Abstract

We report the first experimental demonstration of the so-called three-Airy beams. Such beams represent a two-dimensional field that is a product (rather than simple superposition) of three Airy beams. Our experiments show that, in contrast to conventional Airy beams, this new family of Airy beams can be realized even without the use of truncation by finite apertures. Furthermore, we study linear and nonlinear propagation of the three-Airy beams in a photorefractive medium. It is found that a three-Airy beam tends to linearly diffract into a super-Gaussian-like beam, while under nonlinear propagation it either turns into three intensity spots with a self-defocusing nonlinearity or evolves into a self-trapped channel with a self-focusing nonlinearity.

© 2013 OSA

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  1. G.A. Siviloglou and D.N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007).
    [CrossRef] [PubMed]
  2. G.A. Siviloglou, J. Broky, A. Dogariu, and D.N. Christodoulides, “Observation of accelerating Airy Beams,” Phys. Rev. Lett.99, 213901 (2007).
    [CrossRef]
  3. Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
    [CrossRef]
  4. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2, 675–678 (2008).
    [CrossRef]
  5. P. Polynkin, M. Kolesik, J.V. Moloney, G.A. Siviloglou, and D.N. Christodoulides, “Curved plasma channel generation using ultraintense Airy Beams,” Science324, 229–232 (2009).
    [CrossRef] [PubMed]
  6. A. Chong, W. Renninger, D.N. Christodoulides, and F.W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
    [CrossRef]
  7. T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3, 395–398 (2009).
    [CrossRef]
  8. S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
    [CrossRef] [PubMed]
  9. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).
    [CrossRef] [PubMed]
  10. Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett.35, 3952–3954 (2010).
    [CrossRef] [PubMed]
  11. Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett.36, 3230–3232 (2011).
    [CrossRef] [PubMed]
  12. Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37, 3201–3203 (2012).
    [CrossRef] [PubMed]
  13. I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
    [CrossRef] [PubMed]
  14. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35, 4045–4047 (2010).
    [CrossRef] [PubMed]
  15. I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett.36, 1890–1892 (2011).
    [CrossRef] [PubMed]
  16. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett.36, 1842–1844 (2011).
    [CrossRef] [PubMed]
  17. P. Zhang, J. Prakash, Z. Zhang, M. Mills, N. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett.36, 2883–2885 (2011).
    [CrossRef] [PubMed]
  18. I. Chremmos, Z. Chen, N. K. Efremidis, and D. N. Christodoulides, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85, 023828 (2012).
    [CrossRef]
  19. E. Abramochkin and E. Razueva, “Product of three Airy beams,” Opt. Lett.36, 3732–3734 (2011).
    [CrossRef] [PubMed]
  20. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express16, 9411–9416 (2008).
    [CrossRef] [PubMed]
  21. J. Broky, G. A. Siviloglou, A. Dogariu, and D.N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 12880–12891 (2008).
    [CrossRef] [PubMed]
  22. Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).
  23. H. Barwick, “Accelerating regular polygon beams,” Opt. Lett.35, 4118–4120 (2010).
    [CrossRef] [PubMed]

2012

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37, 3201–3203 (2012).
[CrossRef] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
[CrossRef] [PubMed]

I. Chremmos, Z. Chen, N. K. Efremidis, and D. N. Christodoulides, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85, 023828 (2012).
[CrossRef]

2011

2010

H. Barwick, “Accelerating regular polygon beams,” Opt. Lett.35, 4118–4120 (2010).
[CrossRef] [PubMed]

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett.35, 3952–3954 (2010).
[CrossRef] [PubMed]

A. Chong, W. Renninger, D.N. Christodoulides, and F.W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35, 4045–4047 (2010).
[CrossRef] [PubMed]

2009

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3, 395–398 (2009).
[CrossRef]

P. Polynkin, M. Kolesik, J.V. Moloney, G.A. Siviloglou, and D.N. Christodoulides, “Curved plasma channel generation using ultraintense Airy Beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

2008

2007

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]

Abramochkin, E.

Alfano, R. R.

Arie, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3, 395–398 (2009).
[CrossRef]

Barwick, H.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2, 675–678 (2008).
[CrossRef]

Bongiovanni, D.

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D.N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 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]

Chen, Z.

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37, 3201–3203 (2012).
[CrossRef] [PubMed]

I. Chremmos, Z. Chen, N. K. Efremidis, and D. N. Christodoulides, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85, 023828 (2012).
[CrossRef]

P. Zhang, J. Prakash, Z. Zhang, M. Mills, N. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett.36, 2883–2885 (2011).
[CrossRef] [PubMed]

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett.36, 3230–3232 (2011).
[CrossRef] [PubMed]

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett.35, 3952–3954 (2010).
[CrossRef] [PubMed]

Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
[CrossRef]

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Chong, A.

