Abstract

Direct observation of Gouy phase shift on an optical vortex was presented through investigating the intensity profiles of a modified LGpm beam with an asymmetric defect, around at the focal point. In addition, the three-dimensional trajectory of the defect was found to describe a uniform straight line. It was quantitatively found that the rotation profile of a modified LGpm beam manifests the Gouy phase effect where the rotation direction depends on only the sign of topological charge m. This profile measurement method by introducing an asymmetric defect is a simple and useful technique for obtaining the information of the Gouy phase shift, without need of a conventional interference method.

© 2006 Optical Society of America

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  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]
  2. A. Ashkin , “ Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime ,” Biophys. J.   61 , 569 – 582 ( 1992 ).
    [Crossref] [PubMed]
  3. A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
    [Crossref] [PubMed]
  4. K. T. Gahagan and G. A. Swartzlander , “ Optical vortex trapping of particles ,” Opt. Lett.   21 , 827 – 829 ( 1996 ).
    [Crossref] [PubMed]
  5. T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
    [Crossref]
  6. E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
    [Crossref]
  7. J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
    [Crossref]
  8. N. B. Simpson , K. Dholakia , L. Allen , and M. J. Padgett , “ Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner ,” Opt. Lett.   22 , 52 – 54 ( 1997 ).
    [Crossref] [PubMed]
  9. L. Paterson , M. P. MacDonald , J. Arlt , W. Sibbet , P. E. Bryant , and K. Dholaki , “ Controlled rotation of optically trapped microscopic particles ,” Science   292 , 912 – 914 ( 2001 ).
    [Crossref] [PubMed]
  10. V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
    [Crossref] [PubMed]
  11. A. Mair , A. Vaziri , G. Weihs , and A. Zeilinger , “ Entanglement of the orbital angular momentum states of photons ,” Nature   412 , 313 – 316 ( 2001 ).
    [Crossref] [PubMed]
  12. A. Vaziri , G. Weihs , and A. Zeilinger , “ Experimental two-photon, three-dimensional entanglement for quantum communication ,” Phys. Rev. Lett.   89 , 240401 -1-4 ( 2002 ).
    [Crossref] [PubMed]
  13. 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 -1-4 ( 2001 ).
    [Crossref]
  14. K. Dholakia , N. B. Simpson , M. J. Padgett , and L. Allen , “ Second-harmonic generation and the orbital angular momentum of light ,” Phys. Rev. A   54 , R3742 – 3745 ( 1996 ).
    [Crossref] [PubMed]
  15. D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
    [Crossref]
  16. A. Vinçotte and L. Bergé , “ Femtosecond optical vortices in air ,” Phys. Rev. Lett.   95 , 193901 -1-4 ( 2005 ).
    [Crossref] [PubMed]
  17. D. Neshev , A. Nepomnyashchy , and Y. S. Kivshar , “ Nonlinear Aharonov-Bohm scattering by optical vortices ,” Phys. Rev. Lett.   87 , 043901 -1-4 ( 2001 ).
    [Crossref] [PubMed]
  18. M. V. Berry , “ Quantal phase factors accompanying adiabatic changes ,” Proc. R. Soc. London A   392 , 45 – 57 ( 1984 ).
    [Crossref]
  19. R. Simon and N. Mukunda , “ Bargmann invariant and the geometry of the Gouy effect ,” Phys. Rev. Lett.   70 , 880 – 883 ( 1993 ).
    [Crossref] [PubMed]
  20. D. Subbarao , “ Topological phase in Gaussian beam optics ,” Opt. Lett.   20 , 2162 – 2164 ( 1995 ).
    [Crossref] [PubMed]
  21. S. Feng and H. G. Winful , “ Physical origin of the Gouy phase shift ,” Opt. Lett.   26 , 485 – 487 ( 2001 ).
    [Crossref]
  22. J. A. Jones , V. Vedral , A. Ekert , and G. Castagnoli , “ Geometric quantum computation using nuclear magnetic resonance ,” Nature   403 , 869 – 871 ( 2000 ).
    [Crossref] [PubMed]
  23. L.-M. Duan , J. I. Cirac , and P. Zoller , “ Geometric manipulation of trapped ions for quantum computation ,” Science   292 , 1695 – 1697 ( 2001 ).
    [Crossref] [PubMed]
  24. A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
    [Crossref]
  25. R. W. McGown , R. A. Cheville , and D. Grischkowsky , “ Direct observation of the Gouy phase shift in THz impulse ranging ,” Appl. Phys. Lett.   76 , 670 – 672 ( 2000 ).
    [Crossref]
  26. F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
    [Crossref] [PubMed]
  27. L. G. Gouy , “ Sur une propriété nouvelle des ondes lumineuses ,” Compt. Rendue Acad. Sci. (Paris)   110 , 1251 – 1253 ( 1890 ).
  28. C. R. Carpenter , “ Gouy phase advance with microwaves ,” Am. J. Phys.   27 , 98 – 100 ( 1959 ).
  29. J. H. Chow , G. de Vine , M. B. Gray , and D. E. McClelland , “ Measurement of Gouy phase evolution by use ofmode interference ,” Opt. Lett.   29 , 2339 – 2341 ( 2004 ).
    [Crossref] [PubMed]
  30. J. Arlt , “ Handedness and azimuthal energy flow of optical vortex beams ,” J. Mod. Opt.   50 , 1573 – 1580 ( 2003 ).
  31. B. Luther-Davies , R. Powels , and V. Tikhonenko , “ Nonlinear rotation of three-dimensional dark solitons in a Gaussian laser beam ,” Opt. Lett.   19 , 1816 – 1818 ( 1994 ).
    [Crossref] [PubMed]
  32. F. Flossmann , U. T. Schwarz , and M. Maier , “ Optical vortices in a Laguerre-Gaussian LG01beam ,” J. Mod. Opt.   52 , 1009 – 1017 ( 2005 ).
    [Crossref]
  33. 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 , 3039 – 3044 ( 2006 ).
    [Crossref]
  34. M. J. Padgett and L. Allen , “ The Poynting vector in Laguerre-Gaussian laser modes ,” Opt. Commun.   121 , 36 – 40 ( 1995 ).
    [Crossref]

