Abstract

Based on the extended Huygens-Fresnel principle, the analytical expressions for the cross-spectral density function of circular edge dislocation beams propagating through atmospheric turbulence and free space have been derived, and used to study the dynamic evolution of circular edge dislocations. It is shown that the number of circular edge dislocations on propagation equals that at the source plane when propagating through free space. The radius of circular edge dislocations increases with increasing propagation distance z. n-circular edge dislocations vanish and transform to n pairs of optical vortices with the opposite topological charge when propagating through atmospheric turbulence, and the position of each pair of optical vortices are symmetric about the slanted axis y = x. All the optical vortices will annihilate as soon as the propagation distance becomes large enough. The smaller radius of circular edge dislocation corresponds with the sooner annihilation of optical vortices. The structure constant affects the annihilation distance of the pairs of optical vortices, and the annihilation distance of the pairs of optical vortices will increase with the decrement of the structure constant.

© 2017 Optical Society of America

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  1. J. Nye and M. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(2), 165–190 (1974).
    [Crossref]
  2. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
    [Crossref]
  3. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42(4), 219–276 (2001).
    [Crossref]
  4. B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
    [Crossref]
  5. B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
    [Crossref] [PubMed]
  6. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
    [Crossref] [PubMed]
  7. J. Li, W. Wang, M. Duan, and J. Wei, “Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams,” Opt. Express 24(18), 20413–20423 (2016).
    [Crossref] [PubMed]
  8. J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
    [Crossref]
  9. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
    [Crossref] [PubMed]
  10. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
    [Crossref]
  11. N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
    [Crossref]
  12. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
    [Crossref] [PubMed]
  13. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [Crossref] [PubMed]
  14. J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
    [Crossref] [PubMed]
  15. M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
    [Crossref] [PubMed]
  16. M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
    [Crossref]
  17. R. Paez-Lopez, U. Ruiz, V. Arrizon, and R. Ramos-Garcia, “Optical manipulation using optimal annular vortices,” Opt. Lett. 41(17), 4138–4141 (2016).
    [Crossref] [PubMed]
  18. V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
    [Crossref] [PubMed]
  19. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral interferometry,” Opt. Lett. 30(15), 1953–1955 (2005).
    [Crossref] [PubMed]
  20. J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander., “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97(5), 053901 (2006).
    [Crossref] [PubMed]
  21. G. A. Swartzlander., “The optical vortex coronagraph,” J. Opt. A 11(9), 094022 (2009).
    [Crossref]
  22. A. Abulikemu, T. Yusufu, R. Mamuti, K. Miyamoto, and T. Omatsu, “Widely-tunable vortex output from a singly resonant optical parametric oscillator,” Opt. Express 23(14), 18338–18344 (2015).
    [Crossref] [PubMed]
  23. A. Abulikemu, T. Yusufu, R. Mamuti, S. Araki, K. Miyamoto, and T. Omatsu, “Octave-band tunable optical vortex parametric oscillator,” Opt. Express 24(14), 15204–15211 (2016).
    [Crossref] [PubMed]
  24. M. Luo, Q. Chen, L. Hua, and D. Zhao, “Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues,” Phys. Lett. A 378(3), 308–314 (2014).
    [Crossref]
  25. L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
    [Crossref] [PubMed]
  26. E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1), 123–135 (1991).
    [Crossref]
  27. M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
    [Crossref]
  28. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
    [Crossref] [PubMed]
  29. S. Li and Z. Wang, “Generation of optical vortex based on computer-generated holographic gratings by photolithography,” Appl. Phys. Lett. 103(14), 141110 (2013).
    [Crossref]
  30. C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43(12), 2397–2399 (2004).
    [Crossref] [PubMed]
  31. Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
    [Crossref] [PubMed]
  32. V. V. Kotlyar and A. A. Kovalev, “Fraunhofer diffraction of the plane wave by a multilevel (quantized) spiral phase plate,” Opt. Lett. 33(2), 189–191 (2008).
    [Crossref] [PubMed]
  33. M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464(7289), 737–739 (2010).
    [Crossref] [PubMed]
  34. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
    [Crossref] [PubMed]
  35. G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27(21), 1875–1877 (2002).
    [Crossref] [PubMed]
  36. Ya. Izdebskaya, V. Shvedov, and A. Volyar, “Generation of higher-order optical vortices by a dielectric wedge,” Opt. Lett. 30(18), 2472–2474 (2005).
    [Crossref] [PubMed]
  37. X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
    [Crossref]
  38. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
    [Crossref] [PubMed]
  39. E. Rueda, D. Muñetón, J. A. Gómez, and A. Lencina, “High-quality optical vortex-beam generation by using a multilevel vortex-producing lens,” Opt. Lett. 38(19), 3941–3944 (2013).
