Abstract

We study both analytically and numerically nonparaxial propagation dynamics of the Chirped Airy vortex (CAiV) beams in uniaxial crystal orthogonal to the optical axis. The propagation trajectory, the intensity, the radiation forces, the Poynting vector and the angular momentum (AM) of the CAiV beams are illustrated by numerical examples. The influences of the ratio of the extraordinary refractive index to the ordinary refractive index, the linear chirp factor and the quadratic chirp factor on the nonparaxial evolution of the CAiV beams are examined in detail. Results show that the linear chirp factor provides an intensity concentration, which is totally different with the influence of the quadratic chirp. Besides, the uniaxial crystals with different refractive index ratios can be used to control the intensity of optical lobes. Moreover, the value and the direction of the radiation forces depend on the propagation distance and the chirp factor. The chirp factor acting on the Poynting vector and the AM mainly occurs in the direction of vectors. The nonparaxial propagation characteristics of the CAiV beams provide a convenient method to the intensity modulation and the optical manipulation of micro particles.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis

Xun Wang, Zhirong Liu, and Daomu Zhao
J. Opt. Soc. Am. A 31(10) 2268-2274 (2014)

Nonparaxial propagation of Lorentz–Gauss beams in uniaxial crystal orthogonal to the optical axis

Xun Wang, Zhirong Liu, and Daomu Zhao
J. Opt. Soc. Am. A 31(4) 872-878 (2014)

Nonparaxial evolution of the Airy–Gaussian vortex beam in uniaxial crystal

Dongdong Li, Xi Peng, Yulian Peng, Liping Zhang, and Dongmei Deng
J. Opt. Soc. Am. B 34(4) 891-898 (2017)

References

  • View by:
  • |
  • |
  • |

  1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 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(21), 213901 (2007).
    [Crossref]
  3. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
    [Crossref] [PubMed]
  4. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
    [Crossref] [PubMed]
  5. Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
    [Crossref] [PubMed]
  6. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy Light Bullets in the Linear and Nonlinear Regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
    [Crossref]
  7. P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
    [Crossref] [PubMed]
  8. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
    [Crossref]
  9. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
    [Crossref] [PubMed]
  10. P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
    [Crossref] [PubMed]
  11. Y. Zhang, X. Liu, M. R. Belic, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
    [Crossref] [PubMed]
  12. H. Zhong, Y. Zhang, Z. Zhang, C. Li, D. Zhang, Y. Zhang, and M. R. Belic, “Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency,” Opt. Lett. 41(24), 5644–5647 (2016).
    [Crossref] [PubMed]
  13. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [Crossref] [PubMed]
  14. J. Ng, Z. Lin, and C. T. Chan, “Theory of Optical Trapping by an Optical Vortex Beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
    [Crossref] [PubMed]
  15. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
    [Crossref]
  16. J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
    [Crossref]
  17. G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A: Pure Appl. Opt. 11(9), 094021 (2009).
    [Crossref]
  18. A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18(7), 1656–1661 (2001).
    [Crossref]
  19. A. Ciattoni, G. Cincotti, and C. Palma, “Nonparaxial description of reflection and transmission at the interface between an isotropic medium and a uniaxial crystal,” J. Opt. Soc. Am. A 19(7), 1422–1431 (2002).
    [Crossref]
  20. L. Zhang and Y. Cai, “Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal,” Opt. Express 19(14), 13312–13325 (2011).
    [Crossref] [PubMed]
  21. X. Wang, Z. Liu, and D. Zhao, “Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis,” J. Opt. Soc. Am. A 31(10), 2268–2274 (2014).
    [Crossref]
  22. F. Deng and D. Deng, “Nonparaxial propagation of an Airy-Gaussian beam in uniaxial crystal orthogonal to the optical axis,” Opt. Commun. 380, 280–286 (2016).
    [Crossref]
  23. Y. Zhang, M. R. Belic, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
    [Crossref] [PubMed]
  24. A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20(11), 2163–2171 (2003).
    [Crossref]
  25. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).
  26. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5–6), 529–541 (1996).
    [Crossref]
  27. M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University, 1999).
    [Crossref]
  28. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008).
    [Crossref] [PubMed]

2016 (2)

2015 (2)

2014 (1)

2013 (2)

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (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,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

2012 (1)

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

2011 (2)

2010 (2)

J. Ng, Z. Lin, and C. T. Chan, “Theory of Optical Trapping by an Optical Vortex Beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[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(25), 253901 (2010).
[Crossref]

2009 (3)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A: Pure Appl. Opt. 11(9), 094021 (2009).
[Crossref]

2008 (4)

2007 (2)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

2003 (1)

2002 (1)

2001 (1)

1996 (1)

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5–6), 529–541 (1996).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

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(25), 253901 (2010).
[Crossref]

Ahmed, N.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Alfano, R. R.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5–6), 529–541 (1996).
[Crossref]

Baumgartl, J.

