Abstract

We introduce a method to tune the local orbital angular momentum density in an optical vortex beam without changing its topological charge or geometric intensity distribution. We show that adjusting the relative amplitudes a and b of two interfering collinear vortex beams of equal but opposite helicity provides the smooth variation of the orbital angular momentum density in the resultant vortex beam. Despite the azimuthal intensity modulations that arise from the interference, the local orbital angular momentum remains constant on the vortex annulus and scales with the modulation parameter, c = (a-b)/(a+b).

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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  13. K. T. Kapale and J. P. Dowling, "Vortex Phase Qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams," Phys. Rev. Lett. 95, 173601 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  30. A. T. O’Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the doubling of the spin and orbital angular momentum with an optical spanner," Opt. Commun. 185, 139-143 (2000).
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  32. The general expression for the phase of a beam resulting from the collinear superposition of two optical vortex beams of equal but opposite topological charge is phi(theta) = arctan[ctan(ℓ (theta +α))]+π Round [ℓ(theta +α)/π]+2π +(phia +phib)/2, for c = 0 or theta +α 6= nπ/(2ℓ) with n = 1,3,5...(4ℓ−1) and phi(theta) = (cℓ/|c|)(theta +α)+2πℓ+(phia +phib)/2, for theta +α = nπ/(2ℓ) with n = 1,3,5...(4ℓ−1). The function Round(x) rounds the argument to its closest integer.
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    [CrossRef] [PubMed]
  37. K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
    [CrossRef]
  38. V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
    [CrossRef] [PubMed]
  39. S. S. R. Oemrawsingh, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, "Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices," J. Opt. Soc. Am. A 21, 2089-2096 (2004).
    [CrossRef]
  40. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun. 144, 210-213 (1997).
    [CrossRef]
  41. J. E. Curtis, C. H. J. Schmitz, and J. P. Spatz, "Symmetry dependence of holograms for optical trapping," Opt. Lett. 30, 2086-2088 (2005).
    [CrossRef] [PubMed]
  42. J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, "Angular momentum of optical vortex arrays," Opt. Express 14, 938-949 (2006).
    [CrossRef] [PubMed]
  43. A. Lafong, W. J. Hossack, J. Arlt, T. J. Nowakowski, and N. D. Read, "Time-Multiplexed Laguerre-Gaussian holographic optical tweezers for biological applications," Opt. Express 14, 3065-3072 (2006).
    [CrossRef] [PubMed]

2006 (4)

2005 (7)

2004 (5)

2003 (5)

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

I. D. Maleev and G. A. Swartzlander, "Composite optical vortices," J. Opt. Soc. Am. B 20, 1169-1176 (2003).
[CrossRef]

A. V. J.-W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum," Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

2002 (7)

G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 24041 (2002).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169 (2002).
[CrossRef]

A. T. O’Neil, I. MacVicar, L. Allen, and M. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

2001 (2)

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

M. Solja˘ci´c and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420-423 (2001).
[CrossRef] [PubMed]

2000 (2)

M. J. Padgett and L. Allen, "Light with a twist in its tail," Contemp. Phys. 41, 275-285 (2000).
[CrossRef]

A. T. O’Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the doubling of the spin and orbital angular momentum with an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

1999 (1)

J.W. R. Tabosa and D. V. Petrov, "Optical pumping of orbital angular momentum of light in cold cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

1998 (1)

M. E. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microparticles," Nature 394, 348-350 (1998).
[CrossRef]

1997 (3)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4074 (1997).
[CrossRef]

K.-P. Marzlin and W. Zhang, "Vortex coupler for atomic Bose-Einstein condensates," Phys. Rev. Lett. 79, 4728 (1997).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun. 144, 210-213 (1997).
[CrossRef]

1995 (2)

H. He, M. E. 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]

M. J. Padgett and L. Allen, "The Poynting vector in Laguerre-Gaussian laser modes," Opt. Commmun. 121, 36-40 (1995).
[CrossRef]

1992 (1)

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

1936 (1)

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

1909 (1)

J. H. Poynting, "The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of cicularly polarised light," Proc. R. Soc. London A 82, 560-567 (1909).
[CrossRef]

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

M. J. Padgett and L. Allen, "Light with a twist in its tail," Contemp. Phys. 41, 275-285 (2000).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun. 144, 210-213 (1997).
[CrossRef]

M. J. Padgett and L. Allen, "The Poynting vector in Laguerre-Gaussian laser modes," Opt. Commmun. 121, 36-40 (1995).
[CrossRef]

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

Arlt, J.