    [Crossref] [PubMed]
  40. S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
    [Crossref]
  41. K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
    [Crossref] [PubMed]
  42. R. K. Tyson, M. Scipioni, and J. Viegas, “Generation of an optical vortex with a segmented deformable mirror,” Appl. Opt. 47(33), 6300–6306 (2008).
    [Crossref] [PubMed]
  43. S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46(15), 2893–2898 (2007).
    [Crossref] [PubMed]
  44. S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46(32), 7862–7867 (2007).
    [Crossref] [PubMed]
  45. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
    [Crossref] [PubMed]
  46. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
    [Crossref]
  47. G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
    [Crossref] [PubMed]
  48. R. P. Singh and S. R. Chowdhury, “Noncanonical vortex transformation and propagation in a two-dimensional optical system,” J. Opt. Soc. Am. A 20(3), 573–576 (2003).
    [Crossref] [PubMed]
  49. F. S. Roux, “Paraxial modal analysis technique for optical vortex trajectories,” J. Opt. Soc. Am. B 20(7), 1575–1580 (2003).
    [Crossref]
  50. F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242(1), 45–55 (2004).
    [Crossref]
  51. A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
    [Crossref] [PubMed]
  52. J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
    [Crossref]
  53. J. Li and B. Lü, “Composite coherence vortices in superimposed partially coherent vortex beams and their propagation through atmospheric turbulence,” J. Opt. A 11(7), 075401 (2009).
    [Crossref]
  54. J. Li, H. Zhang, and B. Lü, “Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution,” Opt. Laser Technol. 42(2), 428–433 (2010).
    [Crossref]
  55. J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. 12(6), 065401 (2010).
    [Crossref]
  56. J. Li, J. Zeng, and M. Duan, “Classification of coherent vortices creation and distance of topological charge conservation in non-Kolmogorov atmospheric turbulence,” Opt. Express 23(9), 11556–11565 (2015).
    [Crossref] [PubMed]
  57. J. Zeng and J. Li, “Dynamic evolution and classification of coherent vortices in atmospheric turbulence,” Opt. Appl. 45(3), 299–308 (2015).
  58. A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54(1), 870–879 (1996).
    [Crossref] [PubMed]
  59. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices,” Phys. Rev. Lett. 76(13), 2262–2265 (1996).
    [Crossref] [PubMed]
  60. M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).
    [Crossref] [PubMed]
  61. S. G. Reddy, S. Prabhakar, A. Aadhi, J. Banerji, and R. P. Singh, “Propagation of an arbitrary vortex pair through an astigmatic optical system and determination of its topological charge,” J. Opt. Soc. Am. A 31(6), 1295–1302 (2014).
    [Crossref] [PubMed]
  62. M. Vasnetsov, V. Gorshkov, I. Marienko, and M. Soskin, “Wavefront motion in the vicinity of a phase dislocation:“optical vortex,” Opt. Spectrosc. 88(2), 260–265 (2000).
    [Crossref]
  63. C. Ding, L. Pan, and B. Lü, “Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams,” J. Opt. Soc. Am. A 26(12), 2654–2661 (2009).
    [Crossref] [PubMed]
  64. H. Yan and B. Lü, “Dynamic evolution of an edge dislocation through aligned and misaligned paraxial optical ABCD systems,” J. Opt. Soc. Am. A 26(4), 985–992 (2009).
    [Crossref] [PubMed]
  65. J. Li and B. Lü, “The transformation of an edge dislocation in atmospheric turbulence,” Opt. Commun. 284(1), 1–7 (2011).
    [Crossref]
  66. E. Zauderer, “Complex argument Hermite–Gaussian and Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 3(4), 465–469 (1986).
    [Crossref]
  67. J. Qu, Y. Zhong, Z. Cui, and Y. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283(14), 2772–2781 (2010).
    [Crossref]
  68. I. Kimel and L. R. Elias, “Relations between hermite and laguerre gaussian modes,” IEEE J. Quantum Electron. 29(9), 2562–2567 (1993).
    [Crossref]
  69. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  70. S. C. H. Wang and M. A. Plonus, “Optical beam propagation for a partially coherent source in the turbulent atmosphere,” J. Opt. Soc. Am. 69(9), 1297–1304 (1979).
    [Crossref]
  71. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2007).
  72. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  73. G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1–6), 117–125 (2003).
    [Crossref]
  74. I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
    [Crossref] [PubMed]
  75. M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80(1), 013824 (2009).
    [Crossref]
  76. M. Chen, C. Dainty, and F. S. Roux, “Speckle evolution with multiple steps of least-squares phase removal,” Phys. Rev. A 84(2), 023846 (2011).
    [Crossref]

2016 (5)

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

A. Abulikemu, T. Yusufu, R. Mamuti, S. Araki, K. Miyamoto, and T. Omatsu, “Octave-band tunable optical vortex parametric oscillator,” Opt. Express 24(14), 15204–15211 (2016).
[Crossref] [PubMed]

J. Li, W. Wang, M. Duan, and J. Wei, “Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams,” Opt. Express 24(18), 20413–20423 (2016).
[Crossref] [PubMed]

R. Paez-Lopez, U. Ruiz, V. Arrizon, and R. Ramos-Garcia, “Optical manipulation using optimal annular vortices,” Opt. Lett. 41(17), 4138–4141 (2016).
[Crossref] [PubMed]

2015 (5)

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
[Crossref]

J. Zeng and J. Li, “Dynamic evolution and classification of coherent vortices in atmospheric turbulence,” Opt. Appl. 45(3), 299–308 (2015).

