Abstract

We demonstrate a simple and versatile method for generating various configurations of optical vortices from a Gaussian light beam by using glass plates and an astigmatic mode converter (AMC). The glass plates are inserted into the Gaussian beam to imprint nodal lines along the edges, and the AMC then transforms the beam with the nodes into a vortex beam. The procedures are discussed in terms of a transverse-mode expansion of the paraxial light beam, in which each Hermite–Gaussian mode is converted into the corresponding Laguerre–Gaussian mode by the AMC. We generated several vortex configurations, and the results show good agreement with the theoretical predictions.

© 2002 Optical Society of America

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  5. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
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    [CrossRef] [PubMed]
  10. A. W. Snyder, L. Poladian, D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
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    [CrossRef]
  26. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of optical angular momentum,” Opt. Commun. 96, 123–132 (1993).
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1999 (1)

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

1997 (5)

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

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
[CrossRef]

G.-H. Kim, J.-H. Joen, K.-H. Ko, H.-J. Moon, J.-H. Lee, J.-S. Chang, “Optical vortices produced with a nonspiral phase plate,” Appl. Opt. 36, 8614–8621 (1997).
[CrossRef]

1995 (2)

F. S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215–1221 (1995).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

1994 (2)

C. D’Heren, E. W. Dearden, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Measurements of the optical force and trapping range of a single-beam optical trap for micron-sized latex spheres,” J. Mod. Opt. 41, 595–601 (1994).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (3)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of optical angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

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

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

1992 (6)

V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

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

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Sqreeuw, 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]

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

A. W. Snyder, L. Poladian, D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992).
[CrossRef] [PubMed]

1991 (1)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

1983 (2)

1974 (1)

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of optical angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Sqreeuw, 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]

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Arfken, G.

G. Arfken, H.-J. Weber, Mathematical Methods for Physicists, 5th ed. (Academic, New York, 2001).

Baranova, N. B.

Basistiy, I. V.

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Battipede, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

Bazhenov, V. Y.

V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of optical angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Sqreeuw, 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]

Berry, M. V.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Brambilla, M.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

Chang, J.-S.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Cornell, E. A.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

D’Heren, C.

C. D’Heren, E. W. Dearden, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Measurements of the optical force and trapping range of a single-beam optical trap for micron-sized latex spheres,” J. Mod. Opt. 41, 595–601 (1994).
[CrossRef]

Dearden, E. W.

C. D’Heren, E. W. Dearden, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Measurements of the optical force and trapping range of a single-beam optical trap for micron-sized latex spheres,” J. Mod. Opt. 41, 595–601 (1994).
[CrossRef]

Donnelly, R. J.

R. J. Donnelly, Quantized Vortices in Helium II (Cambridge U. Press, Cambridge, UK, 1991).

Firth, W. J.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Haljan, P. C.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Hall, D. S.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

C. D’Heren, E. W. Dearden, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Measurements of the optical force and trapping range of a single-beam optical trap for micron-sized latex spheres,” J. Mod. Opt. 41, 595–601 (1994).
[CrossRef]

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

Hirano, T.

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

Indebetouw, G.

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

Joen, J.-H.

Kim, G.-H.

Ko, K.-H.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Kuga, T.

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

Law, C. T.

D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
[CrossRef]

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

Lee, J.-H.

Lugiato, L. A.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Mamaev, A. V.

Matthews, M. R.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

McDonald, G. S.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

McDuff, R.

Mitchell, D. J.

Moon, H.-J.

Nye, J. F.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Penna, V.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

Pilipetsky, N. F.

Poladian, L.

Prati, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

Roux, F. S.

Rozas, D.

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
[CrossRef]

Rubinsztein-Dunlop, H.

C. D’Heren, E. W. Dearden, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Measurements of the optical force and trapping range of a single-beam optical trap for micron-sized latex spheres,” J. Mod. Opt. 41, 595–601 (1994).
[CrossRef]

Sacks, Z. S.

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

Sasada, H.

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

Shimizu, Y.

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

Shkunov, V. V.

Smith, C. P.

Snyder, A. W.

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Sqreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Sqreeuw, 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.

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
[CrossRef]

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

Syed, K. S.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

Tamm, C.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

Tinkham, M.

M. Tinkham, Introduction to Superconductivity (McGraw-Hill, New York, 1996).

Torii, Y.

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

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of optical angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Vaughan, J. M.

Weber, H.-J.

G. Arfken, H.-J. Weber, Mathematical Methods for Physicists, 5th ed. (Academic, New York, 2001).

Weiss, C. O.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

White, A. G.