2006 (1)

2005 (2)

F. Flossmann , U. T. Schwarz , and M. Maier , “ Optical vortices in a Laguerre-Gaussian LG01beam ,” J. Mod. Opt.   52 , 1009 – 1017 ( 2005 ).
[Crossref]

A. Vinçotte and L. Bergé , “ Femtosecond optical vortices in air ,” Phys. Rev. Lett.   95 , 193901 -1-4 ( 2005 ).
[Crossref] [PubMed]

2004 (2)

J. H. Chow , G. de Vine , M. B. Gray , and D. E. McClelland , “ Measurement of Gouy phase evolution by use ofmode interference ,” Opt. Lett.   29 , 2339 – 2341 ( 2004 ).
[Crossref] [PubMed]

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

2003 (2)

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

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

2002 (2)

A. Vaziri , G. Weihs , and A. Zeilinger , “ Experimental two-photon, three-dimensional entanglement for quantum communication ,” Phys. Rev. Lett.   89 , 240401 -1-4 ( 2002 ).
[Crossref] [PubMed]

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

2001 (8)

D. Neshev , A. Nepomnyashchy , and Y. S. Kivshar , “ Nonlinear Aharonov-Bohm scattering by optical vortices ,” Phys. Rev. Lett.   87 , 043901 -1-4 ( 2001 ).
[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 -1-4 ( 2001 ).
[Crossref]

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

E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
[Crossref]

J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
[Crossref]

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

S. Feng and H. G. Winful , “ Physical origin of the Gouy phase shift ,” Opt. Lett.   26 , 485 – 487 ( 2001 ).
[Crossref]

L.-M. Duan , J. I. Cirac , and P. Zoller , “ Geometric manipulation of trapped ions for quantum computation ,” Science   292 , 1695 – 1697 ( 2001 ).
[Crossref] [PubMed]

2000 (2)

J. A. Jones , V. Vedral , A. Ekert , and G. Castagnoli , “ Geometric quantum computation using nuclear magnetic resonance ,” Nature   403 , 869 – 871 ( 2000 ).
[Crossref] [PubMed]

R. W. McGown , R. A. Cheville , and D. Grischkowsky , “ Direct observation of the Gouy phase shift in THz impulse ranging ,” Appl. Phys. Lett.   76 , 670 – 672 ( 2000 ).
[Crossref]

1999 (2)

A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
[Crossref]

A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
[Crossref] [PubMed]

1997 (2)

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

N. B. Simpson , K. Dholakia , L. Allen , and M. J. Padgett , “ Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner ,” Opt. Lett.   22 , 52 – 54 ( 1997 ).
[Crossref] [PubMed]