J. Li, J. Zeng, and M. Duan, “Classification of coherent vortices creation and distance of topological charge conservation in non-Kolmogorov atmospheric turbulence,” Opt. Express 23(9), 11556–11565 (2015).
[Crossref] [PubMed]

A. Abulikemu, T. Yusufu, R. Mamuti, K. Miyamoto, and T. Omatsu, “Widely-tunable vortex output from a singly resonant optical parametric oscillator,” Opt. Express 23(14), 18338–18344 (2015).
[Crossref] [PubMed]

2014 (4)

S. G. Reddy, S. Prabhakar, A. Aadhi, J. Banerji, and R. P. Singh, “Propagation of an arbitrary vortex pair through an astigmatic optical system and determination of its topological charge,” J. Opt. Soc. Am. A 31(6), 1295–1302 (2014).
[Crossref] [PubMed]

B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
[Crossref]

M. Luo, Q. Chen, L. Hua, and D. Zhao, “Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues,” Phys. Lett. A 378(3), 308–314 (2014).
[Crossref]

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

2013 (4)

2011 (4)

J. Li and B. Lü, “The transformation of an edge dislocation in atmospheric turbulence,” Opt. Commun. 284(1), 1–7 (2011).
[Crossref]

M. Chen, C. Dainty, and F. S. Roux, “Speckle evolution with multiple steps of least-squares phase removal,” Phys. Rev. A 84(2), 023846 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

2010 (5)

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464(7289), 737–739 (2010).
[Crossref] [PubMed]

J. Qu, Y. Zhong, Z. Cui, and Y. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283(14), 2772–2781 (2010).
[Crossref]

J. Li, H. Zhang, and B. Lü, “Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution,” Opt. Laser Technol. 42(2), 428–433 (2010).
[Crossref]

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. 12(6), 065401 (2010).
[Crossref]

2009 (7)

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80(1), 013824 (2009).
[Crossref]

H. Yan and B. Lü, “Dynamic evolution of an edge dislocation through aligned and misaligned paraxial optical ABCD systems,” J. Opt. Soc. Am. A 26(4), 985–992 (2009).
[Crossref] [PubMed]

C. Ding, L. Pan, and B. Lü, “Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams,” J. Opt. Soc. Am. A 26(12), 2654–2661 (2009).
[Crossref] [PubMed]

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

J. Li and B. Lü, “Composite coherence vortices in superimposed partially coherent vortex beams and their propagation through atmospheric turbulence,” J. Opt. A 11(7), 075401 (2009).
[Crossref]

G. A. Swartzlander., “The optical vortex coronagraph,” J. Opt. A 11(9), 094022 (2009).
[Crossref]

2008 (3)

2007 (4)

S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46(15), 2893–2898 (2007).
[Crossref] [PubMed]

S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46(32), 7862–7867 (2007).
[Crossref] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

2006 (3)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander., “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97(5), 053901 (2006).
[Crossref] [PubMed]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
[Crossref] [PubMed]

2005 (3)

2004 (3)

2003 (4)

2002 (1)

2001 (4)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42(4), 219–276 (2001).
[Crossref]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
[Crossref] [PubMed]

2000 (1)

M. Vasnetsov, V. Gorshkov, I. Marienko, and M. Soskin, “Wavefront motion in the vicinity of a phase dislocation:“optical vortex,” Opt. Spectrosc. 88(2), 260–265 (2000).
[Crossref]

1997 (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

1996 (3)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54(1), 870–879 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices,” Phys. Rev. Lett. 76(13), 2262–2265 (1996).
[Crossref] [PubMed]

1994 (1)

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

1993 (3)

I. Kimel and L. R. Elias, “Relations between hermite and laguerre gaussian modes,” IEEE J. Quantum Electron. 29(9), 2562–2567 (1993).
[Crossref]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

1992 (1)

1991 (1)

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1), 123–135 (1991).
[Crossref]

1986 (1)

1979 (1)

1974 (1)

J. Nye and M. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(2), 165–190 (1974).
[Crossref]

Aadhi, A.

Abramochkin, E.

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1), 123–135 (1991).
[Crossref]

Abulikemu, A.

Agrawal, A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Ahluwalia, B.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Ahmed, M.

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Allen, L.

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

Anderson, D. Z.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54(1), 870–879 (1996).
[Crossref] [PubMed]

Anderson, I. M.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Araki, S.

Arita, Y.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Arrizon, V.

Bakry, A.

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Banerji, J.

Barnett, S.

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

Bernet, S.

Berry, M.

J. Nye and M. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(2), 165–190 (1974).
[Crossref]

Biener, G.

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Bu, J.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Buchleitner, A.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

Burge, R.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Cai, Y.