A. Chong, W. Renninger, D.N. Christodoulides, and F.W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Chremmos, I.

I. Chremmos, Z. Chen, N. K. Efremidis, and D. N. Christodoulides, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85, 023828 (2012).
[CrossRef]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett.36, 1890–1892 (2011).
[CrossRef] [PubMed]

Christodoulides, D. N.

I. Chremmos, Z. Chen, N. K. Efremidis, and D. N. Christodoulides, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85, 023828 (2012).
[CrossRef]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett.36, 1842–1844 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. Mills, N. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett.36, 2883–2885 (2011).
[CrossRef] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett.36, 1890–1892 (2011).
[CrossRef] [PubMed]

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

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35, 4045–4047 (2010).
[CrossRef] [PubMed]

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
[CrossRef] [PubMed]

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Christodoulides, D.N.

A. Chong, W. Renninger, D.N. Christodoulides, and F.W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, J.V. Moloney, G.A. Siviloglou, and D.N. Christodoulides, “Curved plasma channel generation using ultraintense Airy Beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D.N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 12880–12891 (2008).
[CrossRef] [PubMed]

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]

Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
[CrossRef]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2, 675–678 (2008).
[CrossRef]

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D.N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 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]

Dolev, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
[CrossRef] [PubMed]

Efremidis, N.

Efremidis, N. K.

Efremidis, N.K.

Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
[CrossRef]

Ellenbogen, T.

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3, 395–398 (2009).
[CrossRef]

Fleischer, J. W.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
[CrossRef] [PubMed]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3, 395–398 (2009).
[CrossRef]

Hu, Y.

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37, 3201–3203 (2012).
[CrossRef] [PubMed]

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett.36, 3230–3232 (2011).
[CrossRef] [PubMed]

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett.35, 3952–3954 (2010).
[CrossRef] [PubMed]

Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
[CrossRef]

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Huang, S.

Jia, S.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
[CrossRef] [PubMed]

Jiang, D.

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Kaminer, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
[CrossRef] [PubMed]

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

Kolesik, M.

P. Polynkin, M. Kolesik, J.V. Moloney, G.A. Siviloglou, and D.N. Christodoulides, “Curved plasma channel generation using ultraintense Airy Beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Lee, J.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
[CrossRef] [PubMed]

Liu, J.

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Liu, S.

Lou, C.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2, 675–678 (2008).
[CrossRef]

Mills, M.

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,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Morandotti, R.

Ni, P.

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Papazoglou, D. G.

Polynkin, P.

P. Polynkin, M. Kolesik, J.V. Moloney, G.A. Siviloglou, and D.N. Christodoulides, “Curved plasma channel generation using ultraintense Airy Beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Prakash, J.

P. Zhang, J. Prakash, Z. Zhang, M. Mills, N. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett.36, 2883–2885 (2011).
[CrossRef] [PubMed]

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Razueva, E.

Renninger, W.

A. Chong, W. Renninger, D.N. Christodoulides, and F.W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Segev, M.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
[CrossRef] [PubMed]

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

Shapira, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
[CrossRef] [PubMed]

Siviloglou, G. A.

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
[CrossRef] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D.N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 12880–12891 (2008).
[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,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

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]

Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
[CrossRef]

Song, D.

Sun, Z.

Sztul, H. I.

Tzortzakis, S.

Voloch, N.

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3, 395–398 (2009).
[CrossRef]

Wise, F.W.

A. Chong, W. Renninger, D.N. Christodoulides, and F.W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Xu, J.

Ye, Z.

Zhang, P

Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
[CrossRef]

Zhang, P.

Zhang, Z.

P. Zhang, J. Prakash, Z. Zhang, M. Mills, N. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett.36, 2883–2885 (2011).
[CrossRef] [PubMed]

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

Zhao, J.