1996 (2)

K. T. Gahagan and G. A. Swartzlander , “ Optical vortex trapping of particles ,” Opt. Lett.   21 , 827 – 829 ( 1996 ).
[Crossref] [PubMed]

K. Dholakia , N. B. Simpson , M. J. Padgett , and L. Allen , “ Second-harmonic generation and the orbital angular momentum of light ,” Phys. Rev. A   54 , R3742 – 3745 ( 1996 ).
[Crossref] [PubMed]

1995 (2)

D. Subbarao , “ Topological phase in Gaussian beam optics ,” Opt. Lett.   20 , 2162 – 2164 ( 1995 ).
[Crossref] [PubMed]

M. J. Padgett and L. Allen , “ The Poynting vector in Laguerre-Gaussian laser modes ,” Opt. Commun.   121 , 36 – 40 ( 1995 ).
[Crossref]

1994 (1)

1993 (1)

R. Simon and N. Mukunda , “ Bargmann invariant and the geometry of the Gouy effect ,” Phys. Rev. Lett.   70 , 880 – 883 ( 1993 ).
[Crossref] [PubMed]

1992 (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]

A. Ashkin , “ Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime ,” Biophys. J.   61 , 569 – 582 ( 1992 ).
[Crossref] [PubMed]

1984 (1)

M. V. Berry , “ Quantal phase factors accompanying adiabatic changes ,” Proc. R. Soc. London A   392 , 45 – 57 ( 1984 ).
[Crossref]

1959 (1)

C. R. Carpenter , “ Gouy phase advance with microwaves ,” Am. J. Phys.   27 , 98 – 100 ( 1959 ).

1890 (1)

L. G. Gouy , “ Sur une propriété nouvelle des ondes lumineuses ,” Compt. Rendue Acad. Sci. (Paris)   110 , 1251 – 1253 ( 1890 ).

Abraham, E. R. I.

J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
[Crossref]

Allen, L.

N. B. Simpson , K. Dholakia , L. Allen , and M. J. Padgett , “ Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner ,” Opt. Lett.   22 , 52 – 54 ( 1997 ).
[Crossref] [PubMed]

K. Dholakia , N. B. Simpson , M. J. Padgett , and L. Allen , “ Second-harmonic generation and the orbital angular momentum of light ,” Phys. Rev. A   54 , R3742 – 3745 ( 1996 ).
[Crossref] [PubMed]

M. J. Padgett and L. Allen , “ The Poynting vector in Laguerre-Gaussian laser modes ,” Opt. Commun.   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]

Almeida, M. P.

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

Arlt, J.

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

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

E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
[Crossref]

Ashkin, A.

A. Ashkin , “ Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime ,” Biophys. J.   61 , 569 – 582 ( 1992 ).
[Crossref] [PubMed]

Baltuška, A.

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 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]

Bergé, L.

A. Vinçotte and L. Bergé , “ Femtosecond optical vortices in air ,” Phys. Rev. Lett.   95 , 193901 -1-4 ( 2005 ).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry , “ Quantal phase factors accompanying adiabatic changes ,” Proc. R. Soc. London A   392 , 45 – 57 ( 1984 ).
[Crossref]

Bryant, P. E.

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

Caetano, D. P.

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

Carpenter, C. R.

C. R. Carpenter , “ Gouy phase advance with microwaves ,” Am. J. Phys.   27 , 98 – 100 ( 1959 ).

Castagnoli, G.

J. A. Jones , V. Vedral , A. Ekert , and G. Castagnoli , “ Geometric quantum computation using nuclear magnetic resonance ,” Nature   403 , 869 – 871 ( 2000 ).
[Crossref] [PubMed]

Cheville, R. A.

R. W. McGown , R. A. Cheville , and D. Grischkowsky , “ Direct observation of the Gouy phase shift in THz impulse ranging ,” Appl. Phys. Lett.   76 , 670 – 672 ( 2000 ).
[Crossref]

Chow, J. H.

Cirac, J. I.

L.-M. Duan , J. I. Cirac , and P. Zoller , “ Geometric manipulation of trapped ions for quantum computation ,” Science   292 , 1695 – 1697 ( 2001 ).
[Crossref] [PubMed]

Coutinho dos Santos, B.

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

de Vine, G.

Dennis, M. R.

Devreese, J. T.

J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
[Crossref]

Dholaki, K.

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

Dholakia, K.

