Abstract

We present a method to measure the skew angle of the wave-fronts in an optical vortex, which is directly related with the energy flux. It is based on the analysis of the evolution on propagation of the near-field diffraction pattern generated by a single-slit, consisting of two main lobes that shift in opposite directions depending on the vortex helicity. The transverse displacement of each lobe as a function of the propagation distance allows to quantify the energy circulation. Analytical, numerical and experimental results are compared, showing good agreement. We illustrate the method for the case of Bessel beams, although we also discuss other types of helical beams, such as Laguerre-Gauss and Mathieu beams.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  39. J. L. Thomas and R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett.91, 244302 (2003).
    [CrossRef] [PubMed]
  40. K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, “An acoustic spanner and its associated rotational Doppler shift,” New J. Phys.10, 013018 (2008).
    [CrossRef]
  41. 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,” Science331, 192–195 (2011).
    [CrossRef] [PubMed]
  42. A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett.27, 1752–1754 (2002).
    [CrossRef]

2012 (1)

H. Tao, Y. Liu, Z. Chen, and J. Pu, “Measuring the topological charge of vortex beams by using an annular ellipse aperture,” Appl. Phys. B: Lasers Opt.106, 927–932 (2012).
[CrossRef]

2011 (4)

M. V. Berry and M. R. Dennis, “Stream function for optical energy flow,” J. Opt.13, 064004 (2011).
[CrossRef]

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

Y. Han and G. Zhao, “Measuring the topological charge of optical vortices with an axicon,” Opt. Lett.36, 2017–2019 (2011).
[CrossRef] [PubMed]

P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, “Engineering a square truncated lattice with light’s orbital angular momentum,” Opt. Express19, 20616–20621 (2011).
[CrossRef] [PubMed]

2010 (4)

I. Ricardez-Vargas and K. Volke-Sepúlveda, “Experimental generation and dynamical reconfiguration of different circular optical lattices for applications in atom trapping,” J. Opt. Soc. Am. B27, 948–955 (2010).
[CrossRef]

R. J. Hernández-Hernández, R. A. Terborg, I. Ricardez-Vargas, and K. Volke-Sepúlveda, “Experimental generation of Mathieu-Gauss beams with a phase-only spatial light modulator,” Appl. Opt.49, 6903–6909 (2010).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105, 053904 (2010).
[CrossRef] [PubMed]

A. Kumar, P. Vaity, and R. Singh, “Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm,” Opt. Commun.283, 4141–4145 (2010).
[CrossRef]

2009 (6)

D. Ghai, P. Senthilkumaran, and R. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng.47, 123–126 (2009).
[CrossRef]

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B: At. Mol. Opt.42, 085303 (2009).
[CrossRef]

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt.11, 094001 (2009).
[CrossRef]

A. Y. Bekshaev, “Oblique section of a paraxial light beam: criteria for azimuthal energy flow and orbital angular momentum,” J. Opt. A: Pure Appl. Opt.11, 094003 (2009).
[CrossRef]

V. Arrizón, D. Sánchez-de-la Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett.34, 1456–1458 (2009).
[CrossRef] [PubMed]

C. Guo, L. Lu, and H. Wang, “Characterizing topological charge of optical vortices by using an annular aperture,” Opt. Lett.34, 3686–3688 (2009).
[CrossRef] [PubMed]

2008 (3)

A. Ruelas, S. Lopez-Aguayo, and J. C. Gutiérrez-Vega, “Stable solitons in elliptical photonic lattices,” Opt. Lett.33, 2785–2787 (2008).
[CrossRef] [PubMed]

K. Volke-Sepúlveda, A. O. Santillán, and R. Boullosa, “Transfer of angular momentum to matter from acoustical vortices in free space,” Phys. Rev. Lett.100, 024302 (2008).
[CrossRef] [PubMed]

K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, “An acoustic spanner and its associated rotational Doppler shift,” New J. Phys.10, 013018 (2008).
[CrossRef]

2007 (3)

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett.98, 203601 (2007).
[CrossRef] [PubMed]

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

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32, 2291–2293 (2007).
[CrossRef] [PubMed]

2006 (5)

2005 (2)

2003 (3)

J. Leach and M. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys.5, 154.1–154.7 (2003).
[CrossRef]

J. L. Thomas and R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett.91, 244302 (2003).
[CrossRef] [PubMed]

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt.50, 1573–1580 (2003).