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[Crossref] [PubMed]

J. Qu, Y. Zhong, Z. Cui, and Y. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283(14), 2772–2781 (2010).
[Crossref]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Chen, H.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Chen, M.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

M. Chen, C. Dainty, and F. S. Roux, “Speckle evolution with multiple steps of least-squares phase removal,” Phys. Rev. A 84(2), 023846 (2011).
[Crossref]

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80(1), 013824 (2009).
[Crossref]

M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).
[Crossref] [PubMed]

Chen, Q.

M. Luo, Q. Chen, L. Hua, and D. Zhao, “Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues,” Phys. Lett. A 378(3), 308–314 (2014).
[Crossref]

Chowdhury, S. R.

Courtial, J.

Cui, Z.

J. Qu, Y. Zhong, Z. Cui, and Y. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283(14), 2772–2781 (2010).
[Crossref]

Dainty, C.

M. Chen, C. Dainty, and F. S. Roux, “Speckle evolution with multiple steps of least-squares phase removal,” Phys. Rev. A 84(2), 023846 (2011).
[Crossref]

Dennis, M. R.

Dholakia, K.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Ding, C.

Dipankar, A.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

Dong, Y.

Duan, M.

Elias, L. R.

I. Kimel and L. R. Elias, “Relations between hermite and laguerre gaussian modes,” IEEE J. Quantum Electron. 29(9), 2562–2567 (1993).
[Crossref]

Foo, G.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander., “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97(5), 053901 (2006).
[Crossref] [PubMed]

Franke-Arnold, S.

Freund, I.

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

Fürhapter, S.

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gao, Z.

B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
[Crossref]

Gbur, G.

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1–6), 117–125 (2003).
[Crossref]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gibson, G.

Gómez, J. A.

Gorshkov, V.

M. Vasnetsov, V. Gorshkov, I. Marienko, and M. Soskin, “Wavefront motion in the vicinity of a phase dislocation:“optical vortex,” Opt. Spectrosc. 88(2), 260–265 (2000).
[Crossref]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Gu, X.

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Hasman, E.

Heckenberg, N. R.

Hell, S. W.

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

Hershcovitz, O.

Herzing, A. A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Hua, L.

M. Luo, Q. Chen, L. Hua, and D. Zhao, “Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues,” Phys. Lett. A 378(3), 308–314 (2014).
[Crossref]

Huang, T. W.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

Izdebskaya, Ya.

Jesacher, A.

Johnson, E. G.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander., “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97(5), 053901 (2006).
[Crossref] [PubMed]

Ju, L. B.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Kimel, I.

I. Kimel and L. R. Elias, “Relations between hermite and laguerre gaussian modes,” IEEE J. Quantum Electron. 29(9), 2562–2567 (1993).
[Crossref]

Kleiner, V.

Kotlyar, V. V.

Kovalev, A. A.

Koyama, F.

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Lee, J. H.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander., “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97(5), 053901 (2006).
[Crossref] [PubMed]

Lencina, A.

Leonhard, N. D.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

Lezec, H. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Li, J.

J. Li, W. Wang, M. Duan, and J. Wei, “Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams,” Opt. Express 24(18), 20413–20423 (2016).
[Crossref] [PubMed]

J. Li, J. Zeng, and M. Duan, “Classification of coherent vortices creation and distance of topological charge conservation in non-Kolmogorov atmospheric turbulence,” Opt. Express 23(9), 11556–11565 (2015).
[Crossref] [PubMed]

J. Zeng and J. Li, “Dynamic evolution and classification of coherent vortices in atmospheric turbulence,” Opt. Appl. 45(3), 299–308 (2015).

J. Li and B. Lü, “The transformation of an edge dislocation in atmospheric turbulence,” Opt. Commun. 284(1), 1–7 (2011).
[Crossref]

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. 12(6), 065401 (2010).
[Crossref]

J. Li, H. Zhang, and B. Lü, “Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution,” Opt. Laser Technol. 42(2), 428–433 (2010).
[Crossref]

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

J. Li and B. Lü, “Composite coherence vortices in superimposed partially coherent vortex beams and their propagation through atmospheric turbulence,” J. Opt. A 11(7), 075401 (2009).
[Crossref]

Li, R.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Li, S.

S. Li and Z. Wang, “Generation of optical vortex based on computer-generated holographic gratings by photolithography,” Appl. Phys. Lett. 103(14), 141110 (2013).
[Crossref]

Lin, J.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Lipson, S. G.

Long, T. Y.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Lü, B.

J. Li and B. Lü, “The transformation of an edge dislocation in atmospheric turbulence,” Opt. Commun. 284(1), 1–7 (2011).
[Crossref]

J. Li, H. Zhang, and B. Lü, “Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution,” Opt. Laser Technol. 42(2), 428–433 (2010).
[Crossref]

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. 12(6), 065401 (2010).
[Crossref]

J. Li and B. Lü, “Composite coherence vortices in superimposed partially coherent vortex beams and their propagation through atmospheric turbulence,” J. Opt. A 11(7), 075401 (2009).
[Crossref]

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

C. Ding, L. Pan, and B. Lü, “Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams,” J. Opt. Soc. Am. A 26(12), 2654–2661 (2009).
[Crossref] [PubMed]

H. Yan and B. Lü, “Dynamic evolution of an edge dislocation through aligned and misaligned paraxial optical ABCD systems,” J. Opt. Soc. Am. A 26(4), 985–992 (2009).
[Crossref] [PubMed]

Luo, M.