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

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A: Pure Appl. Opt. 11(9), 094021 (2009).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Belic, M. R.

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A: Pure Appl. Opt. 11(9), 094021 (2009).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University, 1999).
[Crossref]

Broky, J.

Cai, Y.

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of Optical Trapping by an Optical Vortex Beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 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(21), 213901 (2007).
[Crossref]

Ciattoni, A.

Cincotti, G.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

Couairon, A.

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

Crosignani, B.

Deng, D.

F. Deng and D. Deng, “Nonparaxial propagation of an Airy-Gaussian beam in uniaxial crystal orthogonal to the optical axis,” Opt. Commun. 380, 280–286 (2016).
[Crossref]

Deng, F.

F. Deng and D. Deng, “Nonparaxial propagation of an Airy-Gaussian beam in uniaxial crystal orthogonal to the optical axis,” Opt. Commun. 380, 280–286 (2016).
[Crossref]

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

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

Dogariu, A.

Dolinar, S.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Fazal, I. M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).

Harada, Y.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5–6), 529–541 (1996).
[Crossref]

Huang, H.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Kolesik, M.

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

Li, C.

Li, Y.

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, “Theory of Optical Trapping by an Optical Vortex Beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Liu, X.

Liu, Z.

Lu, K.

Mazilu, M.

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

Moloney, J.

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

Ng, J.

J. Ng, Z. Lin, and C. T. Chan, “Theory of Optical Trapping by an Optical Vortex Beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Palma, C.

Panagiotopoulos, P.

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

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,” Nat. Commun. 4, 2622 (2013).
[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(25), 253901 (2010).
[Crossref]

Polynkin, P.

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

Porto, P. Di

Ren, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 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(21), 213901 (2007).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[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(25), 253901 (2010).
[Crossref]

Sztul, H. I.

Tur, M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Tzortzakis, S.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[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(25), 253901 (2010).
[Crossref]

Wang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Wang, R.

Wang, X.

Wen, F.

Willner, A. E.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University, 1999).
[Crossref]

Wu, Z.

Yan, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Yang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Yue, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Zhang, D.

Zhang, L.

Zhang, Y.

H. Zhong, Y. Zhang, Z. Zhang, C. Li, D. Zhang, Y. Zhang, and M. R. Belic, “Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency,” Opt. Lett. 41(24), 5644–5647 (2016).
[Crossref] [PubMed]

H. Zhong, Y. Zhang, Z. Zhang, C. Li, D. Zhang, Y. Zhang, and M. R. Belic, “Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency,” Opt. Lett. 41(24), 5644–5647 (2016).
[Crossref] [PubMed]

Y. Zhang, M. R. Belic, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
[Crossref] [PubMed]

Y. Zhang, M. R. Belic, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
[Crossref] [PubMed]

Y. Zhang, X. Liu, M. R. Belic, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
[Crossref] [PubMed]

Y. Zhang, X. Liu, M. R. Belic, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
[Crossref] [PubMed]

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref] [PubMed]

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref] [PubMed]

Zhang, Z.

Zhao, D.

Zheng, H.

Zhong, H.

Zhong, W.

Zhu, D.

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

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A: Pure Appl. Opt. 11(9), 094021 (2009).
[Crossref]

J. Opt. Soc. Am. A (4)

Nat. Commun. (1)

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

Nat. Photon. (3)

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

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon. 6, 488–496 (2012).
[Crossref]

Opt. Commun. (2)

F. Deng and D. Deng, “Nonparaxial propagation of an Airy-Gaussian beam in uniaxial crystal orthogonal to the optical axis,” Opt. Commun. 380, 280–286 (2016).
[Crossref]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5–6), 529–541 (1996).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

J. Ng, Z. Lin, and C. T. Chan, “Theory of Optical Trapping by an Optical Vortex Beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[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(25), 253901 (2010).
[Crossref]

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultra intense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University, 1999).
[Crossref]

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Numerically simulated side-view in the x-direction of the nonparaxial propagation trajectory of a LCAiV beam in uniaxial crystal orthogonal to optical axis with ne = 1.5no: (a) β1x = β1y = 0, (b) β1x = β1y = 1, (c) β1x = β1y = 3, (d) β1x = β1y = 5.