Wieman, C. E.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Willetts, D. V.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of optical angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Sqreeuw, 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]

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 6.

Zel’dovich, B. Y.

Appl. Opt. (1)

J. Mod. Opt. (3)

V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

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

C. D’Heren, E. W. Dearden, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Measurements of the optical force and trapping range of a single-beam optical trap for micron-sized latex spheres,” J. Mod. Opt. 41, 595–601 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (2)

Opt. Commun. (5)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of optical angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[CrossRef] [PubMed]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Sqreeuw, 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]

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[CrossRef]

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram for generating linear phase dislocations along the y direction in a light beam. Thin glass plates are inserted into a Gaussian beam to create phase shifts. Two circles indicate the phase distribution in the transversal cross section.

Fig. 2
Fig. 2

Histograms of the mode contents of the quasi-HGN,0 beams as a function of the mode index of the HG modes for N=1 to 3.

Fig. 3
Fig. 3

Experimental setup for generating optical vortices: GP, glass plates; BS, beam splitter; PBS, polarization beam splitter; QWP, quarter-wave plate; ML, mode-matching spherical lens; CL, cylindrical lens; CCD, charge-coupled-device camera.

Fig. 4
Fig. 4

Observed quasi-HG1,0 beam in the (a) near field and (b) far field, (c) interference pattern with the Gaussian beam, (d) far-field profile calculated from Eq. (9).

Fig. 5
Fig. 5

(a) Observed quasi-LG0,1 beam in the far field, (b) its interferogram, and (c) calculated beam profile. Crosses in (c) represent the calculated singular positions.

Fig. 6
Fig. 6

Observed quasi-HG beam for N=2 and 3: (a) and (d) are the intensity profiles in the near field, (b) and (e) are those in the far field, and (c) and (f) are theoretical predictions.

Fig. 7
Fig. 7

Observed quasi-LG beam for N=2 and 3: (a) and (d) are the obtained beam profiles. Arrows indicate the singular positions determined by the interferograms in (b) and (e), and (c) and (f) are the calculated beam profiles.

Fig. 8
Fig. 8

Optical vortices generated at off-axial positions: (a) a=0, φπ and (c) φ=π, a0. Arrows indicate the direction of the vortex movement. Trajectories of the vortices are plotted as a function of (b) incident angle to the glass plate and (c) position of the glass edge. Solid (dashed) curves represent the theoretical curves calculated by considering two (five) dominant LG modes.

Fig. 9
Fig. 9

Experimental generation of the vortex array: (a) schematic diagram of the amplitude mask to generate the vortex array, (b) mode-converted light beam (small arrows indicate the singular positions), (c) theoretical intensity pattern, (d) interference fringe of (b).

Equations (20)

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Ti(x)=exp[-iφi(θi)](x<ai)1(xai),
φi(θi)=kdnr-1+1-1nrθi22,
uˆn,mHG(x, y, z)=Cn,mHG(1/w)Hn(2x/w)Hm(2y/w)×exp[-(x2+y2)(1/w2+ik/2R)]×exp[-i(n+m+1)ψ],
uˆp,lLG(r, ϕ, z)=Cp,lLG(1/w)(-1)p(2r/w)lLpl(2r2/w2)×exp(-r2/w2-ikr2/2R)×exp(-ilϕ)×exp[-i(2p+l+1)ψ],
w(z)=w0(1+z2/zR2)1/2,
R(z)=(zR2+z2)/z,
ψ(z)=arctan(z/zR)
zR=kw022.
uˆt(x, y, z)=n,m=0An,muˆn,mHG(x, y, z).
An,m=uˆn,mHG*(x, y, 0)uˆt(x, y, 0)dxdy=uˆn,mHG*(x, y, 0)T(x, y)uˆ0,0(x, y, 0)dxdy.
uˆc(r, ϕ, z)=n,m=0An,muˆmin(n, m),n-mLG(r, ϕ, z),
uˆc(r, ϕ, z)=0,
n=0An,0C0,nLG(2r/w)n exp[-in(ϕ+ψ)]=0.
T(x; a, θ)=exp[-iφ(θ)](x<a)1(xa).
A0,0=1+exp(-iφ)+[exp(-iφ)-1]erf(2a)2,
A1,0=exp(-2a2)[1-exp(-iφ)]2π.
rw=12A0,0A1,0,
ϕ=argA1,0A0,0-ψ.
rw=π2cotφ2,ϕ=π2-ψ.
rw=π2erf(2a)exp(-2a2),φ=-ψ

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