2002 (2)

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum S. Opt.4, S82–S89 (2002).
[CrossRef]

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett.27, 1752–1754 (2002).
[CrossRef]

2001 (1)

2000 (1)

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun.175, 289–294 (2000).
[CrossRef]

1999 (2)

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[CrossRef]

B. T. Hefner and P. L. Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am.106, 3313–3316 (1999).
[CrossRef]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75, 826–829 (1995).
[CrossRef] [PubMed]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett.69, 2503–2506 (1992).
[CrossRef] [PubMed]

1989 (1)

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1974).
[CrossRef]

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

Aksenov, V. P.

Alfano, R.

Allen, L.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt.50, 1573–1580 (2003).

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum S. Opt.4, S82–S89 (2002).
[CrossRef]

Arrizón, V.

Atuchin, V. V.

Babiker, M.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Bekshaev, A. Y.

A. Y. Bekshaev, “Oblique section of a paraxial light beam: criteria for azimuthal energy flow and orbital angular momentum,” J. Opt. A: Pure Appl. Opt.11, 094003 (2009).
[CrossRef]

Bernet, S.

Berry, M. V.

M. V. Berry and M. R. Dennis, “Stream function for optical energy flow,” J. Opt.13, 064004 (2011).
[CrossRef]

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt.11, 094001 (2009).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1974).
[CrossRef]

Boullosa, R.

K. Volke-Sepúlveda, A. O. Santillán, and R. Boullosa, “Transfer of angular momentum to matter from acoustical vortices in free space,” Phys. Rev. Lett.100, 024302 (2008).
[CrossRef] [PubMed]

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105, 053904 (2010).
[CrossRef] [PubMed]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum S. Opt.4, S82–S89 (2002).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett.26, 1803–1805 (2001).
[CrossRef]

Chen, Z.

H. Tao, Y. Liu, Z. Chen, and J. Pu, “Measuring the topological charge of vortex beams by using an annular ellipse aperture,” Appl. Phys. B: Lasers Opt.106, 927–932 (2012).
[CrossRef]

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[CrossRef] [PubMed]

Davidson, N.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett.98, 203601 (2007).
[CrossRef] [PubMed]

Dennis, M. R.

M. V. Berry and M. R. Dennis, “Stream function for optical energy flow,” J. Opt.13, 064004 (2011).
[CrossRef]

Dholakia, K.

C. López-Mariscal, J. Gutiérrez-Vega, G. Milne, and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express14, 4182–4187 (2006).
[CrossRef] [PubMed]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum S. Opt.4, S82–S89 (2002).
[CrossRef]

Edgar, M.

K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, “An acoustic spanner and its associated rotational Doppler shift,” New J. Phys.10, 013018 (2008).
[CrossRef]

Egorov, A. A.

Firstenberg, O.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett.98, 203601 (2007).
[CrossRef] [PubMed]

Fonseca, E. J. S.

P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, “Engineering a square truncated lattice with light’s orbital angular momentum,” Opt. Express19, 20616–20621 (2011).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105, 053904 (2010).
[CrossRef] [PubMed]

Foo, G.

Friberg, A. T.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75, 826–829 (1995).
[CrossRef] [PubMed]

Fürhapter, S.

Garcés-Chávez, V.

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum S. Opt.4, S82–S89 (2002).
[CrossRef]

Ghai, D.

D. Ghai, P. Senthilkumaran, and R. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng.47, 123–126 (2009).
[CrossRef]

Guo, C.

Gutiérrez-Vega, J.

Gutiérrez-Vega, J. C.

Han, Y.

Harvey, E.

Hayes, J. P.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75, 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75, 826–829 (1995).
[CrossRef] [PubMed]

Hefner, B. T.

B. T. Hefner and P. L. Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am.106, 3313–3316 (1999).
[CrossRef]

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[CrossRef] [PubMed]

Hernández-Hernández, R. J.

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

Hickmann, J. M.