Fig. 2
Fig. 2

The transverse intensity of a LCAiV beam in uniaxial crystal orthogonal to optical axis with ne = 1.5no: (a) β1x = β1y = 1, (b) β1x = β1y = 3, (c) β1x = β1y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 3
Fig. 3

The transverse gradient force pattern (background) and the transverse gradient force flows (red arrows) of an extraordinary LCAiV beam on a Rayleigh particle in uniaxial crystal orthogonal to optical axis with ne = 1.5no: (a) β1x = β1y = 1, (b) β1x = β1y = 3, (c) β1x = β1y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 4
Fig. 4

The scattering force of an extraordinary LCAiV beam on a Rayleigh particle in uniaxial crystal orthogonal to the optical axis, with different β1x,y and at different propagation distance, where a = 0.5, ne = 1.5no.

Fig. 5
Fig. 5

The total energy flow (background) and the transverse energy flow (blue arrows) of an extraordinary LCAiV beam in uniaxial crystal orthogonal to the optical axis with ne = 1.5no: (a) β1x = β1y = 1, (b) β1x = β1y = 3, (c) β1x = β1y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 6
Fig. 6

The total AM density (background) and the transverse AM density flow (blue arrows) of an extraordinary LCAiV beam in uniaxial crystal orthogonal to the optical axis with ne = 1.5no: (a) β1x = β1y = 1, (b) β1x = β1y = 3, (c) β1x = β1y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 7
Fig. 7

The transverse intensity of a QCAiV beam in uniaxial crystal orthogonal to optical axis with ne = 1.5no: (a) β2x = β2y = 1, (b) β2x = β2y = 3, (c) β2x = β2y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 8
Fig. 8

The peak intensity distribution of a QCAiV beam in uniaxial crystal orthogonal to optical axis with ne = 1.5no.

Fig. 9
Fig. 9

The transverse gradient force pattern (background) and the gradient force flows (red arrows) of an extraordinary QCAiV beam on a Rayleigh particle in uniaxial crystal orthogonal to optical axis with ne = 1.5no: (a) β2x = β2y = 1, (b) β2x = β2y = 3, (c) β2x = β2y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 10
Fig. 10

The scattering force of an extraordinary QCAiV beam on a Rayleigh particle in uniaxial crystal orthogonal to the optical axis, with different β2x,y and at different propagation distance, where a = 0.5, ne = 1.5no.

Fig. 11
Fig. 11

The total energy flow (background) and the transverse energy flow (blue arrows) of an extraordinary QCAiV beam in uniaxial crystal orthogonal to the optical axis with ne = 1.5no: (a) β2x = β2y = 1, (b) β2x = β2y = 3, (c) β2x = β2y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 12
Fig. 12

The total AM density (background) and the transverse AM density flow (blue arrows) of an extraordinary QCAiV beam in the uniaxial crystal orthogonal to the optical axis with ne = 1.5no: (a) β2x = β2y = 1, (b) β2x = β2y = 3, (c) β2x = β2y = 5, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Fig. 13
Fig. 13

Evolution of the intensity as a function of x for the CAiV beams with different β1x,y and β2x,y in uniaxial crystal orthogonal to optical axis with ne = 1.5no: (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 1ZR, (a3)–(c3) z = 2ZR.

Fig. 14
Fig. 14

The transverse intensity of the CAiV beams in uniaxial crystal orthogonal to optical axis with β1x,y = β2x,y = 1: (a) ne = 0.5no, (b) ne = 1.5no, (c) ne = 2.0no, (a1)–(c1) z = 0.1ZR, (a2)–(c2) z = 2ZR, (a3)–(c3) z = 8ZR.

Equations (20)

