Abstract

Beam wander of an Airy beam with a spiral phase in turbulence is investigated. Using the Wigner distribution function, analytical expressions for the second-order moments and second central moments of an Airy beam with a spiral phase in turbulence are derived. A general expression of the beam wander for an Airy beam with a spiral phase is obtained. Based on the derived formula, various factors that impact on the beam wander are illustrated numerically. The results show that increasing the topological charge and the characteristic scale, or decreasing the exponential truncation factor, can be used to decrease the beam wander.

© 2014 Optical Society of America

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    [CrossRef]
  2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [CrossRef]
  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. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
    [CrossRef]
  5. X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
    [CrossRef]
  6. D. M. Cottrell, J. A. Davis, and T. M. Hazard, “Direct generation of accelerating Airy beams using a 3/2 phase-only pattern,” Opt. Lett. 34, 2634–2636 (2009).
    [CrossRef]
  7. E. Abramochkin and E. Razueva, “Product of three Airy beams,” Opt. Lett. 36, 3732–3734 (2011).
    [CrossRef]
  8. Y. Liang, Z. Ye, D. Song, C. Lou, X. Zhang, J. Xu, and Z. Chen, “Generation of linear and nonlinear propagation of three-Airy beams,” Opt. Express 21, 1615–1622 (2013).
    [CrossRef]
  9. D. Luo, H. T. Dai, X. W. Sun, and H. V. Demir, “Electrically switchable finite energy Airy beams generated by a liquid crystal cell with patterned electrode,” Opt. Commun. 283, 3846–3849 (2010).
    [CrossRef]
  10. B. Yalizay, B. Soylu, and S. Akturk, “Optical element for generation of accelerating Airy beams,” J. Opt. Soc. Am. A 27, 2344–2346 (2010).
    [CrossRef]
  11. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
    [CrossRef]
  12. S. Longhi, “Airy beams from a microchip laser,” Opt. Lett. 36, 716–718 (2011).
    [CrossRef]
  13. H. Deng and L. Yuan, “Generation of Airy-like wave with one-dimensional waveguide array,” Opt. Lett. 38, 1645–1647 (2013).
    [CrossRef]
  14. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
    [CrossRef]
  15. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
    [CrossRef]
  16. I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).
    [CrossRef]
  17. X. Chu, Z. Liu, and P. Zhou, “Generation of a high-power Airy beam by coherent combining technology,” Laser Phys. Lett. 10, 125102 (2013).
    [CrossRef]
  18. N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
    [CrossRef]
  19. J. D. Ring, C. J. Howls, and M. R. Dennis, “Incomplete Airy beams: finite energy from a sharp spectral cutoff,” Opt. Lett. 38, 1639–1641 (2013).
    [CrossRef]
  20. J. Baumgart, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
    [CrossRef]
  21. 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]
  22. Z. Zheng, B. F. Zhang, H. Chen, J. Ding, and H. T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. 50, 43–49 (2011).
    [CrossRef]
  23. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
    [CrossRef]
  24. J. X. Li, W. P. Zang, and J. G. Tian, “Analysis of electron capture acceleration channel in an Airy beam,” Opt. Lett. 35, 3258–3260 (2010).
    [CrossRef]
  25. J. X. Li, X. L. Fan, W. P. Zang, and J. G. Tian, “Vacuum electron acceleration driven by two crossed Airy beams,” Opt. Lett. 36, 648–650 (2011).
    [CrossRef]
  26. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
    [CrossRef]
  27. 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]
  28. P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
    [CrossRef]
  29. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
    [CrossRef]
  30. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
    [CrossRef]
  31. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [CrossRef]
  32. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [CrossRef]
  33. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [CrossRef]
  34. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
    [CrossRef]
  35. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
    [CrossRef]
  36. H. T. Dai, Y. J. Liu, D. Luo, and X. W. Sun, “Propagation dynamics of an optical vortex imposed on an Airy beam,” Opt. Lett. 35, 4075–4077 (2010).
    [CrossRef]
  37. H. T. Dai, Y. J. Liu, D. Luo, and X. W. Sun, “Propagation properties of an optical vortex carried by an Airy beam: experimental implementation,” Opt. Lett. 36, 1617–1619 (2011).
    [CrossRef]
  38. M. Mazilu, J. Baumgartl, T. i már, and K. Dholakia, “Accelerating vortices in Airy beams,” Proc. SPIE 7430, 74300C (2009).
    [CrossRef]
  39. K. Cheng, X. Zhong, and A. Xiang, “Propagation dynamics, Poynting vector and accelerating vortices of afocused Airy vortex beam,” Opt. Laser Technol. 57, 77–83 (2014).
    [CrossRef]
  40. D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013).
    [CrossRef]
  41. R. Chen and C. H. Raymond Ooi, “Nonclassicality of vortex Airy beams in the Wigner representation,” Phys. Rev. A 84, 043846 (2011).
    [CrossRef]
  42. R. Chen, L. Zhong, Q. Wu, and K. Chew, “Propagation properties and M2 factors of a vortex Airy beam,” Opt. Laser Technol. 44, 2015–2019 (2012).
    [CrossRef]
  43. R. Chen and K. Chew, “Far-field properties of a vortex Airy beam,” Laser Part. Beams 31, 9–15 (2013).
    [CrossRef]
  44. R. Chen, K. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1–9 (2013).
  45. C. Rosales-Guzmán, M. Mazilu, J. Baumgartl, V. Rodríguez-Fajardo, R. Ramos-García, and K. Dholakia, “Collision of propagating vortices embedded within Airy beams,” J. Opt. 15, 044001 (2013).
    [CrossRef]
  46. X. Chu, “Propagation of an Airy beam with a spiral phase,” Opt. Lett. 37, 5202–5204 (2012).
    [CrossRef]
  47. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  48. D. Y. Vasylyev, A. A. Semenov, and W. Vogel, “Toward global quantum communication: beam wandering preserves nonclassicality,” Phys. Rev. Lett. 108, 220501 (2012).
    [CrossRef]
  49. G. P. Berman, A. A. Chumak, and V. N. Gorshkov, “Beam wandering in the atmosphere: the effect of partial coherence,” Phys. Rev. E 76, 056606 (2007).
    [CrossRef]
  50. C. Chen and H. Yang, “Temporal spectrum of beam wander for Gaussian Shell-model beams propagating in atmospheric turbulence with finite outer scale,” Opt. Lett. 38, 1887–1889 (2013).
    [CrossRef]
  51. S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo, and W. Gu, “Beam wander of electromagnetic Gaussian–Schell model beams propagating in atmospheric turbulence,” Appl. Opt. 51, 7581–7585 (2012).
    [CrossRef]
  52. H. T. Eyyuboğlu and C. Z. Cil, “Beam wander of dark hollow, flat-topped and annular beams,” Appl. Phys. B 93, 595–604 (2008).
    [CrossRef]
  53. C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
    [CrossRef]
  54. C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J0- and I0-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B 98, 195–202 (2010).
    [CrossRef]
  55. D. G. Pérez and G. Funes, “Beam wandering statistics of twin thin laser beam propagation under generalized atmospheric conditions,” Opt. Express 20, 27766–27780 (2012).
    [CrossRef]
  56. C. Si and Y. Zhang, “Beam wander of quantization beam in a non-Kolmogorov turbulent atmosphere,” Optik 124, 1175–1178 (2013).
    [CrossRef]
  57. H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987).
    [CrossRef]
  58. X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. 36, 2701–2703 (2011).
    [CrossRef]

