## Beam wander of an Airy beam with a spiral phase |

JOSA A, Vol. 31, Issue 4, pp. 685-690 (2014)

http://dx.doi.org/10.1364/JOSAA.31.000685

Acrobat PDF (563 KB)

### 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

## 1. INTRODUCTION

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

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]

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]

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]

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]

*et al.*and Cheng

*et al.*have investigated the propagation properties of a vortex Airy beam in ABCD optical system [38

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]

*et al.*have investigated the propagation properties of a vortex Airy beam in uniaxial crystals [40

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]

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]

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]

54. C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J_{0}- and I_{0}-Bessel Gaussian beams propagating in turbulent atmosphere,” Appl. Phys. B **98**, 195–202 (2010). [CrossRef]

*et al.*have discussed the influence of the initial spatially coherent length on the beam wander [49

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]

*et al.*and Yu

*et al.*have investigated the temporal spectrum of beam wander for Gaussian Schell-model beams and the beam wander of electromagnetic Gaussian–Schell beams [50

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 J_{0}- and I_{0}-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]

## 2. FORMULATION

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

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

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

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

## 3. NUMERICAL RESULTS AND ANALYSIS

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

**37**, 5202–5204 (2012). [CrossRef]

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

## 4. CONCLUSION

## APPENDIX A

**37**, 5202–5204 (2012). [CrossRef]

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

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

## ACKNOWLEDGMENTS

## REFERENCES

1. | J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. |

2. | G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. |

3. | G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. |

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

5. | X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A |

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. |

7. | E. Abramochkin and E. Razueva, “Product of three Airy beams,” Opt. Lett. |

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 |

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. |

10. | B. Yalizay, B. Soylu, and S. Akturk, “Optical element for generation of accelerating Airy beams,” J. Opt. Soc. Am. A |

11. | T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics |

12. | S. Longhi, “Airy beams from a microchip laser,” Opt. Lett. |

13. | H. Deng and L. Yuan, “Generation of Airy-like wave with one-dimensional waveguide array,” Opt. Lett. |

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. |

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. |

16. | I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. |

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

18. | N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature |

19. | J. D. Ring, C. J. Howls, and M. R. Dennis, “Incomplete Airy beams: finite energy from a sharp spectral cutoff,” Opt. Lett. |

20. | J. Baumgart, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics |

21. | P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science |

22. | Z. Zheng, B. F. Zhang, H. Chen, J. Ding, and H. T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. |

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. |

24. | J. X. Li, W. P. Zang, and J. G. Tian, “Analysis of electron capture acceleration channel in an Airy beam,” Opt. Lett. |

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. |

26. | A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics |

27. | D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. |

28. | P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. |

29. | D. G. Grier, “A revolution in optical manipulation,” Nature |

30. | K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. |

31. | A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature |

32. | G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. |

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 |

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 |

35. | A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. |

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. |

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. |

38. | M. Mazilu, J. Baumgartl, T. i már, and K. Dholakia, “Accelerating vortices in Airy beams,” Proc. SPIE |

39. | K. Cheng, X. Zhong, and A. Xiang, “Propagation dynamics, Poynting vector and accelerating vortices of afocused Airy vortex beam,” Opt. Laser Technol. |

40. | D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B |

41. | R. Chen and C. H. Raymond Ooi, “Nonclassicality of vortex Airy beams in the Wigner representation,” Phys. Rev. A |

42. | R. Chen, L. Zhong, Q. Wu, and K. Chew, “Propagation properties and M2 factors of a vortex Airy beam,” Opt. Laser Technol. |

43. | R. Chen and K. Chew, “Far-field properties of a vortex Airy beam,” Laser Part. Beams |

44. | R. Chen, K. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. |

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. |

46. | X. Chu, “Propagation of an Airy beam with a spiral phase,” Opt. Lett. |

47. | L. C. Andrews and R. L. Phillips, |

48. | D. Y. Vasylyev, A. A. Semenov, and W. Vogel, “Toward global quantum communication: beam wandering preserves nonclassicality,” Phys. Rev. Lett. |

49. | G. P. Berman, A. A. Chumak, and V. N. Gorshkov, “Beam wandering in the atmosphere: the effect of partial coherence,” Phys. Rev. E |

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. |

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. |

52. | H. T. Eyyuboğlu and C. Z. Cil, “Beam wander of dark hollow, flat-topped and annular beams,” Appl. Phys. B |

53. | C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Beam wander characteristics of cos and cosh-Gaussian beams,” Appl. Phys. B |

54. | C. Z. Cil, H. T. Eyyuboğlu, Y. Baykal, O. Korotkova, and Y. Cai, “Beam wander of J |

55. | D. G. Pérez and G. Funes, “Beam wandering statistics of twin thin laser beam propagation under generalized atmospheric conditions,” Opt. Express |

56. | C. Si and Y. Zhang, “Beam wander of quantization beam in a non-Kolmogorov turbulent atmosphere,” Optik |

57. | H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A |

58. | X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. |

**OCIS Codes**

(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(080.4865) Geometric optics : Optical vortices

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: December 17, 2013

Revised Manuscript: January 23, 2014

Manuscript Accepted: January 24, 2014

Published: March 6, 2014

**Citation**

Wei Wen and Xiuxiang Chu, "Beam wander of an Airy beam with a spiral phase," J. Opt. Soc. Am. A **31**, 685-690 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-4-685

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### References

- J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [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]
- 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]
- 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. 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]
- E. Abramochkin and E. Razueva, “Product of three Airy beams,” Opt. Lett. 36, 3732–3734 (2011). [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]
- 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]
- 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]
- S. Longhi, “Airy beams from a microchip laser,” Opt. Lett. 36, 716–718 (2011). [CrossRef]
- H. Deng and L. Yuan, “Generation of Airy-like wave with one-dimensional waveguide array,” Opt. Lett. 38, 1645–1647 (2013). [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]
- I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012). [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]
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