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
[Crossref]

N. B. Simpson , K. Dholakia , L. Allen , and M. J. Padgett , “ Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner ,” Opt. Lett.   22 , 52 – 54 ( 1997 ).
[Crossref] [PubMed]

K. Dholakia , N. B. Simpson , M. J. Padgett , and L. Allen , “ Second-harmonic generation and the orbital angular momentum of light ,” Phys. Rev. A   54 , R3742 – 3745 ( 1996 ).
[Crossref] [PubMed]

Duan, L.-M.

L.-M. Duan , J. I. Cirac , and P. Zoller , “ Geometric manipulation of trapped ions for quantum computation ,” Science   292 , 1695 – 1697 ( 2001 ).
[Crossref] [PubMed]

Dultz, W.

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

Ekert, A.

J. A. Jones , V. Vedral , A. Ekert , and G. Castagnoli , “ Geometric quantum computation using nuclear magnetic resonance ,” Nature   403 , 869 – 871 ( 2000 ).
[Crossref] [PubMed]

Feng, S.

S. Feng and H. G. Winful , “ Physical origin of the Gouy phase shift ,” Opt. Lett.   26 , 485 – 487 ( 2001 ).
[Crossref]

A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
[Crossref]

Flossmann, F.

F. Flossmann , U. T. Schwarz , and M. Maier , “ Optical vortices in a Laguerre-Gaussian LG01beam ,” J. Mod. Opt.   52 , 1009 – 1017 ( 2005 ).
[Crossref]

Gahagan, K. T.

J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
[Crossref]

E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
[Crossref]

K. T. Gahagan and G. A. Swartzlander , “ Optical vortex trapping of particles ,” Opt. Lett.   21 , 827 – 829 ( 1996 ).
[Crossref] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

Goulielmarkis, E.

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

Gouy, L. G.

L. G. Gouy , “ Sur une propriété nouvelle des ondes lumineuses ,” Compt. Rendue Acad. Sci. (Paris)   110 , 1251 – 1253 ( 1890 ).

Gray, M. B.

Grischkowsky, D.

R. W. McGown , R. A. Cheville , and D. Grischkowsky , “ Direct observation of the Gouy phase shift in THz impulse ranging ,” Appl. Phys. Lett.   76 , 670 – 672 ( 2000 ).
[Crossref]

Hirano, T.

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

Huguenin, J. A. O.

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

Jones, J. A.

J. A. Jones , V. Vedral , A. Ekert , and G. Castagnoli , “ Geometric quantum computation using nuclear magnetic resonance ,” Nature   403 , 869 – 871 ( 2000 ).
[Crossref] [PubMed]

Karusz, F.

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

Khoury, A. Z.

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

Kivshar, Y. S.

D. Neshev , A. Nepomnyashchy , and Y. S. Kivshar , “ Nonlinear Aharonov-Bohm scattering by optical vortices ,” Phys. Rev. Lett.   87 , 043901 -1-4 ( 2001 ).
[Crossref] [PubMed]

Kuga, T.

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

Lezius, M.

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

Lindner, F.

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

Luther-Davies, B.

MacDonald, M. P.

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

Maier, M.

F. Flossmann , U. T. Schwarz , and M. Maier , “ Optical vortices in a Laguerre-Gaussian LG01beam ,” J. Mod. Opt.   52 , 1009 – 1017 ( 2005 ).
[Crossref]

Mair, A.

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

McClelland, D. E.

McGloin, D. M.

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

McGown, R. W.

R. W. McGown , R. A. Cheville , and D. Grischkowsky , “ Direct observation of the Gouy phase shift in THz impulse ranging ,” Appl. Phys. Lett.   76 , 670 – 672 ( 2000 ).
[Crossref]

Mehta, A. D.

A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
[Crossref] [PubMed]

Molina-Terriza, G.

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 -1-4 ( 2001 ).
[Crossref]

Mukunda, N.

R. Simon and N. Mukunda , “ Bargmann invariant and the geometry of the Gouy effect ,” Phys. Rev. Lett.   70 , 880 – 883 ( 1993 ).
[Crossref] [PubMed]

Nepomnyashchy, A.

D. Neshev , A. Nepomnyashchy , and Y. S. Kivshar , “ Nonlinear Aharonov-Bohm scattering by optical vortices ,” Phys. Rev. Lett.   87 , 043901 -1-4 ( 2001 ).
[Crossref] [PubMed]

Neshev, D.