2014 (1)

K. Cheng, X. Zhong, and A. Xiang, “Propagation dynamics, Poynting vector and accelerating vortices of afocused Airy vortex beam,” Opt. Laser Technol. 57, 77–83 (2014).
[CrossRef]

2013 (14)

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013).
[CrossRef]

R. Chen and K. Chew, “Far-field properties of a vortex Airy beam,” Laser Part. Beams 31, 9–15 (2013).
[CrossRef]

R. Chen, K. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1–9 (2013).

C. Rosales-Guzmán, M. Mazilu, J. Baumgartl, V. Rodríguez-Fajardo, R. Ramos-García, and K. Dholakia, “Collision of propagating vortices embedded within Airy beams,” J. Opt. 15, 044001 (2013).
[CrossRef]

C. Chen and H. Yang, “Temporal spectrum of beam wander for Gaussian Shell-model beams propagating in atmospheric turbulence with finite outer scale,” Opt. Lett. 38, 1887–1889 (2013).
[CrossRef]

C. Si and Y. Zhang, “Beam wander of quantization beam in a non-Kolmogorov turbulent atmosphere,” Optik 124, 1175–1178 (2013).
[CrossRef]

Y. Liang, Z. Ye, D. Song, C. Lou, X. Zhang, J. Xu, and Z. Chen, “Generation of linear and nonlinear propagation of three-Airy beams,” Opt. Express 21, 1615–1622 (2013).
[CrossRef]

X. Chu, Z. Liu, and P. Zhou, “Generation of a high-power Airy beam by coherent combining technology,” Laser Phys. Lett. 10, 125102 (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]

J. D. Ring, C. J. Howls, and M. R. Dennis, “Incomplete Airy beams: finite energy from a sharp spectral cutoff,” Opt. Lett. 38, 1639–1641 (2013).
[CrossRef]

H. Deng and L. Yuan, “Generation of Airy-like wave with one-dimensional waveguide array,” Opt. Lett. 38, 1645–1647 (2013).
[CrossRef]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[CrossRef]