A. Lafong, W. J. Hossack, J. Arlt, T. J. Nowakowski, and N. D. Read, "Time-Multiplexed Laguerre-Gaussian holographic optical tweezers for biological applications," Opt. Express 14, 3065-3072 (2006).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[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, 912-914 (2001).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Bartlett, S. D.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Beijersbergen, M. W.

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

Beth, R. A.

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

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, 912-914 (2001).
[CrossRef] [PubMed]

Burge, R. E.

Chavez-Cerda, S.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Courtial, J.

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, "Angular momentum of optical vortex arrays," Opt. Express 14, 938-949 (2006).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun. 144, 210-213 (1997).
[CrossRef]

Curtis, J. E.

Dalton, R. B.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Dennis, M. R.

Dholakia, K.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[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, 912-914 (2001).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun. 144, 210-213 (1997).
[CrossRef]

Dowling, J. P.

K. T. Kapale and J. P. Dowling, "Vortex Phase Qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams," Phys. Rev. Lett. 95, 173601 (2005).
[CrossRef] [PubMed]

Dultz, W.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

Dutton, Z.

Z. Dutton and J. Ruostekoski, "Transfer and storage of vortex states in light and matter waves," Phys. Rev. Lett. 93, 193602 (2004).
[CrossRef] [PubMed]

Eliel, E. R.

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Friese, M. E.

M. E. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microparticles," Nature 394, 348-350 (1998).
[CrossRef]

H. He, M. E. 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]

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Gilchrist, A.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4074 (1997).
[CrossRef]

Grier, D. G.

S. Lee and D. G. Grier, "Giant colloidal diffusivity on corrugated optical vortices," Phys. Rev. Lett.,  96, 190601 (2006).
[CrossRef] [PubMed]

S.-H. Lee, and D. G. Grier, "Robustness of holographic optical traps against phase scaling errors", Opt. Express 13, 7458-7464 (2005).
[CrossRef] [PubMed]

K. Ladavac and D. G. Grier, "Colloidal hydrodynamic coupling in concentric optical vortices," Europhys. Lett. 70, 548-554 (2005).
[CrossRef]

K. Ladavac and D. G. Grier, "Microoptomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169 (2002).
[CrossRef]

Harvey, M. D.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

He, H.

H. He, M. E. 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.

M. E. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microparticles," Nature 394, 348-350 (1998).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4074 (1997).
[CrossRef]

H. He, M. E. 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]

Hossack, W. J.

Jennewein, T.

A. V. J.-W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum," Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

Jesacher, A.

Kapale, K. T.

K. T. Kapale and J. P. Dowling, "Vortex Phase Qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams," Phys. Rev. Lett. 95, 173601 (2005).
[CrossRef] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169 (2002).
[CrossRef]

Ladavac, K.

K. Ladavac and D. G. Grier, "Colloidal hydrodynamic coupling in concentric optical vortices," Europhys. Lett. 70, 548-554 (2005).
[CrossRef]

K. Ladavac and D. G. Grier, "Microoptomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
[CrossRef] [PubMed]

Lafong, A.

Langford, N. K.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Lee, S.

S. Lee and D. G. Grier, "Giant colloidal diffusivity on corrugated optical vortices," Phys. Rev. Lett.,  96, 190601 (2006).
[CrossRef] [PubMed]

Lee, S.-H.

Lin, J.

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[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, 912-914 (2001).
[CrossRef] [PubMed]

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Maleev, I. D.

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4074 (1997).
[CrossRef]

Marzlin, K.-P.

K.-P. Marzlin and W. Zhang, "Vortex coupler for atomic Bose-Einstein condensates," Phys. Rev. Lett. 79, 4728 (1997).
[CrossRef]

McGloin, D.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, "Experimental quantum coin tossing," Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef] [PubMed]

Nieminen, T. A.

M. E. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microparticles," Nature 394, 348-350 (1998).
[CrossRef]

Nienhuis, G.

Niu, H. B.

Nowakowski, T. J.

O’Brien, J. L.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

A. T. O’Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the doubling of the spin and orbital angular momentum with an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

Oemrawsingh, S. S. R.

Padgett, M.

A. T. O’Neil, I. MacVicar, L. Allen, and M. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Padgett, M. J.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

M. J. Padgett and L. Allen, "Light with a twist in its tail," Contemp. Phys. 41, 275-285 (2000).
[CrossRef]

A. T. O’Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the doubling of the spin and orbital angular momentum with an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun. 144, 210-213 (1997).
[CrossRef]

M. J. Padgett and L. Allen, "The Poynting vector in Laguerre-Gaussian laser modes," Opt. Commmun. 121, 36-40 (1995).
[CrossRef]

Pan, A. V. J.-W.