P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, “Engineering a square truncated lattice with light’s orbital angular momentum,” Opt. Express19, 20616–20621 (2011).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105, 053904 (2010).
[CrossRef] [PubMed]

Izmailov, I. V.

Jáuregui, R.

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B: At. Mol. Opt.42, 085303 (2009).
[CrossRef]

Jesacher, A.

Jesus-Silva, A. J.

Kanev, F. Y.

Kartashov, Y. V.

Keen, S.

Kochemasov, G. G.

Kulikov, S. M.

Kumar, A.

A. Kumar, P. Vaity, and R. Singh, “Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm,” Opt. Commun.283, 4141–4145 (2010).
[CrossRef]

Lai, B.

Law, C. T.

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett.69, 2503–2506 (1992).
[CrossRef] [PubMed]

Leach, J.

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

Liu, Y.

H. Tao, Y. Liu, Z. Chen, and J. Pu, “Measuring the topological charge of vortex beams by using an annular ellipse aperture,” Appl. Phys. B: Lasers Opt.106, 927–932 (2012).
[CrossRef]

Lopez-Aguayo, S.

López-Mariscal, C.

Love, G. D.

Lu, L.

Manachinsky, A. N.

Mancuso, A. P.

Marchiano, R.

J. L. Thomas and R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett.91, 244302 (2003).
[CrossRef] [PubMed]

Marston, P. L.

B. T. Hefner and P. L. Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am.106, 3313–3316 (1999).
[CrossRef]

Masajada, J.

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun.175, 289–294 (2000).
[CrossRef]

Maslov, N. V.

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

McMahon, P. J.

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

McNulty, I.

Méndez, G.

Mesquita, P. H. F.

Milne, G.

Molina-Terriza, G.

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

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[CrossRef] [PubMed]

New, G. H. C.

Nugent, K. A.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1974).
[CrossRef]

Ogorodnikov, A. V.

Padgett, M.

J. Leach and M. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys.5, 154.1–154.7 (2003).
[CrossRef]

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[CrossRef]

Padgett, M. J.

K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, “An acoustic spanner and its associated rotational Doppler shift,” New J. Phys.10, 013018 (2008).
[CrossRef]

J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express14, 11919–11924 (2006).
[CrossRef] [PubMed]

Palacios, D. M.

Paterson, D.

Peele, A. G.

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[CrossRef] [PubMed]

Pu, J.

H. Tao, Y. Liu, Z. Chen, and J. Pu, “Measuring the topological charge of vortex beams by using an annular ellipse aperture,” Appl. Phys. B: Lasers Opt.106, 927–932 (2012).
[CrossRef]

Pugatch, R.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett.98, 203601 (2007).
[CrossRef] [PubMed]

Ricardez-Vargas, I.

Ritsch-Marte, M.

Ron, A.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett.98, 203601 (2007).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75, 826–829 (1995).
[CrossRef] [PubMed]

Ruelas, A.

Ruiz, U.

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[CrossRef] [PubMed]

Sánchez-de-la Llave, D.

Santillán, A. O.

K. Volke-Sepúlveda, A. O. Santillán, and R. Boullosa, “Transfer of angular momentum to matter from acoustical vortices in free space,” Phys. Rev. Lett.100, 024302 (2008).
[CrossRef] [PubMed]

Saunter, C.

Senthilkumaran, P.

D. Ghai, P. Senthilkumaran, and R. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng.47, 123–126 (2009).
[CrossRef]

Shuker, M.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett.98, 203601 (2007).
[CrossRef] [PubMed]

Singh, R.

A. Kumar, P. Vaity, and R. Singh, “Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm,” Opt. Commun.283, 4141–4145 (2010).
[CrossRef]

Sirohi, R.

D. Ghai, P. Senthilkumaran, and R. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng.47, 123–126 (2009).
[CrossRef]

Skeldon, K. D.

K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, “An acoustic spanner and its associated rotational Doppler shift,” New J. Phys.10, 013018 (2008).
[CrossRef]

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105, 053904 (2010).
[CrossRef] [PubMed]

Soldatenkov, I. S.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Starikov, F. A.

Sukharev, S. A.

Swartzlander, G. A.

G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett.30, 3308–3310 (2005).
[CrossRef]

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett.69, 2503–2506 (1992).
[CrossRef] [PubMed]

Sztul, H.

