Abstract

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

© 2015 Optical Society of America

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  1. M. V. Berry and N. L. Balazs, “Non spreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
    [Crossref]
  2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [Crossref] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [Crossref]
  4. J. Durnin, J.J. Miceli, and J.H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  5. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33, 1678–1680 (2008).
    [Crossref] [PubMed]
  6. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
    [Crossref] [PubMed]
  7. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
    [Crossref]
  8. P. Panagiotopoulos, D.G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nature Communications 4, 2622 (2013).
    [Crossref] [PubMed]
  9. Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express 19, 17298–17307 (2011).
    [Crossref] [PubMed]
  10. Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
    [Crossref] [PubMed]
  11. A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
    [Crossref]
  12. P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
    [Crossref]
  13. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
    [Crossref] [PubMed]
  14. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwells equations,” Phys. Rev. Lett. 108, 163901 (2012).
    [Crossref]
  15. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
    [Crossref] [PubMed]
  16. J. Baungartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nature Photon. 2, 675–678 (2008).
    [Crossref]
  17. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
    [Crossref] [PubMed]
  18. N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
    [Crossref] [PubMed]
  19. M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
    [Crossref] [PubMed]
  20. M. A. Porras and C. Ruiz-Jiménez, “Nondiffracting and non-atenuating vortex light beams in media with nonlinear absorption of orbital angular momentum,” J. Opt. Soc. Am. B 31, 2657–2664 (2014).
    [Crossref]
  21. A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
    [Crossref]
  22. W. J. Olver, NIST Handbook of mathematical functions (Cambridge University, 2010).
  23. Note that the signs in the exponentials are opposite in [11].
  24. M. A. Porras, “A dissipative attractor in the spatiotemporal collapse of ultrashort light pulses,” Opt. Express. 18, 7377–7383 (2010).
    [Crossref]
  25. O. V. Borovkova, Y. V. Kartashov, V. A. Vysloukh, V. E. Lobanov, B. A. Malomed, and L. Torner, “Solitons supported by spatially inhomogeneous nonlinear losses,” Opt. Express 20, 2657–2667 (2012).
    [Crossref] [PubMed]
  26. P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
    [Crossref]
  27. V. Jukna, C. Milián, C. Xie, T. Itina, J. Dudley, F. Courvoisier, and A. Couairon, “Filamentation with nonlinear Bessel vortices,” Opt. Express 22, 25410–25425 (2014).
    [Crossref] [PubMed]

2014 (3)

2013 (3)

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

P. Panagiotopoulos, D.G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nature Communications 4, 2622 (2013).
[Crossref] [PubMed]

2012 (4)

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwells equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

O. V. Borovkova, Y. V. Kartashov, V. A. Vysloukh, V. E. Lobanov, B. A. Malomed, and L. Torner, “Solitons supported by spatially inhomogeneous nonlinear losses,” Opt. Express 20, 2657–2667 (2012).
[Crossref] [PubMed]

2011 (3)

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[Crossref] [PubMed]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express 19, 17298–17307 (2011).
[Crossref] [PubMed]

2010 (2)

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

M. A. Porras, “A dissipative attractor in the spatiotemporal collapse of ultrashort light pulses,” Opt. Express. 18, 7377–7383 (2010).
[Crossref]

2009 (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (3)

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

2004 (1)

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

1987 (1)

J. Durnin, J.J. Miceli, and J.H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

1979 (1)

M. V. Berry and N. L. Balazs, “Non spreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Abdollahpour, D.

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

Arie, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Non spreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Bandres, M. A.

Baungartl, J.

J. Baungartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nature Photon. 2, 675–678 (2008).
[Crossref]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwells equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Belic, M.

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry and N. L. Balazs, “Non spreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Borovkova, O. V.

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Cannan, D.

Chen, Z.

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[Crossref] [PubMed]

Couairon, A.

V. Jukna, C. Milián, C. Xie, T. Itina, J. Dudley, F. Courvoisier, and A. Couairon, “Filamentation with nonlinear Bessel vortices,” Opt. Express 22, 25410–25425 (2014).
[Crossref] [PubMed]

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

P. Panagiotopoulos, D.G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nature Communications 4, 2622 (2013).
[Crossref] [PubMed]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

Courvoisier, F.

V. Jukna, C. Milián, C. Xie, T. Itina, J. Dudley, F. Courvoisier, and A. Couairon, “Filamentation with nonlinear Bessel vortices,” Opt. Express 22, 25410–25425 (2014).
[Crossref] [PubMed]

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

Dholakia, K.

J. Baungartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nature Photon. 2, 675–678 (2008).
[Crossref]

Di Trapani, P.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Dubietis, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Dudley, J.

Dudley, J. M.

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

Durnin, J.

J. Durnin, J.J. Miceli, and J.H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J.H.

J. Durnin, J.J. Miceli, and J.H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Faccio, D.

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Fattal, Y.

Gover, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Hu, Y.

Itina, T.