D. Neshev , A. Nepomnyashchy , and Y. S. Kivshar , “ Nonlinear Aharonov-Bohm scattering by optical vortices ,” Phys. Rev. Lett.   87 , 043901 -1-4 ( 2001 ).
[Crossref] [PubMed]

O’Holleran, K.

Padgett, M. J.

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 , 3039 – 3044 ( 2006 ).
[Crossref]

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

N. B. Simpson , K. Dholakia , L. Allen , and M. J. Padgett , “ Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner ,” Opt. Lett.   22 , 52 – 54 ( 1997 ).
[Crossref] [PubMed]

K. Dholakia , N. B. Simpson , M. J. Padgett , and L. Allen , “ Second-harmonic generation and the orbital angular momentum of light ,” Phys. Rev. A   54 , R3742 – 3745 ( 1996 ).
[Crossref] [PubMed]

M. J. Padgett and L. Allen , “ The Poynting vector in Laguerre-Gaussian laser modes ,” Opt. Commun.   121 , 36 – 40 ( 1995 ).
[Crossref]

Paterson, L.

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

Paulus, G. G.

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

Powels, R.

Rief, M.

A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
[Crossref] [PubMed]

Rudd, J. V.

A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
[Crossref]

Ruffin, A. B.

A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
[Crossref]

Sasada, H.

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

Schmitzer, H.

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

Schwarz, U. T.

F. Flossmann , U. T. Schwarz , and M. Maier , “ Optical vortices in a Laguerre-Gaussian LG01beam ,” J. Mod. Opt.   52 , 1009 – 1017 ( 2005 ).
[Crossref]

Shimizu, Y.

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

Shiokawa, N.

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

Sibbet, W.

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

Simmons, R. M.

A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
[Crossref] [PubMed]

Simon, R.

R. Simon and N. Mukunda , “ Bargmann invariant and the geometry of the Gouy effect ,” Phys. Rev. Lett.   70 , 880 – 883 ( 1993 ).
[Crossref] [PubMed]

Simpson, N. B.

N. B. Simpson , K. Dholakia , L. Allen , and M. J. Padgett , “ Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner ,” Opt. Lett.   22 , 52 – 54 ( 1997 ).
[Crossref] [PubMed]

K. Dholakia , N. B. Simpson , M. J. Padgett , and L. Allen , “ Second-harmonic generation and the orbital angular momentum of light ,” Phys. Rev. A   54 , R3742 – 3745 ( 1996 ).
[Crossref] [PubMed]

Smith, D. A.

A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
[Crossref] [PubMed]

Souto Ribeiro, P. H.

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

Spreeuw, R. J. C.

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

Spudich, J. A.

A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
[Crossref] [PubMed]

Subbarao, D.

Swartzlander, G. A.

E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
[Crossref]

J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
[Crossref]

K. T. Gahagan and G. A. Swartzlander , “ Optical vortex trapping of particles ,” Opt. Lett.   21 , 827 – 829 ( 1996 ).
[Crossref] [PubMed]

Tempere, J.

J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
[Crossref]

Tikhonenko, V.

Torii, Y.

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

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 -1-4 ( 2001 ).
[Crossref]

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 -1-4 ( 2001 ).
[Crossref]

Vaziri, A.

A. Vaziri , G. Weihs , and A. Zeilinger , “ Experimental two-photon, three-dimensional entanglement for quantum communication ,” Phys. Rev. Lett.   89 , 240401 -1-4 ( 2002 ).
[Crossref] [PubMed]

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

Vedral, V.

J. A. Jones , V. Vedral , A. Ekert , and G. Castagnoli , “ Geometric quantum computation using nuclear magnetic resonance ,” Nature   403 , 869 – 871 ( 2000 ).
[Crossref] [PubMed]

Vinçotte, A.

A. Vinçotte and L. Bergé , “ Femtosecond optical vortices in air ,” Phys. Rev. Lett.   95 , 193901 -1-4 ( 2005 ).
[Crossref] [PubMed]

Walther, H.

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

Weihs, G.

A. Vaziri , G. Weihs , and A. Zeilinger , “ Experimental two-photon, three-dimensional entanglement for quantum communication ,” Phys. Rev. Lett.   89 , 240401 -1-4 ( 2002 ).
[Crossref] [PubMed]

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

Whitaker, J. F.

A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
[Crossref]

Winful, H. G.

S. Feng and H. G. Winful , “ Physical origin of the Gouy phase shift ,” Opt. Lett.   26 , 485 – 487 ( 2001 ).
[Crossref]

A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
[Crossref]

Woerdman, J. P.