Tao, H.

H. Tao, Y. Liu, Z. Chen, and J. Pu, “Measuring the topological charge of vortex beams by using an annular ellipse aperture,” Appl. Phys. B: Lasers Opt.106, 927–932 (2012).
[CrossRef]

Terborg, R. A.

Thomas, J. L.

J. L. Thomas and R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett.91, 244302 (2003).
[CrossRef] [PubMed]

Torner, L.

Torres, J.

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

Tran, C. Q.

Turunen, J.

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

Vaity, P.

A. Kumar, P. Vaity, and R. Singh, “Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm,” Opt. Commun.283, 4141–4145 (2010).
[CrossRef]

Vasara, A.

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[CrossRef] [PubMed]

Volke-Sepúlveda, K.

R. J. Hernández-Hernández, R. A. Terborg, I. Ricardez-Vargas, and K. Volke-Sepúlveda, “Experimental generation of Mathieu-Gauss beams with a phase-only spatial light modulator,” Appl. Opt.49, 6903–6909 (2010).
[CrossRef] [PubMed]

I. Ricardez-Vargas and K. Volke-Sepúlveda, “Experimental generation and dynamical reconfiguration of different circular optical lattices for applications in atom trapping,” J. Opt. Soc. Am. B27, 948–955 (2010).
[CrossRef]

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B: At. Mol. Opt.42, 085303 (2009).
[CrossRef]

K. Volke-Sepúlveda, A. O. Santillán, and R. Boullosa, “Transfer of angular momentum to matter from acoustical vortices in free space,” Phys. Rev. Lett.100, 024302 (2008).
[CrossRef] [PubMed]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum S. Opt.4, S82–S89 (2002).
[CrossRef]

Vysloukh, V. A.

Wang, H.

Wilson, C.

K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, “An acoustic spanner and its associated rotational Doppler shift,” New J. Phys.10, 013018 (2008).
[CrossRef]

Woerdman, J.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Zhao, G.

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (1)

H. Tao, Y. Liu, Z. Chen, and J. Pu, “Measuring the topological charge of vortex beams by using an annular ellipse aperture,” Appl. Phys. B: Lasers Opt.106, 927–932 (2012).
[CrossRef]

J. Acoust. Soc. Am. (1)

B. T. Hefner and P. L. Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am.106, 3313–3316 (1999).
[CrossRef]

J. Mod. Opt. (1)

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt.50, 1573–1580 (2003).

J. Opt. (1)

M. V. Berry and M. R. Dennis, “Stream function for optical energy flow,” J. Opt.13, 064004 (2011).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (2)

A. Y. Bekshaev, “Oblique section of a paraxial light beam: criteria for azimuthal energy flow and orbital angular momentum,” J. Opt. A: Pure Appl. Opt.11, 094003 (2009).
[CrossRef]

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt.11, 094001 (2009).
[CrossRef]

J. Opt. B: Quantum S. Opt. (1)

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum S. Opt.4, S82–S89 (2002).
[CrossRef]

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

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

J. Phys. B: At. Mol. Opt. (1)

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B: At. Mol. Opt.42, 085303 (2009).
[CrossRef]

Nat. Phys. (1)

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

New J. Phys. (2)

J. Leach and M. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys.5, 154.1–154.7 (2003).
[CrossRef]

K. D. Skeldon, C. Wilson, M. Edgar, and M. J. Padgett, “An acoustic spanner and its associated rotational Doppler shift,” New J. Phys.10, 013018 (2008).
[CrossRef]

Opt. Commun. (2)

A. Kumar, P. Vaity, and R. Singh, “Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm,” Opt. Commun.283, 4141–4145 (2010).
[CrossRef]

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun.175, 289–294 (2000).
[CrossRef]

Opt. Express (4)

Opt. Laser Eng. (1)

D. Ghai, P. Senthilkumaran, and R. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng.47, 123–126 (2009).
[CrossRef]

Opt. Lett. (10)

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32, 2291–2293 (2007).
[CrossRef] [PubMed]