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

ε = ( n e 2 0 0 0 n o 2 0 0 0 n o 2 ) ,
[ E x x 0 , y 0 , 0 E y x 0 , y 0 , 0 ] = [ Ai ( x 0 w 0 ) Ai ( y 0 w 0 ) exp ( a x 0 w 0 + a y 0 w 0 + i β 1 x x 0 w 0 + i β 2 x x 0 2 w 0 2 + i β 1 y y 0 w 0 + i β 2 y y 0 2 w 0 2 ) ( x 0 w 0 + i y 0 w 0 ) 0 ] ,
E x , y , z = d 2 k exp ( i k r + i k e z z ) ( E ˜ x k k x k y k 2 n o 2 k x 2 E ˜ x k k e z k x k 2 n o 2 k x 2 E ˜ x k ) + d 2 k × exp ( i k r + i k o z z ) ( 0 k x k y k 2 n o 2 k x 2 E ˜ x k + E ˜ y k k y k o z [ k x k y k 2 n o 2 k x 2 E ˜ x k + E ˜ y k ] ) ,
k e z = [ k 2 n e 2 ( n e 2 n o 2 ) k x 2 k y 2 ] 1 2 , k o z = ( k 2 n o 2 k x 2 k y 2 ) 1 2 ,
E x x , y , z = k n o 2 π i z + E x x 0 , y 0 , 0 A e r , r 0 d x 0 d y 0 ,
E y x , y , z = i k n o 2 π z 3 + x x 0 y y 0 E x x 0 , y 0 , 0 [ A e r , r 0 A o r , r 0 ] d x 0 d y 0 + k n o 2 π i z + E y x 0 , y 0 , 0 A o r , r 0 d x 0 d y 0 ,
E z x , y , z = i k n o 2 π z 2 + [ x x 0 E x x 0 , y 0 , 0 A e r , r 0 + y y 0 E y x 0 , y 0 , 0 A o r , r 0 ] d x 0 d y 0 ,
A e r , r 0 = exp i k n e z exp { k 2 i z n e n o 2 x x 0   2 + n e 2 y y 0   2 } ,
A o r , r 0 = exp i k n o z exp { k n o 2 i z x x 0   2 + y y 0   2 } .
E x x , y , z = k n o 2 π i z exp i k n e z exp ( k o 2 2 i z n e x 2 k n e 2 i z y 2 ) ( 1 w 0 L 1 K 2 + i w 0 K 1 L 2 ) ,
E y x , y , z = i k n o 2 π z 3 { exp i k n e z exp ( k n o 2 2 i z n e x 2 k n e 2 i z y 2 ) [ x y w 0 L 1 K 2 ( x w 0 + i y w 0 ) L 1 L 2 y w 0 M 1 K 2 + 1 w 0 M 1 L 2 + i x y w 0 K 1 L 2 i x w 0 K 1 M 2 + i w 0 L 1 M 2 ] exp i k n o z × exp ( k n o 2 i z x 2 k n o 2 i z y 2 ) [ x y w 0 L 3 K 4 ( x w 0 + i y w 0 ) L 3 L 4 y w 0 M 3 K 4 + 1 w 0 M 3 L 4 + i x y w 0 K 3 L 4 i x w 0 K 3 M 4 + i w 0 L 3 L 4 ] } ,
E z x , y , z = i k n o 2 π z 2 exp i k n e z exp ( k n o 2 2 i z n e x 2 k n e 2 i z y 2 ) ( x w 0 L 1 K 2 + i x w 0 K 1 L 2 1 w 0 M 1 K 2 i w 0 L 1 L 2 ) ,
K n = π b n exp ( c n 2 4 b n + c n 8 w 0 3 b n 2 1 96 w 0 6 b n 3 ) Ai ( 1 16 w 0 4 b n 2 c n 2 w 0 b n ) ,
L n = π b n exp ( c n 2 4 b n + c n 8 w 0 3 b n 2 1 96 w 0 6 b n 3 ) [ ( c n 2 b n + 1 8 w 0 3 b n 2 ) Ai ( 1 16 w 0 4 b n 2 c n 2 w 0 b n ) 1 2 w 0 b n A i ( 1 16 w 0 4 b n 2 c n 2 w 0 b n ) ] ,
M n = π b n exp ( c n 2 4 b n + c n 8 w 0 3 b n 2 1 96 w 0 6 b n 3 ) [ ( 1 2 b n ) Ai ( 1 16 w 0 4 b n 2 c n 2 w 0 b n ) + 1 4 ( c n 2 b n 2 c n w 0 3 b n 3 + 1 8 w 0 6 b n 4 ) Ai ( 1 16 w 0 4 b n 2 c n 2 w 0 b n ) + 1 2 ( 1 4 w 0 4 b n 3 + c n w 0 b n 2 ) × A i ( 1 16 w 0 4 b n 2 c n 2 w 0 b 0 ) ] ,
F g r a d x , y , z = 2 π n 2 r 0 3 c ( m 2 1 m 2 + 2 ) I x , y , z ,
F s c a t x , y , z = 8 n 2 π k 4 r 0 6 3 c ( m 2 1 m 2 + 2 ) 2 I x , y , z e z ,
I x , y , z = c n 2 ε 0 | E x , y , z | 2 2 ,
S = E × H = c 4 π E × B , | S | = S x 2 + S y 2 + S z 2 ,
J = r × E × B , | J | = J x 2 + J y 2 + J z 2 .