A. V. J.-W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum," Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[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, 912-914 (2001).
[CrossRef] [PubMed]

Peng, X.

Petrov, D. V.

J.W. R. Tabosa and D. V. Petrov, "Optical pumping of orbital angular momentum of light in cold cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

Poynting, J. H.

J. H. Poynting, "The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of cicularly polarised light," Proc. R. Soc. London A 82, 560-567 (1909).
[CrossRef]

Pryde, G. J.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Read, N. D.

Rubinsztein-Dunlop, H.

M. E. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microparticles," Nature 394, 348-350 (1998).
[CrossRef]

H. He, M. E. 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]

Ruostekoski, J.

Z. Dutton and J. Ruostekoski, "Transfer and storage of vortex states in light and matter waves," Phys. Rev. Lett. 93, 193602 (2004).
[CrossRef] [PubMed]

Schmitz, C. H. J.

Schmitzer, H.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

Segev, M.

M. Solja˘ci´c and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420-423 (2001).
[CrossRef] [PubMed]

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[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, 912-914 (2001).
[CrossRef] [PubMed]

Soljacic, M.

M. Solja˘ci´c and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420-423 (2001).
[CrossRef] [PubMed]

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4074 (1997).
[CrossRef]

Spatz, J. P.

Spreeuw, R. J. C.

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

Swartzlander, G. A.

Tabosa, J.W. R.

J.W. R. Tabosa and D. V. Petrov, "Optical pumping of orbital angular momentum of light in cold cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

Tao, S. H.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef] [PubMed]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef] [PubMed]

Ursin, R.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, "Experimental quantum coin tossing," Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

Vasnetsov, M.

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4074 (1997).
[CrossRef]

Vaziri, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, "Experimental quantum coin tossing," Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 24041 (2002).
[CrossRef]

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Weihs, G.

A. V. J.-W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum," Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 24041 (2002).
[CrossRef]

White, A. G.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Woerdman, J. P.

S. S. R. Oemrawsingh, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, "Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices," J. Opt. Soc. Am. A 21, 2089-2096 (2004).
[CrossRef]

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

Yuan, X. C.

Zambrini, R.

Zeilinger, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, "Experimental quantum coin tossing," Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

A. V. J.-W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum," Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 24041 (2002).
[CrossRef]

Zhang, W.

K.-P. Marzlin and W. Zhang, "Vortex coupler for atomic Bose-Einstein condensates," Phys. Rev. Lett. 79, 4728 (1997).
[CrossRef]

Contemp. Phys. (1)

M. J. Padgett and L. Allen, "Light with a twist in its tail," Contemp. Phys. 41, 275-285 (2000).
[CrossRef]

Europhys. Lett. (1)

K. Ladavac and D. G. Grier, "Colloidal hydrodynamic coupling in concentric optical vortices," Europhys. Lett. 70, 548-554 (2005).
[CrossRef]

J. Opt. B (1)

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

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

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

Nature (1)

M. E. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microparticles," Nature 394, 348-350 (1998).
[CrossRef]

Opt. Commmun. (1)

M. J. Padgett and L. Allen, "The Poynting vector in Laguerre-Gaussian laser modes," Opt. Commmun. 121, 36-40 (1995).
[CrossRef]

Opt. Commun. (3)

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169 (2002).
[CrossRef]

A. T. O’Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the doubling of the spin and orbital angular momentum with an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Gaussian beams with very high orbital angular momentum," Opt. Commun. 144, 210-213 (1997).
[CrossRef]

Opt. Express (8)

Opt. Lett. (2)

Phys. Rev. (1)

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Phys. Rev. A (2)

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

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4074 (1997).
[CrossRef]

Phys. Rev. Lett. (16)

M. Solja˘ci´c and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420-423 (2001).
[CrossRef] [PubMed]

S. Lee and D. G. Grier, "Giant colloidal diffusivity on corrugated optical vortices," Phys. Rev. Lett.,  96, 190601 (2006).
[CrossRef] [PubMed]

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

A. T. O’Neil, I. MacVicar, L. Allen, and M. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 24041 (2002).
[CrossRef]

A. V. J.-W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, "Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum," Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, "Measuring entangled qutrits and their use for quantum bit commitment," Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, "Experimental quantum coin tossing," Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

K.-P. Marzlin and W. Zhang, "Vortex coupler for atomic Bose-Einstein condensates," Phys. Rev. Lett. 79, 4728 (1997).
[CrossRef]

J.W. R. Tabosa and D. V. Petrov, "Optical pumping of orbital angular momentum of light in cold cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

Z. Dutton and J. Ruostekoski, "Transfer and storage of vortex states in light and matter waves," Phys. Rev. Lett. 93, 193602 (2004).
[CrossRef] [PubMed]