M. Luo, Q. Chen, L. Hua, and D. Zhao, “Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues,” Phys. Lett. A 378(3), 308–314 (2014).
[Crossref]

Luo, Y.

B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
[Crossref]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54(1), 870–879 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices,” Phys. Rev. Lett. 76(13), 2262–2265 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[Crossref] [PubMed]

Mamuti, R.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Marchiano, R.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

Marienko, I.

M. Vasnetsov, V. Gorshkov, I. Marienko, and M. Soskin, “Wavefront motion in the vicinity of a phase dislocation:“optical vortex,” Opt. Spectrosc. 88(2), 260–265 (2000).
[Crossref]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Matsutani, A.

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Mazilu, M.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

McClelland, J. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

McDuff, R.

McMorran, B. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Miyamoto, K.

Mochizuki, S.

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Moed, S.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
[Crossref] [PubMed]

Muñetón, D.

Niu, H.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Niv, A.

Nye, J.

J. Nye and M. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(2), 165–190 (1974).
[Crossref]

O’Holleran, K.

Omatsu, T.

Padgett, M.

Padgett, M. J.

Paez-Lopez, R.

Pan, L.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Pas’ko, V.

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Peng, X.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Plonus, M. A.

Prabhakar, S.

Qiao, B.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Qu, J.

J. Qu, Y. Zhong, Z. Cui, and Y. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283(14), 2772–2781 (2010).
[Crossref]

Ramos-Garcia, R.

Recolons, J.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
[Crossref] [PubMed]

Reddy, S. G.

Ritsch-Marte, M.

Rotschild, C.

Roux, F. S.

M. Chen, C. Dainty, and F. S. Roux, “Speckle evolution with multiple steps of least-squares phase removal,” Phys. Rev. A 84(2), 023846 (2011).
[Crossref]

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80(1), 013824 (2009).
[Crossref]

M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).
[Crossref] [PubMed]

F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242(1), 45–55 (2004).
[Crossref]

F. S. Roux, “Paraxial modal analysis technique for optical vortex trajectories,” J. Opt. Soc. Am. B 20(7), 1575–1580 (2003).
[Crossref]

Ruan, S. C.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Rueda, E.

Ruiz, U.

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices,” Phys. Rev. Lett. 76(13), 2262–2265 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54(1), 870–879 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[Crossref] [PubMed]

Sagaut, P.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

Schattschneider, P.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Scipioni, M.

Senthilkumaran, P.

Shatokhin, V. N.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

Shvartsman, N.

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

Shvedov, V.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Singh, R. P.

Smith, C. P.

Soskin, M.

M. Vasnetsov, V. Gorshkov, I. Marienko, and M. Soskin, “Wavefront motion in the vicinity of a phase dislocation:“optical vortex,” Opt. Spectrosc. 88(2), 260–265 (2000).
[Crossref]

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42(4), 219–276 (2001).
[Crossref]

Swartzlander, G. A.

G. A. Swartzlander., “The optical vortex coronagraph,” J. Opt. A 11(9), 094022 (2009).
[Crossref]

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander., “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97(5), 053901 (2006).
[Crossref] [PubMed]

Tanabe, K.

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Tang, B.

B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
[Crossref]

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Tian, H.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Tonomura, A.

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464(7289), 737–739 (2010).
[Crossref] [PubMed]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
[Crossref] [PubMed]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
[Crossref] [PubMed]

Tyson, R. K.

Uchida, M.

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464(7289), 737–739 (2010).
[Crossref] [PubMed]

Unguris, J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Vanderveen, H.

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

Vasnetsov, M.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref] [PubMed]

M. Vasnetsov, V. Gorshkov, I. Marienko, and M. Soskin, “Wavefront motion in the vicinity of a phase dislocation:“optical vortex,” Opt. Spectrosc. 88(2), 260–265 (2000).
[Crossref]

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42(4), 219–276 (2001).
[Crossref]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Verbeeck, J.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Viegas, J.

Visser, T. D.

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1–6), 117–125 (2003).
[Crossref]

Volostnikov, V.

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1), 123–135 (1991).
[Crossref]

Volyar, A.

Vyas, S.

Wang, J.

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

Wang, S. C. H.

Wang, W.

Wang, Z.

S. Li and Z. Wang, “Generation of optical vortex based on computer-generated holographic gratings by photolithography,” Appl. Phys. Lett. 103(14), 141110 (2013).
[Crossref]

Wei, J.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Westphal, V.

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

Wright, E. M.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
[Crossref] [PubMed]

Wu, G. Z.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Wu, S. Z.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Xiao, K. D.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Yan, H.

Yang, S. L.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Yang, Y.