2012 (7)

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).
[CrossRef]

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[CrossRef]

D. G. Pérez and G. Funes, “Beam wandering statistics of twin thin laser beam propagation under generalized atmospheric conditions,” Opt. Express 20, 27766–27780 (2012).
[CrossRef]

S. Yu, Z. Chen, T. Wang, G. Wu, H. Guo, and W. Gu, “Beam wander of electromagnetic Gaussian–Schell model beams propagating in atmospheric turbulence,” Appl. Opt. 51, 7581–7585 (2012).
[CrossRef]

R. Chen, L. Zhong, Q. Wu, and K. Chew, “Propagation properties and M2 factors of a vortex Airy beam,” Opt. Laser Technol. 44, 2015–2019 (2012).
[CrossRef]

X. Chu, “Propagation of an Airy beam with a spiral phase,” Opt. Lett. 37, 5202–5204 (2012).
[CrossRef]

D. Y. Vasylyev, A. A. Semenov, and W. Vogel, “Toward global quantum communication: beam wandering preserves nonclassicality,” Phys. Rev. Lett. 108, 220501 (2012).
[CrossRef]

2011 (10)

R. Chen and C. H. Raymond Ooi, “Nonclassicality of vortex Airy beams in the Wigner representation,” Phys. Rev. A 84, 043846 (2011).
[CrossRef]

H. T. Dai, Y. J. Liu, D. Luo, and X. W. Sun, “Propagation properties of an optical vortex carried by an Airy beam: experimental implementation,” Opt. Lett. 36, 1617–1619 (2011).
[CrossRef]

X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. 36, 2701–2703 (2011).
[CrossRef]

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

S. Longhi, “Airy beams from a microchip laser,” Opt. Lett. 36, 716–718 (2011).
[CrossRef]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Z. Zheng, B. F. Zhang, H. Chen, J. Ding, and H. T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. 50, 43–49 (2011).
[CrossRef]

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

J. X. Li, X. L. Fan, W. P. Zang, and J. G. Tian, “Vacuum electron acceleration driven by two crossed Airy beams,” Opt. Lett. 36, 648–650 (2011).
[CrossRef]

2010 (7)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[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]

J. X. Li, W. P. Zang, and J. G. Tian, “Analysis of electron capture acceleration channel in an Airy beam,” Opt. Lett. 35, 3258–3260 (2010).
[CrossRef]

H. T. Dai, Y. J. Liu, D. Luo, and X. W. Sun, “Propagation dynamics of an optical vortex imposed on an Airy beam,” Opt. Lett. 35, 4075–4077 (2010).
[CrossRef]

D. Luo, H. T. Dai, X. W. Sun, and H. V. Demir, “Electrically switchable finite energy Airy beams generated by a liquid crystal cell with patterned electrode,” Opt. Commun. 283, 3846–3849 (2010).
[CrossRef]

B. Yalizay, B. Soylu, and S. Akturk, “Optical element for generation of accelerating Airy beams,” J. Opt. Soc. Am. A 27, 2344–2346 (2010).
[CrossRef]

C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J0- and I0-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B 98, 195–202 (2010).
[CrossRef]

2009 (5)

C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[CrossRef]

M. Mazilu, J. Baumgartl, T. i már, and K. Dholakia, “Accelerating vortices in Airy beams,” Proc. SPIE 7430, 74300C (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

D. M. Cottrell, J. A. Davis, and T. M. Hazard, “Direct generation of accelerating Airy beams using a 3/2 phase-only pattern,” Opt. Lett. 34, 2634–2636 (2009).
[CrossRef]

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]

2008 (3)

J. Baumgart, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
[CrossRef]

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]

H. T. Eyyuboğlu and C. Z. Cil, “Beam wander of dark hollow, flat-topped and annular beams,” Appl. Phys. B 93, 595–604 (2008).
[CrossRef]

2007 (4)

G. P. Berman, A. A. Chumak, and V. N. Gorshkov, “Beam wandering in the atmosphere: the effect of partial coherence,” Phys. Rev. E 76, 056606 (2007).
[CrossRef]

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

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

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

2005 (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

2004 (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef]

1987 (2)

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

H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987).
[CrossRef]

Abdollahpour, D.

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]

Abramochkin, E.

Akturk, S.

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

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]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[CrossRef]

Baumgart, J.

J. Baumgart, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
[CrossRef]

Baumgartl, J.

C. Rosales-Guzmán, M. Mazilu, J. Baumgartl, V. Rodríguez-Fajardo, R. Ramos-García, and K. Dholakia, “Collision of propagating vortices embedded within Airy beams,” J. Opt. 15, 044001 (2013).
[CrossRef]

M. Mazilu, J. Baumgartl, T. i már, and K. Dholakia, “Accelerating vortices in Airy beams,” Proc. SPIE 7430, 74300C (2009).
[CrossRef]

Baykal, Y.