K. T. Kapale and J. P. Dowling, "Vortex Phase Qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams," Phys. Rev. Lett. 95, 173601 (2005).
[CrossRef] [PubMed]

H. He, M. E. 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. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. London A (1)

J. H. Poynting, "The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of cicularly polarised light," Proc. R. Soc. London A 82, 560-567 (1909).
[CrossRef]

Science (2)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and Manipulation of Three-Dimensional Optically Trapped Structures," Science 296, 1101-1103 (2002).
[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, 912-914 (2001).
[CrossRef] [PubMed]

Other (1)

The general expression for the phase of a beam resulting from the collinear superposition of two optical vortex beams of equal but opposite topological charge is phi(theta) = arctan[ctan(ℓ (theta +α))]+π Round [ℓ(theta +α)/π]+2π +(phia +phib)/2, for c = 0 or theta +α 6= nπ/(2ℓ) with n = 1,3,5...(4ℓ−1) and phi(theta) = (cℓ/|c|)(theta +α)+2πℓ+(phia +phib)/2, for theta +α = nπ/(2ℓ) with n = 1,3,5...(4ℓ−1). The function Round(x) rounds the argument to its closest integer.

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Figures (4)

Fig. 1.
Fig. 1.

(a-c)Phase masks of interference vortices with ℓ = 20 and (d-f) their measured intensity for mixing amplitudes: c = 1,0.2 and 0. As c decreases, more intensity is directed from the minima to the 2ℓ maxima on the ring to the maxima. A mixing amplitude c = 0 gives a binary intensity distribution.

Fig. 2.
Fig. 2.

Azimuthal dependence of the normalized intensity, I/(a 2 + b 2) and the normalized phase derivative and local wavefront helicity, (∂φ/∂θ)/#x2113;. The lines represent calculated values using Eqns. 3 and 5 with ℓ = 20 and c = 0.6 (dark lines) and c = 0.2 (light lines). The data symbols represent the measured local intensities whose errors are in the range of the symbol size.

Fig. 3.
Fig. 3.

(a) The measured period T for the modulation parameter c = 1.0,0.3,0.2,0.1 depends parabolically on the mean helicity or equivalently the topological charge, Q.(b) The relative rotational frequency Ω = T min /T as a function of c. The line represents s(c)-1 in Eq. (6), which is expressed analytically in Eq. (10). The maximum rotational speed (c = ±1) was 13 μm/s.

Fig. 4.
Fig. 4.

An optical vortex array consisting of three optical vortices with ℓ = 8. c 1 of vortex 1 is varied between 1 and -1 while vortices 2 and 3 have fixed c 2 = 0.17 and c 3 = -1. The time series shows the independent control of the rotation of three colloidal rings: (a) Ring 1 is slowly rotated counterclockwise, (b) stopped, and (c) rotated clockwise with increasing speed (c,d). The other rings (2,3) are rotated with constant velocity of different magnitude and sign. The bead in the center is fixed by a regular optical trap.

Equations (10)

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u i v = A ( r ) [ a e i ( θ + φ a ) + b e i ( θ + φ b ) ] = B ( r , θ ) e i φ ( θ ) ,
φ ( θ ) = arctan [ c tan ( ( θ + α ) ) ] + ( φ a + φ b ) 2 ,
I u ˜ i v ( r ' , θ ' ) 2 = A ˜ ( r ' ) 2 [ a 2 + b 2 + 2 ab cos ( 2 ( θ ' + α ) ) ] ,
u ˜ i v ( r ' , θ ' ) = A ˜ ( r ' ) [ a e i ( θ ' + φ a ) + b e i ( θ ' φ b ) ] = B ˜ ( r ' , θ ' ) e i φ ˜ ( θ ' ) ,
φ θ = c cos 2 [ ( θ + α ) ] + c 2 sin 2 [ ( θ + α ) ] ,
T = s ( c ) [ 1 + t 2 ] .
p = ε 0 2 Re [ E * × B + E × B * ] = i ω ε 0 2 ( u * u u u * ) + ω k ε 0 u 2 z ̂ .
p = ε 0 ω [ 1 r φ θ u 2 ] θ ̂ .
M z = ε 0 ω φ θ u ˜ i v 2 = ε 0 ω 4 a 2 c ( 1 + c ) 2 A ˜ ( r ' ) 2 = ε 0 ω 4 b 2 c ( 1 + c ) 2 A ˜ ( r ' ) 2 ,
Ω ( c ) = M z ( c ) M z ( c = ± 1 ) = ± 4 c ( 1 ± c ) 2 .

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