Yang, Y. C.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Yuan, X.

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

Yusufu, T.

Zauderer, E.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Zeng, J.

Zhang, H.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. 12(6), 065401 (2010).
[Crossref]

J. Li, H. Zhang, and B. Lü, “Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution,” Opt. Laser Technol. 42(2), 428–433 (2010).
[Crossref]

Zhang, Y.

B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
[Crossref]

Zhao, C.

Zhao, D.

M. Luo, Q. Chen, L. Hua, and D. Zhao, “Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues,” Phys. Lett. A 378(3), 308–314 (2014).
[Crossref]

Zheng, S.

B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
[Crossref]

Zhong, Y.

J. Qu, Y. Zhong, Z. Cui, and Y. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283(14), 2772–2781 (2010).
[Crossref]

Zhou, C. T.

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Zommer, S.

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices,” Phys. Rev. Lett. 76(13), 2262–2265 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54(1), 870–879 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[Crossref] [PubMed]

Appl. Opt. (4)

Appl. Phys. Express (1)

S. Mochizuki, X. Gu, K. Tanabe, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “Generation of vortex beam using Bragg reflector waveguide,” Appl. Phys. Express 7(2), 022502 (2014).
[Crossref]

Appl. Phys. Lett. (2)

S. Li and Z. Wang, “Generation of optical vortex based on computer-generated holographic gratings by photolithography,” Appl. Phys. Lett. 103(14), 141110 (2013).
[Crossref]

X. Yuan, B. Ahluwalia, H. Chen, J. Bu, J. Lin, R. Burge, X. Peng, and H. Niu, “Generation of high-quality optical vortex beams in free-space propagation by microfabricated wedge with spatial filtering technique,” Appl. Phys. Lett. 91(5), 051103 (2007).
[Crossref]

IEEE J. Quantum Electron. (1)

I. Kimel and L. R. Elias, “Relations between hermite and laguerre gaussian modes,” IEEE J. Quantum Electron. 29(9), 2562–2567 (1993).
[Crossref]

J. Mod. Opt. (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

J. Opt. (1)

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. 12(6), 065401 (2010).
[Crossref]

J. Opt. A (3)

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

J. Li and B. Lü, “Composite coherence vortices in superimposed partially coherent vortex beams and their propagation through atmospheric turbulence,” J. Opt. A 11(7), 075401 (2009).
[Crossref]

G. A. Swartzlander., “The optical vortex coronagraph,” J. Opt. A 11(9), 094022 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

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

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Nature (4)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464(7289), 737–739 (2010).
[Crossref] [PubMed]

Opt. Appl. (1)

J. Zeng and J. Li, “Dynamic evolution and classification of coherent vortices in atmospheric turbulence,” Opt. Appl. 45(3), 299–308 (2015).

Opt. Commun. (7)

J. Qu, Y. Zhong, Z. Cui, and Y. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283(14), 2772–2781 (2010).
[Crossref]

J. Li and B. Lü, “The transformation of an edge dislocation in atmospheric turbulence,” Opt. Commun. 284(1), 1–7 (2011).
[Crossref]

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1–6), 117–125 (2003).
[Crossref]

F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242(1), 45–55 (2004).
[Crossref]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1), 123–135 (1991).
[Crossref]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

B. Tang, Y. Luo, Y. Zhang, S. Zheng, and Z. Gao, “Analytical vectorial structure of Gaussian beams carrying mixed screw–edge dislocations in the far field,” Opt. Commun. 324(1), 182–187 (2014).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (1)

J. Li, H. Zhang, and B. Lü, “Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution,” Opt. Laser Technol. 42(2), 428–433 (2010).
[Crossref]

Opt. Lett. (9)

E. Rueda, D. Muñetón, J. A. Gómez, and A. Lencina, “High-quality optical vortex-beam generation by using a multilevel vortex-producing lens,” Opt. Lett. 38(19), 3941–3944 (2013).
[Crossref] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[Crossref] [PubMed]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral interferometry,” Opt. Lett. 30(15), 1953–1955 (2005).
[Crossref] [PubMed]

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[Crossref] [PubMed]

V. V. Kotlyar and A. A. Kovalev, “Fraunhofer diffraction of the plane wave by a multilevel (quantized) spiral phase plate,” Opt. Lett. 33(2), 189–191 (2008).
[Crossref] [PubMed]

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27(21), 1875–1877 (2002).
[Crossref] [PubMed]

Ya. Izdebskaya, V. Shvedov, and A. Volyar, “Generation of higher-order optical vortices by a dielectric wedge,” Opt. Lett. 30(18), 2472–2474 (2005).
[Crossref] [PubMed]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

R. Paez-Lopez, U. Ruiz, V. Arrizon, and R. Ramos-Garcia, “Optical manipulation using optimal annular vortices,” Opt. Lett. 41(17), 4138–4141 (2016).
[Crossref] [PubMed]

Opt. Rev. (1)

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Creating and probing of a perfect vortex in situ with an optically trapped particle,” Opt. Rev. 22(1), 162–165 (2015).
[Crossref]