Jukna, V.

Kaminer, I.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwells equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[Crossref] [PubMed]

Kartashov, Y. V.

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Lereah, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Li, T.

Li, Y.

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Lilach, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Lobanov, V. E.

Lotti, A.

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

Lu, K.

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Malomed, B. A.

Marom, D. M.

Mazilu, M.

J. Baungartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nature Photon. 2, 675–678 (2008).
[Crossref]

Miceli, J.J.

J. Durnin, J.J. Miceli, and J.H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Milián, C.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Morandotti, R.

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwells equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Olver, W. J.

W. J. Olver, NIST Handbook of mathematical functions (Cambridge University, 2010).

Panagiotopoulos, P.

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

P. Panagiotopoulos, D.G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nature Communications 4, 2622 (2013).
[Crossref] [PubMed]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

Papazoglou, D. G.

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

Papazoglou, D.G.

P. Panagiotopoulos, D.G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nature Communications 4, 2622 (2013).
[Crossref] [PubMed]

Parola, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Piskarskas, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

Polesana, P.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Porras, M. A.

M. A. Porras and C. Ruiz-Jiménez, “Nondiffracting and non-atenuating vortex light beams in media with nonlinear absorption of orbital angular momentum,” J. Opt. Soc. Am. B 31, 2657–2664 (2014).
[Crossref]

M. A. Porras, “A dissipative attractor in the spatiotemporal collapse of ultrashort light pulses,” Opt. Express. 18, 7377–7383 (2010).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Porras, M.A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

Rudnick, A.

Ruiz-Jiménez, C.

Salandrino, A.

Segev, M.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwells equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[Crossref] [PubMed]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[Crossref] [PubMed]

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

Torner, L.

Tzortzakis, S.

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

P. Panagiotopoulos, D.G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nature Communications 4, 2622 (2013).
[Crossref] [PubMed]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

Voloch-Bloch, N.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Vysloukh, V. A.

Wu, Z.

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Xie, C.

Zhang, P.

Zhang, X.

Zhang, Y.

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Zheng, H.

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, “Non spreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

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

Nature (1)

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref] [PubMed]

Nature Communications (1)

P. Panagiotopoulos, D.G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nature Communications 4, 2622 (2013).
[Crossref] [PubMed]

Nature Photon. (1)

J. Baungartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nature Photon. 2, 675–678 (2008).
[Crossref]

Opt. Express (4)

Opt. Express. (2)

M. A. Porras, “A dissipative attractor in the spatiotemporal collapse of ultrashort light pulses,” Opt. Express. 18, 7377–7383 (2010).
[Crossref]

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media,” Opt. Express. 22, 7160–7171 (2014).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (2)

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84, 021807(R) (2011).
[Crossref]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A 86, 013842 (2012).
[Crossref]

Phys. Rev. Lett. (7)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

J. Durnin, J.J. Miceli, and J.H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwells equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106, 213903 (2011).
[Crossref] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M.A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive and dissipative Kerr media,” Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

Proc. SPIE (1)

A. Couairon, A. Lotti, P. Panagiotopoulos, D. Abdollahpour, D. Faccio, D. G. Papazoglou, S. Tzortzakis, F. Courvoisier, and J. M. Dudley, “Ultrashort laser pulse filamentation with Airy and Bessel beams,” Proc. SPIE 8770, 87701E (2013).
[Crossref]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Other (2)

W. J. Olver, NIST Handbook of mathematical functions (Cambridge University, 2010).

Note that the signs in the exponentials are opposite in [11].

Supplementary Material (4)

Media 1: MP4 (1678 KB)     
Media 2: MP4 (1751 KB)     
Media 3: MP4 (2004 KB)     
Media 4: MP4 (1323 KB)     

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Figures (7)
Fig. 1
Fig. 1 (a) Gray curves: Intensities profiles of NABs with a0 = 1.500, a0 = 4.000 and a0 = 4.325 in a medium with M = 5 and Kerr nonlinearity α = 1. Black curve: Intensity profile of the LNAB with a0 = a0,max ≃ 4.343. (b) The same but in double logarithmic scale. The curves decay as (−u)−1/2 for the NABs and as (−u)−1/(2M−2) for the LNAB for u → −∞. (c) Nonlinear losses N−∞ and oscillation contrast C ≡ ( 1 − N − ∞ 2 / E 2 ) 1 / 2 of NABs as functions of a0. (d) Amplitudes |ain| and |aout| of the inward and outward Hänkel components of NABs as functions of a0. In (b) and (c), M = 5, and α = 0 (green curves), and α = 1 (black curves).

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Fig. 2
Fig. 2 In a medium with M = 5 and Kerr nonlinearity α = 1, in double logarithmic scale, (a) intensity profile of the NAB with a0 = 4.0 (solid curve), and its asymptotic form in Eq. (6) with |ain| = 3.176 and |aout| = 0.523 (dashed curve); (b) intensity profile of the LNAB with a0,max = 4.343 (solid curve) and its asymptotic form a2 ∼ b2(−u)−2σ with b and σ in Eq. (8) (dashed curve).