C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J0- and I0-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B 98, 195–202 (2010).
[CrossRef]

C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B 95, 763–771 (2009).
[CrossRef]

Berman, G. P.

G. P. Berman, A. A. Chumak, and V. N. Gorshkov, “Beam wandering in the atmosphere: the effect of partial coherence,” Phys. Rev. E 76, 056606 (2007).
[CrossRef]

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

Boguslawski, M.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

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]

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

Cai, Y.

C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J0- and I0-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B 98, 195–202 (2010).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Dimensionless quantity BW of an Airy beam with a spiral phase versus propagation distance for different exponential truncation factors and topological charges. The calculation parameters are w0=5mm, Cn2=1014m2/3, and l0=1mm.

Fig. 2.
Fig. 2.

Dimensionless quantity BW of an Airy beam with a spiral phase versus exponential truncation factors for different topological charges. The calculation parameters are w0=5mm, Cn2=1014m2/3, L=1000m, and l0=1mm.

Fig. 3.
Fig. 3.

Dimensionless quantity BW of an Airy beam with a spiral phase versus propagation distance for different structure constants. The calculation parameters are a=0.11, w0=5mm, and l0=1mm.

Fig. 4.
Fig. 4.

Dimensionless quantity BW of an Airy beam with a spiral phase versus propagation distance for different transverse scales. The calculation parameters are a=0.11, Cn2=1014m2/3, and l0=1mm.

Fig. 5.
Fig. 5.

Dimensionless quantity BW of an Airy beam with a spiral phase versus propagation distance for different inner scales. The calculation parameters are a=0.11, w0=5mm, and Cn2=1014m2/3.

Equations (23)

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u0(x0,y0)=[(x0xd)+i(y0yd)]m[(x0xd)2+(y0yd)2]m/2×Ai(x0/w0)Ai(y0/w0)exp[a(x0+y0)/w0],
I(x,y)=(k2πz)2H(p2,q2)×exp[12D(p2,q2)]exp[ikx(xp2+yq2)]dp2dq2,
H(p2,q2)=(k2πz)2u0(p1+p22,q1+q22)×uo*(p1p22,q1q22)exp[ikx(p1p2+q1q2)]dp1dq1,
D(p2,q2)=8π2k2z001[1J0(κξp22+q22)]Φ(κ)κdξdκ.
Φn(k)=0.033Cn2κ11/3exp(κ2κm2),
(x2y2)=1P(k2πz)2(x2y2)exp[12D(p2,q2)]×exp[ikz(xp2+yq2)]H(p2,q2)dp2dq2dxdy,
P=w028πaexp(4a3/3).
δ(n)(t)=12π(ix)nexp(itx)dx;n=0,1,2,
δ(n)(ax)=an1δ(n)(x);n=0,1,2,
F(x)δ(n)(x)dx=(1)nF(n)(0);n=0,1,2,
x2=y2=A+8πaw02exp(4a3/3)(Bm2z2k2w042Cmzkw02)+D,
A=z24ak2w02+3w0216a2+aw022+a4w02,
B=(q1p12+q12)2exp[2a(p1+q1)]Ai2(p1)Ai2(q1)dp1dq1,
C=(p1q1p12+q12)exp[2a(p1+q1)]Ai2(p1)Ai2(q1)dp1dq1,
D=23π2z30κ3Φn(κ)dκ=0.066π2z3Cn2κm1/3Γ(7/6).
μ2=x2xc2=A+8πaw02exp(4a3/3)(Bm2z2k2w042Cmzkw02)+D[(4a31)w04a8πamzEkw0exp(4a3/3)]2,
E=(q1p12+q12)exp[2a(p1+q1)]Ai2(p1)Ai2(q1)dp1dq1.
WLT(z)=2r2I(r,z)d2r/I(r,z)d2r=2[A+8πaw02exp(4a3/3)(Bm2z2k2w042Cmzkw02)+D[(4a31)w04a8πamzEkw0exp(4a3/3)]2]1/2.
rc2=4πk2WFS20L0κΦn(κ)exp(κ2WLT2)×{1exp[2L2κ2(1z/L)2k2WFS2]}dκdz.
rc2=0.066πΓ(5/6)k2Cn2WFS2×0L{(1κm2+WLT2)5/6[1κm2+WLT2+2L2(1z/L)2k2WFS2]5/6}dz.
x2F=A+8πaw02exp(4a3/3)(Bm2z2k2w042Cmzkw02).
cs=4π2k2z(1)s122s(s!)(2s+1)0κ2s+1Φ(κ)dκ.
x2T=x2F+2z2k2c1,

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