Opt. Spectrosc. (1)

M. Vasnetsov, V. Gorshkov, I. Marienko, and M. Soskin, “Wavefront motion in the vicinity of a phase dislocation:“optical vortex,” Opt. Spectrosc. 88(2), 260–265 (2000).
[Crossref]

Photonics Res. (1)

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

Phys. Lett. A (1)

M. Luo, Q. Chen, L. Hua, and D. Zhao, “Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues,” Phys. Lett. A 378(3), 308–314 (2014).
[Crossref]

Phys. Rev. A (5)

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91(1), 012345 (2015).
[Crossref]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54(1), 870–879 (1996).
[Crossref] [PubMed]

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

M. Chen and F. S. Roux, “Influence of the least-squares phase on optical vortices in strongly scintillated beams,” Phys. Rev. A 80(1), 013824 (2009).
[Crossref]

M. Chen, C. Dainty, and F. S. Roux, “Speckle evolution with multiple steps of least-squares phase removal,” Phys. Rev. A 84(2), 023846 (2011).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

L. B. Ju, T. W. Huang, K. D. Xiao, G. Z. Wu, S. L. Yang, R. Li, Y. C. Yang, T. Y. Long, H. Zhang, S. Z. Wu, B. Qiao, S. C. Ruan, and C. T. Zhou, “Controlling multiple filaments by relativistic optical vortex beams in plasmas,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 94(3), 033202 (2016).
[Crossref] [PubMed]

Phys. Rev. Lett. (7)

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander., “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97(5), 053901 (2006).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[Crossref]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 88(2), 023902 (2001).
[Crossref] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices,” Phys. Rev. Lett. 76(13), 2262–2265 (1996).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

J. Nye and M. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(2), 165–190 (1974).
[Crossref]

Prog. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42(4), 219–276 (2001).
[Crossref]

Science (3)

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Other (3)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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

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Figures (7)

Fig. 1
Fig. 1 (a, b) The intensity and (c, d) phase distribution of (a, c) circular edge dislocation beam and (b, d) vortex beam at the source plane.
Fig. 2
Fig. 2 (a)-(c) Curves of Reμ = 0 (red solid curves) and Imμ = 0 (blue dashed curves) and (d)-(f) contour lines of phase of circular edge dislocations beams at different propagation distance (a) and (d) z = 0, (b) and (e) z = 2km, (c) and (f) z = 5km. The abscissa represents ρ2x direction, ordinate represents ρ2y direction, and their units are cm.
Fig. 3
Fig. 3 Curves of Reμ = 0 (red solid curves) and Imμ = 0 (blue dashed curves) of circular edge dislocations beams at different propagation distance (a) and (d) z = 0, (b) and (e) z = 2km, (c) and (f) z = 5km for different values of (a)-(c) n = 2, (d)-(f) n = 3.
Fig. 4
Fig. 4 Curves of Reμ = 0 (red solid curves) and Imμ = 0 (blue dashed curves) and (e)-(h) contour lines of phase of circular edge dislocations beams propagating through atmospheric turbulence for different propagation distance (a) and (e) z = 0.2km, (b) and (f) z = 1km, (c) and (g) z = 4km, (d) and (h) z = 8km. Their units are cm, “” topological charge is −1, “” topological charge is + 1.
Fig. 5
Fig. 5 Curves of Reμ = 0 (red solid curves) and Imμ = 0 (blue dashed curves) of circular edge dislocations beams propagating through atmospheric turbulence at different propagation distance (a) and (e) z = 0.2km, (b) and (f) z = 1km, (c) and (g) z = 4km, (d) and (h) z = 8km for different values of (a)-(d) n = 2, (e)-(h) n = 3.
Fig. 6
Fig. 6 3D trajectory of the pairs optical vortices in atmospheric turbulence versus the propagation distance z for different values of (a) n = 1, (b) n = 2, (c) n = 3, “” topological charge is −1, “” topological charge is + 1.
Fig. 7
Fig. 7 3D trajectory of the pairs optical vortices in atmospheric turbulence versus the propagation distance z for different structure constant (a) C n 2 = 5 × 10−15 m-2/3, (b) C n 2 = 10−15 m2/3.

Equations (22)