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

Wright, E. M.

E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
[Crossref]

Zeilinger, A.

A. Vaziri , G. Weihs , and A. Zeilinger , “ Experimental two-photon, three-dimensional entanglement for quantum communication ,” Phys. Rev. Lett.   89 , 240401 -1-4 ( 2002 ).
[Crossref] [PubMed]

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

Zoller, P.

L.-M. Duan , J. I. Cirac , and P. Zoller , “ Geometric manipulation of trapped ions for quantum computation ,” Science   292 , 1695 – 1697 ( 2001 ).
[Crossref] [PubMed]

Am. J. Phys. (1)

C. R. Carpenter , “ Gouy phase advance with microwaves ,” Am. J. Phys.   27 , 98 – 100 ( 1959 ).

Appl. Phys. Lett. (1)

R. W. McGown , R. A. Cheville , and D. Grischkowsky , “ Direct observation of the Gouy phase shift in THz impulse ranging ,” Appl. Phys. Lett.   76 , 670 – 672 ( 2000 ).
[Crossref]

Biophys. J. (1)

A. Ashkin , “ Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime ,” Biophys. J.   61 , 569 – 582 ( 1992 ).
[Crossref] [PubMed]

Compt. Rendue Acad. Sci. (Paris) (1)

L. G. Gouy , “ Sur une propriété nouvelle des ondes lumineuses ,” Compt. Rendue Acad. Sci. (Paris)   110 , 1251 – 1253 ( 1890 ).

J. Mod. Opt. (2)

F. Flossmann , U. T. Schwarz , and M. Maier , “ Optical vortices in a Laguerre-Gaussian LG01beam ,” J. Mod. Opt.   52 , 1009 – 1017 ( 2005 ).
[Crossref]

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

Nature (2)

J. A. Jones , V. Vedral , A. Ekert , and G. Castagnoli , “ Geometric quantum computation using nuclear magnetic resonance ,” Nature   403 , 869 – 871 ( 2000 ).
[Crossref] [PubMed]

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

Opt. Commun. (1)

M. J. Padgett and L. Allen , “ The Poynting vector in Laguerre-Gaussian laser modes ,” Opt. Commun.   121 , 36 – 40 ( 1995 ).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (5)

E. M. Wright , J. Arlt , K. Dholakia , K. T. Gahagan , and G. A. Swartzlander , “ Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams ,” Phys. Rev. A   63 , 013608 -1-7 ( 2001 ).
[Crossref]

J. Tempere , J. T. Devreese , E. R. I. Abraham , K. T. Gahagan , and G. A. Swartzlander , “ Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap ,” Phys. Rev. A   64 , 023603 -1-8 ( 2001 ).
[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]

K. Dholakia , N. B. Simpson , M. J. Padgett , and L. Allen , “ Second-harmonic generation and the orbital angular momentum of light ,” Phys. Rev. A   54 , R3742 – 3745 ( 1996 ).
[Crossref] [PubMed]

D. P. Caetano , M. P. Almeida , P. H. Souto Ribeiro , J. A. O. Huguenin , B. Coutinho dos Santos , and A. Z. Khoury , “ Conservation of orbital angular momentum in stimulated down-conversion ,” Phys. Rev. A   66 , R041801 -1-4 ( 2002 ).
[Crossref]

Phys. Rev. Lett. (9)

A. Vinçotte and L. Bergé , “ Femtosecond optical vortices in air ,” Phys. Rev. Lett.   95 , 193901 -1-4 ( 2005 ).
[Crossref] [PubMed]

D. Neshev , A. Nepomnyashchy , and Y. S. Kivshar , “ Nonlinear Aharonov-Bohm scattering by optical vortices ,” Phys. Rev. Lett.   87 , 043901 -1-4 ( 2001 ).
[Crossref] [PubMed]

V. Garcés-Chávez , D. M. 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 -1-4 ( 2003 ).
[Crossref] [PubMed]

A. Vaziri , G. Weihs , and A. Zeilinger , “ Experimental two-photon, three-dimensional entanglement for quantum communication ,” Phys. Rev. Lett.   89 , 240401 -1-4 ( 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 -1-4 ( 2001 ).
[Crossref]

T. Kuga , Y. Torii , N. Shiokawa , T. Hirano , Y. Shimizu , and H. Sasada , “ Novel optical trap of atoms with a doughnut beam ,” Phys. Rev. Lett.   78 , 4713 – 4716 ( 1997 ).
[Crossref]