A. Ruelas, S. Lopez-Aguayo, and J. C. Gutiérrez-Vega, “Stable solitons in elliptical photonic lattices,” Opt. Lett.33, 2785–2787 (2008).
[CrossRef] [PubMed]

V. Arrizón, D. Sánchez-de-la Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett.34, 1456–1458 (2009).
[CrossRef] [PubMed]

C. Guo, L. Lu, and H. Wang, “Characterizing topological charge of optical vortices by using an annular aperture,” Opt. Lett.34, 3686–3688 (2009).
[CrossRef] [PubMed]

G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett.30, 3308–3310 (2005).
[CrossRef]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Shaping soliton properties in Mathieu lattices,” Opt. Lett.31, 238–240 (2006).
[CrossRef] [PubMed]

H. Sztul and R. Alfano, “Double-slit interference with Laguerre-Gaussian beams,” Opt. Lett.31, 999–1001 (2006).
[CrossRef] [PubMed]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett.26, 1803–1805 (2001).
[CrossRef]

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett.27, 1752–1754 (2002).
[CrossRef]

Y. Han and G. Zhao, “Measuring the topological charge of optical vortices with an axicon,” Opt. Lett.36, 2017–2019 (2011).
[CrossRef] [PubMed]

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett.98, 203601 (2007).
[CrossRef] [PubMed]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett.97, 170406 (2006).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75, 826–829 (1995).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105, 053904 (2010).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett.69, 2503–2506 (1992).
[CrossRef] [PubMed]

J. L. Thomas and R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett.91, 244302 (2003).
[CrossRef] [PubMed]

K. Volke-Sepúlveda, A. O. Santillán, and R. Boullosa, “Transfer of angular momentum to matter from acoustical vortices in free space,” Phys. Rev. Lett.100, 024302 (2008).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1974).
[CrossRef]

Prog. Opt. (1)

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[CrossRef]

Science (1)

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,” Science331, 192–195 (2011).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Transverse components of the Poynting vector for different kinds of helical beams: (a) Bessel beam with l = 9; (b) Single-ringed Laguerre-Gauss beam with l = 6 and (c) helical Mathieu beam of order r = 6 and ellipticity parameter q = 12.

Fig. 2
Fig. 2

Experimental setup. Spatial light modulator (SLM) displaying a phase computer generated hologram (CGH); Spatial Filter (SF); Slit (S) of 0.1mm width; CCD camera mounted on a micrometric translation stage, which is free to move along the Z direction.

Fig. 3
Fig. 3

Numerical simulation (gray-scale) and experimental images (green) of the impinging beam (left column) and their diffraction patterns at different z-planes for the helical Bessel beam of order l = 6 (bottom rows) and a non-rotating cosine beam as a reference (top rows). The z = 0mm distance would correspond to the nearest possible position of the CCD detector to the slit. The position of the axis of the slit is shown as a dashed red line. The slit has a width of 0.1mm.

Fig. 4
Fig. 4

Displacement of the maximum intensity points of a rotating mode relative to the reference beam. The upper and lower lobes are analized separately (left and right plots respectively). The red line is the linear fit for the experimental data and the theoretical displacement is shown in green.

Fig. 5
Fig. 5

Simulation of the propagation of single-slit diffraction for a helical MB of order l = 6 and parameter of elipticity q = 12 (top row) and a p = 0, l = 6 LG mode with a Rayleigh range of 59mm (bottom row). The slit is centered at x = 0mm (dashed line) and has a width of 0.1mm.

Tables (2)

Tables Icon

Table 1 Results for (tan αφ) = 〈Sx〉/〈Sz〉 from the experimental and numerical diffractive analisis for Bessel beams of order 6 and 9. For each mode the first and second rows correspond to the upper and lower lobes respectively. The slit is placed at x = 0mm and has a width of 0.1mm.]

Tables Icon

Table 2 Numerical and theoretical results for (tan αφ) = 〈Sx〉/〈Sz〉 from the analisis of the MB and LG mode shown in Fig. 5.

Equations (2)

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

S = C 0 | u | 2 ( ( S ρ ρ + ( l k ρ σ 2 k 1 | u | 2 | u | 2 ρ ) φ + z ) .
tan α φ = ( E × H ) x ( E × H ) z | x = 0 , y = ± y 0 ,

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