Nat. Photonics

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2, 675–678 (2008).
[CrossRef]

A. Chong, W. Renninger, D.N. Christodoulides, and F.W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

T. Ellenbogen, N. Voloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3, 395–398 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

E. Abramochkin and E. Razueva, “Product of three Airy beams,” Opt. Lett.36, 3732–3734 (2011).
[CrossRef] [PubMed]

H. Barwick, “Accelerating regular polygon beams,” Opt. Lett.35, 4118–4120 (2010).
[CrossRef] [PubMed]

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

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett.35, 3952–3954 (2010).
[CrossRef] [PubMed]

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, “Acceleration control of Airy beams with optically induced refractive-index gradient,” Opt. Lett.36, 3230–3232 (2011).
[CrossRef] [PubMed]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37, 3201–3203 (2012).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35, 4045–4047 (2010).
[CrossRef] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett.36, 1890–1892 (2011).
[CrossRef] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett.36, 1842–1844 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. Mills, N. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett.36, 2883–2885 (2011).
[CrossRef] [PubMed]

Phys. Rev. A

I. Chremmos, Z. Chen, N. K. Efremidis, and D. N. Christodoulides, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85, 023828 (2012).
[CrossRef]

Phys. Rev. Lett.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108, 113903 (2012).
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G.A. Siviloglou, J. Broky, A. Dogariu, and D.N. Christodoulides, “Observation of accelerating Airy Beams,” Phys. Rev. Lett.99, 213901 (2007).
[CrossRef]

S. Jia, J. Lee, G. A. Siviloglou, D. N. Christodoulides, and J. W. Fleischer, “Diffusion-trapped Airy Beams in photorefractive Media,” Phys. Rev. Lett.104, 253904 (2010).
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I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).
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Science

P. Polynkin, M. Kolesik, J.V. Moloney, G.A. Siviloglou, and D.N. Christodoulides, “Curved plasma channel generation using ultraintense Airy Beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Other

Y. Hu, G.A. Siviloglou, P Zhang, N.K. Efremidis, D.N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds, (Springer, New York, 2012),1–46.
[CrossRef]

Z. Zhang, J. Liu, P. Zhang, P. Ni, J. Prakash, Y. Hu, D. Jiang, D. N. Christodoulides, and Z. Chen, “Trapping aerosols with optical bottle arrays generated through a superposition of multiple Airy beams,” to be published in Chinese Opt. Lett. (2013).

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Figures (5)

Fig. 1
Fig. 1

The intensity (central bright pattern) and phase (background pattern) distribution of F[tAi(r; b,c)](K) for (a1) a1 = −1.108, (a2) a2 = −3.10, (a3) a1 = −4.82, (b1) a1′ = −2.320, (b2) a2′ = −4.00, (b3) a3′ = −5.52. (c) The intensity profile of the three-Airy beam (solid line) in the Fourier space for a1 = −1.108 and its Gaussian approximation (dashed line).

Fig. 2
Fig. 2

Experimental setup for observation of the three-Airy beams. PC: personal computer; Mask: the phase pattern of the three-Airy beam for a1 = −1.108; SLM: spatial light modulator; BS: beam splitter; L:lens; SBN: strontium-barium-niobate crystal.

Fig. 3
Fig. 3

Experimental results (top row) of transverse intensity patterns for the three-Airy beam after linear propagation to different distances (a) z = 0 mm,(b) the phase relationship of the the three-Airy beam at z = 0 mm, (c) z = 2 mm, (d) z = 4 mm, (e) z = 100 mm. (f)–(j) Corresponding numerical simulation for the same distances. Patterns in (e, j) are zoomed out by a factor of 14.

Fig. 4
Fig. 4

Experimental results of a three-Airy beam propagating through a 1 cm-long nonlinear crystal. (a1)–(c1) input, (a2)–(c2) output intensity patterns, and (a3)–(c3) k-space spectrum corresponding to the second column. (a) without nonlinearity, (b) with self-focusing nonlinearity, and (c) with self-defocusing nonlinearity.

Fig. 5
Fig. 5

Numerical simulation corresponding to Fig. 4. (a1)–(c1) input, (a2)–(c2) output intensity patterns, (a3)–(c3) k-space spectrum corresponding to the second column. (a) no nonlinearity, (b) with self-focusing nonlinearity, and (c) with self-defocusing nonlinearity. (a4)–(c4) Side view of 4 cm propagation through the SBN crystal

Equations (4)

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t A i ( r ; b , c ) = A i ( b x 3 y 2 + c ) A i ( b x 3 y 2 + c ) A i ( b y + c ) ,
F [ t A i ( r ; b , c ) ] ( K ) = 1 3 5 / 6 π b 2 exp ( 2 i K 3 sin 3 ϕ 27 b 3 ) A i ( 3 2 / 3 c + 2 K 2 3 4 / 3 b 2 ) ,
A i ( K 2 ) ~ 1 2 π K exp ( 2 K 3 3 ) , ( K ) ,
ψ 0 = 1 n 3 exp ( α s n ) A i ( s n + c n ) , s n = ( a n x + b n y ) .

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