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Fig. 3
Fig. 3 For a medium with M = 5 and α = 1, (a) Media 1: Change of the intensity profile of an input Airy beam with a0 = 3.5 with propagation distance v. The red curve represents the final attracting NAB with a0 = 4.13, whose inward Hänkel amplitude is |ain| = 3.5. (b) NLLs N − ∞ = 2 ∫ − ∞ ∞ | A ˜ | 2 d u (black curve) and peak intensity (gray curve) of the propagating beam in (a) as a function of propagation distance v. (c) For M = 5 and α = 0 (no Kerr nonlinearity), in green, amplitude a0(∞) of the attracting NAB (solid curve), and its inward and outward Hänkel amplitudes, |ain(∞)| and |aout(∞)| (dashed curves), as functions of the amplitude a0(0) of the input Airy beam. The same lines in black correspond to α = 1 (Kerr medium).

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Fig. 4
Fig. 4 For a medium with M = 5 and α = 1 with entrance plane at v = 0 (abrupt input): (a) Media 2: Change of the intensity profile of an initial exponential-Airy beam with a0 = 3.5 and γ = 0.0025 with propagation distance v. The red curve represents the ideal attracting NAB with a0 = 4.13 (|ain| = 3.5); (b) NLLs and (c) peak intensity versus propagation distance v for γ = 0, or ideal case (light gray), γ = 0.0025 (dark gray), and γ = 0.0075 (black).

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Fig. 5
Fig. 5 For M = 5 and α = 1 and entrance plane at v = −50 (soft input): (a) Media 3: Change of the intensity profile of an initial exponential-Airy beam with a0 = 3.5 and γ = 0.0025 with propagation distance v. The red curve represents the ideal attracting NAB with a0 = 4.13 (|ain| = 3.5); (b) NLLs and (c) peak intensity versus propagation distance v for γ = 0.0025 (dark gray) and γ = 0.0075 (black). The horizontal lines represent the NLLs and the peak intensity of the attracting NAB. The dashed gray curves in (c) represent the peak intensity of exponential-Airy beams propagating linearly.

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Fig. 6
Fig. 6 For M = 5 and α = 1 and entrance plane at v = −75 (soft input): (a) intensity profile at the focus v = 0 of an input exponential-Airy beam with a0 = 7.0 and γ = 0.0025 (black curve), and intensity profile of the LNAB in this medium (red curve). (b) Peak intensity versus propagation distance for γ = 0.0025 (dark gray) and γ = 0.0075 (black). The horizontal line represents the peak intensity of the LNAB. The dashed gray curves represent the peak intensity of exponential-Airy beams propagating linearly.

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Fig. 7
Fig. 7 Dynamics of a linear Airy beam with a0 = 2 entering a nonlinear medium with M = 5 and α = 0 at v = 0 and exiting it at v = 10. (a) Media 4: Change of the intensity profile with propagation distance. The red curve represents the initial lineal Airy. (b) Peak intensity versus propagation distance. The dashed vertical lines represent the region filled by the nonlinear medium.

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Equations (10)

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

∂ z A = i 2 k ∂ x 2 A + i k n 2 n | A | 2 A − β ( M ) 2 | A | 2 M − 2 A ,
∂ v A ˜ = i 2 ∂ u 2 A ˜ + v 2 ∂ u A ˜ + i α | A ˜ | 2 A ˜ − | A ˜ | 2 M − 2 A ˜ ,
a ″ = u a + ( ψ ′ ) 2 a − 2 α a 3 , ψ ″ = − 2 ψ ′ a ′ a − 2 a 2 M − 2 ,
ψ ′ a 2 = 2 ∫ u ∞ a 2 M d u ≡ N u ,
a 2 ⋍ E ( − u ) 1 / 2 { 1 + C sin [ 4 3 ( − u ) 3 / 2 + ϕ ] } ,
A ˜ ⋍ 1 2 − u 3 [ a out e i π / 6 H 1 / 3 ( 1 ) ( ρ ) + a in e − i π / 6 H 1 / 3 ( 2 ) ( ρ ) ] ,
b σ ( σ + 1 ) ( − u ) − σ − 2 + b ( − u ) − σ + 1 − 4 b 4 M − 3 ( 1 − 2 M σ ) 2 ( − u ) 2 − σ ( 4 M − 3 ) + 2 α b 3 ( − u ) − 3 σ ⋍ 0 .
b = [ M − 2 4 ( M − 1 ) ] 1 / ( 2 M − 3 ) ,                         σ = 1 4 M − 4 .
A ˜ ( u , v ) = a 0 A i ( u + i γ v ) e i ϕ L ( u , v ) e γ ( u − v 2 / 4 ) e i v γ 2 / 2
Δ v ~ 2 2 ln ( 0.287 a 0 2 ) / γ

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