F. Lindner , G. G. Paulus , H. Walther , A. Baltuška , E. Goulielmarkis , M. Lezius , and F. Karusz , “ Gouy phase shift for few-cycle-laser pulses ,” Phys. Rev. Lett.   92 , 113001 -1-4 ( 2004 ).
[Crossref] [PubMed]

R. Simon and N. Mukunda , “ Bargmann invariant and the geometry of the Gouy effect ,” Phys. Rev. Lett.   70 , 880 – 883 ( 1993 ).
[Crossref] [PubMed]

A. B. Ruffin , J. V. Rudd , J. F. Whitaker , S. Feng , and H. G. Winful , “ Direct observation of the Gouy phase shift with single-cycle terahertz pulses ,” Phys. Rev. Lett.   83 , 3410 – 3413 ( 1999 ).
[Crossref]

Proc. R. Soc. London A (1)

M. V. Berry , “ Quantal phase factors accompanying adiabatic changes ,” Proc. R. Soc. London A   392 , 45 – 57 ( 1984 ).
[Crossref]

Science (3)

A. D. Mehta , M. Rief , J. A. Spudich , D. A. Smith , and R. M. Simmons , “ Single-molecule biomechanics with optical methods ,” Science   283 , 1689 – 1695 ( 1999 ).
[Crossref] [PubMed]

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

L.-M. Duan , J. I. Cirac , and P. Zoller , “ Geometric manipulation of trapped ions for quantum computation ,” Science   292 , 1695 – 1697 ( 2001 ).
[Crossref] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Experimental setup for spatial evolution measurement of a modified LG beam with an asymmetric defect, (b) a normal spiral hologram pattern, (c) a pure LG beam, (d) a spiral hologram pattern with an asymmetric defect (defect angle π/3), and (e) a modified LG beam with an asymmetric defect.

Fig. 2.
Fig. 2.

Experimantally-observed spatial evolution of modified LG beams with an aymmetric defect for (a) (m, p) = (+10,0), (b) (m, p) = (-10,0) and (c) (m, p) = (0,0). The intensity profiles at z = -15, 0, and +15 cm are magnified 1.7, 2, and 1.7 times, respectively.

Fig. 3.
Fig. 3.

(a) Schematic drawing for an intensity profile of a modified LG beam with an aymmetric defect with the coordinates x, y, z, and average defect angle φ D when observed from +z-direction on CCD. (b) Dependence of observed defect angle φ D on the propagation distance z for modified LG beams with (m, p) = (+10,0) and (-10,0).

Fig. 4.
Fig. 4.

(a) 3D trajectories of the asymmetric defect for modified LG beams with (m, p) = (+10,0) and (-10,0) projected on x-y plane as a function of propagation distance z. (b) Relationship between coordinates x,y and x′, y′. (x′ ,y′, z) coordinates are obtained from (x,y, z) coordinates by a roation of Φ 0 around the z axis. In our experimental configuration, we put φ D = 0 at z = -65 cm with the initial phase Φ 0.

Fig. 5.
Fig. 5.

Distributions of |Cmp |2 as a function of indices m and p for modified LG beams with (a) (m, p) = (+10,0), (b) (m, p) = (-10,0) (c) (m, p) = (0,0) and (d) (m, p) = (+10,5).

Fig. 6.
Fig. 6.

Calculated spatial evolution of modified LG beams with an aymmetric defect for (a) (m, p) = (+10,0), (b) (m, p) = (-10,0), (c) (m, p) = (0,0) and (d) (m, p) = (+10,+5) at propagation distances of z = -∞,-z R,0,-z R, and +∞. Dimensions of beams are scaled by w(z).

Equations (36)