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E(s,θ,0)= ( 2 s w 0 ) m L n m ( 2 s 2 w 0 2 )exp( s 2 w 0 2 )exp(imθ),
exp(imθ) s 2 L n m ( s 2 )= (1) n 2 2n+m n! t=0 n r=0 m i r ( t n ) ( r m ) H 2t+mr ( s x ) H 2n2t+r ( s y ),
E(s,0)= (1) n 2 2n+m n! t=0 n r=0 m i r ( t n ) ( r m ) H 2t+mr ( 2 s x w 0 ) H 2n2t+r ( 2 s y w 0 )exp( s 2 w 0 2 ).
E(s,0)= 1 2 m r=0 m i r ( r m ) H mr ( 2 s x w 0 ) H r ( 2 s y w 0 )exp( s 2 w 0 2 ),
E(s,0)= (1) n 2 2n n! t=0 n ( t n ) H 2t ( 2 s x w 0 ) H 2n2t ( 2 s y w 0 )exp( s 2 w 0 2 ).
W 0 ( s 1 , s 2 ,0)= 1 2 4n (n!) 2 t 1 =0 n t 2 =0 n ( t 1 n ) ( t 2 n ) H 2 t 1 ( 2 s 1x w 0 ) H 2 t 2 ( 2 s 2x w 0 ) × H 2n2 t 1 ( 2 s 1y w 0 ) H 2n2 t 2 ( 2 s 2y w 0 )exp( s 1 2 + s 2 2 w 0 2 ).
W( ρ 1 , ρ 2 ,z)= ( k 2πz ) 2 W 0 ( s 1 , s 2 ,0)exp{ ik 2z [ ( s 1 ρ 1 ) 2 ( s 2 ρ 2 ) 2 ]} ×exp[ψ( s 1 , ρ 1 )+ ψ * ( s 2 , ρ 2 )]d s 1 d s 2 ,
exp[ψ( s 1 , ρ 1 )+ ψ * ( s 2 , ρ 2 )]=exp[ ( s 1 s 2 ) 2 + ( ρ 1 ρ 2 ) 2 +( s 1 s 2 )( ρ 1 ρ 2 ) ρ 0 2 ],
exp[ (xy) 2 ] H n (ax)dx= π (1 a 2 ) n 2 H n ( ay (1 a 2 ) 1/2 ),
x n exp[ (xβ) 2 ]dx= (2i) n π H n (iβ),
H n (x+y)= 1 2 n/2 k=0 n ( k n ) H k ( 2 x) H nk ( 2 y),
H n (x)= m=0 [n/2] (1) m n! m!(n2m)! (2x) n2m ,
W( ρ 1 , ρ 2 ,z)= ( k 2πz ) 2 A x A y exp[ ( ρ 1 ρ 2 ) 2 ρ 0 2 ]exp[ ik 2z ( ρ 1 2 ρ 2 2 )] × 1 2 4n (n!) 2 t 1 =0 n t 2 =0 n ( t 1 n ) ( t 2 n )BC ,
A x =exp[ 1 4D ( ρ 1x ρ 2x ρ 0 2 ik ρ 2x z ) 2 ]exp( F x 2 4G ),
B= c 1 =0 t 1 d 1 =0 2 t 2 e 1 =0 [ d 1 2 ] ( d 1 2 t 2 ) (1) c 1 + e 1 (2i) (2 t 2 2 c 1 + d 1 2 e 1 ) (2 t 1 )! d 1 ! c 1 !(2 t 1 2 c 1 )! e 1 !( d 1 2 e 1 )! ( 2 2 w 0 ) 2 t 1 2 c 1 × π D (1 2 w 0 2 D ) t 2 2 t 2 [ 4 ρ 0 2 w 0 2 D 2 2D ] d 1 2 e 1 ( 1 G ) 2 t 1 2 c 1 + d 1 2 e 1 +1 × H 2 t 2 d 1 [ ( ρ 1x ρ 2x )zik ρ 2x ρ 0 2 ρ 0 2 z w 0 2 D 2 2D ] H 2 t 1 2 c 1 + d 1 2 e 1 (i F x 2 G ) ,
C= c 2 =0 n t 1 d 2 =0 2n2 t 2 e 2 =0 [ d 2 2 ] ( d 2 2n2 t 2 ) (1) c 2 + e 2 (2i) (2n2 t 1 2 c 2 + d 2 2 e 2 ) (2n2 t 1 )! d 2 ! c 2 !(2n2 t 1 2 c 2 )! e 2 !( d 2 2 e 2 )! × π D (1 2 w 0 2 D ) n t 1 2 (n t 1 ) [ 4 ρ 0 2 w 0 2 D 2 2D ] d 2 2 e 2 ( 1 G ) 2n2 t 1 2 c 2 + d 2 2 e 2 +1 × ( 2 2 w 0 ) 2n2 t 1 2 c 2 H 2n2 t 2 d 2 [ ( ρ 1y ρ 2y )zik ρ 2y ρ 0 2 ρ 0 2 z w 0 2 D 2 2D ] H 2n2 t 1 2 c 2 + d 2 2 e 2 (i F y 2 G ),
D= 1 w 0 2 ik 2z + 1 ρ 0 2 ,
F x = ik ρ 1x z ρ 1x ρ 2x ρ 0 2 + 1 D ρ 0 2 ( ρ 1x ρ 2x ρ 0 2 ik ρ 2x z ),
G= 1 w 0 2 + ik 2z + 1 ρ 0 2 1 D ρ 0 4 .
μ( ρ 1 , ρ 2 ,z)= W( ρ 1 , ρ 2 ,z) [ I( ρ 1 ,z)I( ρ 2 ,z) ] 1/2 ,
Re[ μ( ρ 1 , ρ 2 ,z) ]=0,
Im[ μ( ρ 1 , ρ 2 ,z) ]=0.

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