, S. Lopez-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Y. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351–356 (2007).
[CrossRef]

Physica D (1)

B. A. Malomed, L.-C. Crasovan, and D. Mihalache, “Stability of vortex solitons in the cubic-quintic model,” Physica D 161, 187–201 (2002).
[CrossRef]

Prog. Optics (3)

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Optics 42, 219–276 (2001).

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Optics 39, 291–372 (1999).
[CrossRef]

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Optics 45, 119–204 (2003).
[CrossRef]

Quantum Electron. (1)

R. A. Vlasov, O. K. Khasanov, and T. V. Smirnova, “Evolution of tubular singular pulsed beams in a nonlinear dielectric medium upon ionization,” Quantum Electron. 35, 947–952 (2005).
[CrossRef]

Other (3)

A. A. Samarskii, The Theory of Difference Schemes (Marcel Dekker, 2001).

J. P. Torres and L. Torner, eds., Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, L. I. Chen, ed. (Nova Science, 2007), 131–223.

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Figures (9)

Fig. 1.
Fig. 1.

Nonlinear dynamics of the doughnut pulsed beams in bulk fused silica for temporal slice t=0 at m=2, (da/dz)0=0.041, a0=26μm, τp=120fs: potential functions (a), (c) and beam radii (b), (d). At this, (a) and (b) correspond to input laser pulse energy W=3.0μJ and α=5.9; (c) and (d) correspond to W=7.9μJ and α=15.57.

Fig. 2.
Fig. 2.

Beam radius evolution at the propagation a0=26μm, W=7.9μJ, τp=120fs, (da/dz)0=0.041 for two different topological charges 2 and 3.

Fig. 3.
Fig. 3.

Comparative analysis of the location of beam radius minima (a) and intensity peaks (b) at the pulsed beam propagation when a0=22μm; λ=800nm; m=2; I0=4·1016W/m2; α=15.56; (da/dz)0=0.06.

Fig. 4.
Fig. 4.

Singular pulse (m=1) intensity contours at some propagation distances for instantaneous character of plasma: (a) z=0.25; (b) z=1.25; (c) z=2.1 (in units of Ldf).

Fig. 5.
Fig. 5.

Singular pulse (m=1) intensity contours at some propagation distances under conditions of plasma inertia: (a) z=0.5; (b) z=1.25; (c) z=2; (d) z=2.5; (e) z=2.75; (f) z=3 (in units of Ldf).

Fig. 6.
Fig. 6.

Profiles of double charged vortex for instantaneous character of plasma: (a) z=0.2; (b) z=0.7; (c) z=1.25 (in units of Ldf).

Fig. 7.
Fig. 7.

Behavior of the same vortex under conditions of plasma inertia at (a) z=0.25; (b) z=1.2; (c) z=1.7 (in units of Ldf).

Fig. 8.
Fig. 8.

Profiles of triple charged vortex for instantaneous character of plasma at (a) z=0.1; (b) z=0.5; (c) z=0.75 (in units of Ldf).

Fig. 9.
Fig. 9.

Behavior of the same vortex under conditions of plasma inertia at (a) z=0.15; (b) z=0.6; (c) z=0.9 (in units of Ldf).

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

Ez=i2kr2Eiβ222Et2+ik0n2|E|2Eσ2(1+iω0τc)ρEβ(K)2|E|2K2E,
ρt=β(K)Kω|E|2Kρτr.
β(K)=29πω(meω)3/2(qe216meEgω2)Ke2KΦ(s);Φ(s)=es20sex2dx;s=2K2Egω,
E(z=0)=2mm!E0r|m|w0mexp(r22w02t22τp2)exp(imφ),E(r=0)r=E(r=)=0.
ez¯=iΔeiδ2et¯2+8iα|e|2eσ2(1+iωτc)eμK|e|2K2eim2r¯2e.
H=(|e|2δ|et|2c32|e|4+m2r2|e|2)drdt.
P(z)=|e|2drdt.
e(r,t)=wfw02rmexp(wf2w02r2t2τp2ik0wf22fr2),
R¯2(z)1P(z)rt|rr(z)|2|e|2drdt,
T¯2(z)1P(z)rt|tt(z)|2|e|2drdt.
H=12m(π2)32(w02wf2)m1[(32(1+z0f))mm!+(1+z02f2)(m+1)!c3223m+4(w02wf2)m(2m)!],
P=(π2)3212m+1(w0wf)2mm!.
R¯2(z)={8zfz0[32(1+z0f)]m+(1+z02f2)(m+1)2c323m+4(zfz0)m(2m)!m!}z2+(2mk0w02f)(m+1)z+m+12z0zf.
E(r,z,t)=A(r,z,t)·exp{iφ(r,z,t)},
φ(r,z,t)=ψ(r,z,t)+mθ.
2kAz+2Arψr+A2ψr2+ArψrkσρA+kβK|A|2K1=0,
ψz+12k(ψ)212k(2AAkσρω0τcm2r2+2kk0n2A2)=0.
H=12k(ψr)212k(2AAkσρω0τcm2r2+2kk0n2A2).
k2(dadz)2+U(a,t)=0,
V(a,t)=12k{2(2+m)a2kσωτcτg(t)β(K)Kω(2Pinπ)K(mmm!)KeK(m+2τ2)a2K+2kk0n2(2Pinπ)(mmm!)e(m+2τ2)a2}.

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