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

E m p ( ρ , φ , z , t ) = u m p ( ρ , φ , z ) exp [ i ( k z ω t ) ] ,
u m p ( ρ , φ , z ) = 2 p ! π ( p + m ) ! [ 2 ρ w ( z ) ] m L p m ( 2 ρ 2 w ( z ) 2 ) w 0 w ( z )
× exp [ ρ 2 w ( z ) 2 i k ρ 2 2 R ( z ) + i m φ i Φ G ( z ) ] ,
L p m ( x ) = r = 0 p ( 1 ) r p + m p r x r r ! .
R ( z ) = ( z R 2 + z 2 ) z , w ( z ) = w 0 1 z 2 z R 2 .
z R = k w 0 2 2 .
Φ G ( z ) = ( 2 p + m + 1 ) Φ ( z ) ( 2 p + m + 1 ) arctan ( z z R ) ,
sgn ( m ) = { + 1 , m > 0 , 1 , m < 0 .
Ψ m p C ( ρ , φ , z ) = u m p ( ρ , φ , z ) { 1 exp [ φ 2 2 ( δ φ D ) 2 ] } ,
Ψ m p C ( ρ , φ , z ) = p = 0 m = C m p u m p ( ρ , φ , z ) .
C m p = 1 w 0 2 0 d ρ ρ π π d φ u m p * ( ρ , φ , z ) Ψ m p C ( ρ , φ , z ) ,
Ψ m p C ( ρ , φ , z ) 2
= p = 0 m = p = 0 m = C m p * C m p u m p * ( ρ , φ , z ) u m p ( ρ , φ , z )
= 2 π w 0 2 w ( z ) 2 exp [ 2 ρ 2 w ( z ) 2 ] p = 0 m = p = 0 m = C m p * C m p p ! p ( p + m ) ! ( p + m ) !
× [ 2 ρ w ( z ) ] m + m L p m ( 2 ρ 2 w ( z ) 2 ) L p m ( 2 ρ 2 w ( z ) 2 )
× exp { i ( m m ) φ i [ 2 ( p p ) + m m ] Φ ( z ) }
4 π w 0 2 w ( z ) 2 exp [ 2 ρ 2 w ( z ) 2 ] ( A + B + C + D + E ) ,
A = p = 0 m = C m p 2 p ! ( p + m ) ! [ 2 ρ w ( z ) ] 2 m [ L p m ( 2 ρ 2 w ( z ) 2 ) ] 2 ,
B = p = 0 m = m < m C m p * C m p p ! ( p + m ) ! ( p + m ) ! [ 2 ρ w ( z ) ] m + m
× L p m ( 2 ρ 2 w ( z ) 2 ) L p m ( 2 ρ 2 w ( z ) 2 ) cos [ ( m m ) φ ( m m ) Φ ( z ) ] ,
C = p = 0 m = p < p C m p * C m p p ! p ! ( p + m ) ! ( p + m ) !
× [ 2 ρ w ( z ) ] 2 m L p m ( 2 ρ 2 w ( z ) 2 ) L p m ( 2 ρ 2 w ( z ) 2 ) cos { 2 ( p p ) Φ ( z ) } ,
D = p = 0 m = p < p m < m C m p * C m p p ! p ! ( p + m ) ! ( p + m ) !
× [ 2 ρ w ( z ) ] m + m L p m ( 2 ρ 2 w ( z ) 2 ) L p m ( 2 ρ 2 w ( z ) 2 )
× cos { ( m m ) φ [ 2 ( p p ) + m m ] Φ ( z ) } ,
E = p = 0 m = p > p m < m C m p * C m p p ! p ! ( p + m ) ! ( p + m ) !
× [ 2 ρ w ( z ) ] m + m L p m ( 2 ρ 2 w ( z ) 2 ) L p m ( 2 ρ 2 w ( z ) 2 )
× cos { ( m m ) φ [ 2 ( p p ) + m m ] Φ ( z ) } .
m = m + δ m ( δ m m ) ,
m = m + δ m ( δ m m ) .
cos Δ = cos { ( δ m δ m ) [ φ sgn ( m ) Φ ( z ) ] } .
Δ = ( δ m δ m ) φ ( δ m δ m ) Φ ( z )
= { ( δ m δ m ) [ φ Φ ( z ) ] , δ m > 0 , δ m > 0 , ( δ m δ m ) φ ( δ m + δ m ) Φ ( z ) , δ m > 0 , δ m < 0 , ( δ m δ m ) [ φ Φ ( z ) ] , δ m < 0 , δ m < 0 , ( δ m δ m ) φ + ( δ m + δ m ) Φ ( z ) , δ m < 0 , δ m > 0 .
x ( z ) = w ( z ) m 2 cos ( Φ G + Φ 0 ) , y ( z ) = w ( z ) m 2 sin ( Φ G + Φ 0 ) .
[ x y ] = [ cos Φ 0 sin Φ 0 sin Φ 0 cos Φ 0 ] [ x y ] ,
x ( z ) = w 0 m 2 , y ( z ) = w 0 m 2 z z R .

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