Abstract

We produced an axial and canonical optical vortex by using a computer-generated hologram and then converted it to a noncanonical vortex by passing it through a cylindrical lens. We conducted an experimental study of the shape and trajectory of the noncanonical vortex as it propagates in free space and obtained an analytical expression explaining our experimental results. The computed trajectory and shape of the noncanonical vortex agree quite well with our experimental results.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, Vol. XXXIX, E. Wolf, ed. (North-Holland, Amsterdam, 1999) pp. 291–372.
  2. M. Padgett, L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41, 275–285 (2000).
    [CrossRef]
  3. Y. S. Kivshar, A. Ostrovskaya, “Optical vortices: folding and twisting waves of light,” Opt. Photon. News, December2001 pp. 24–29.
  4. M. S. Soskin, M. V. Vasnetsov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (North-Holland, Amsterdam, 2001), pp. 219–276.
  5. Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
    [CrossRef]
  6. 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]
  7. H. He, M. Friese, N. R. Heckenberg, 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]
  8. K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  9. N. B. Simpson, K. Dholakia, L. Allen, M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22, 52–54 (1997).
    [CrossRef] [PubMed]
  10. P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
    [CrossRef]
  11. A. Mair, A. Vaziri, G. Weighs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [CrossRef] [PubMed]
  12. D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
    [CrossRef]
  13. G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
    [CrossRef]
  14. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970).
    [CrossRef]
  15. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
    [CrossRef]
  16. J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
    [CrossRef]
  17. H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
    [CrossRef]
  18. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  19. M. Padgett, J. Arlt, N. Simpson, “An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes,” Am. J. Phys. 64, 77–82 (1996).
    [CrossRef]
  20. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  21. G. Nemes, A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am. A 11, 2257–2264 (1994).
    [CrossRef]
  22. N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).
  23. J. A. Arnaud, “Hamiltonian theory of beam mode propagation,” in Progress in Optics, Vol. XI, E. Wolf, ed. (North-Holland, Amsterdam, 1973), pp. 247–304.
  24. G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902-1–4 (2001).
    [CrossRef]
  25. A. Ya. Beksaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Lett. 75, 127–130 (2002).
    [CrossRef]
  26. I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1997).
    [CrossRef]

2002 (1)

A. Ya. Beksaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Lett. 75, 127–130 (2002).
[CrossRef]

2001 (5)

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902-1–4 (2001).
[CrossRef]

Y. S. Kivshar, A. Ostrovskaya, “Optical vortices: folding and twisting waves of light,” Opt. Photon. News, December2001 pp. 24–29.

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

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

G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
[CrossRef]

2000 (1)

M. Padgett, L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41, 275–285 (2000).
[CrossRef]

1998 (2)

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

1997 (4)

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

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

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1997).
[CrossRef]

1996 (2)

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

M. Padgett, J. Arlt, N. Simpson, “An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes,” Am. J. Phys. 64, 77–82 (1996).
[CrossRef]

1995 (2)

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

H. He, M. Friese, N. R. Heckenberg, 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]

1994 (2)

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

G. Nemes, A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am. A 11, 2257–2264 (1994).
[CrossRef]

1993 (1)

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

1974 (1)

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

1970 (1)

Allen, L.

M. Padgett, L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41, 275–285 (2000).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

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

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

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, Vol. XXXIX, E. Wolf, ed. (North-Holland, Amsterdam, 1999) pp. 291–372.

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, “An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes,” Am. J. Phys. 64, 77–82 (1996).
[CrossRef]

Arnaud, J. A.

J. A. Arnaud, “Hamiltonian theory of beam mode propagation,” in Progress in Optics, Vol. XI, E. Wolf, ed. (North-Holland, Amsterdam, 1973), pp. 247–304.

Babiker, M.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, Vol. XXXIX, E. Wolf, ed. (North-Holland, Amsterdam, 1999) pp. 291–372.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” 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 orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Beksaev, A. Ya.

A. Ya. Beksaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Lett. 75, 127–130 (2002).
[CrossRef]

Berry, M. V.

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

Christou, J.

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
[CrossRef]

Coerwinkel, R. P. C.

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

Collins, S. A.

Denisenko, V. G.

A. Ya. Beksaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Lett. 75, 127–130 (2002).
[CrossRef]

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

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

Freund, I.

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1997).
[CrossRef]

Friese, M.

H. He, M. Friese, N. R. Heckenberg, 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]

Gahagan, K. T.

Galajda, P.

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

He, H.

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

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

Heckenberg, N. R.

H. He, M. Friese, N. R. Heckenberg, 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]

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

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]

Hodgson, N.

N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).

Kivshar, Y. S.

Y. S. Kivshar, A. Ostrovskaya, “Optical vortices: folding and twisting waves of light,” Opt. Photon. News, December2001 pp. 24–29.

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” 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.

Luther-Davies, B.

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
[CrossRef]

Mair, A.

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

Molina-Terriza, G.

G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902-1–4 (2001).
[CrossRef]

Nemes, G.

Nye, J. F.

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

Ormos, P.

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

Ostrovskaya, A.

Y. S. Kivshar, A. Ostrovskaya, “Optical vortices: folding and twisting waves of light,” Opt. Photon. News, December2001 pp. 24–29.

Padgett, M.

M. Padgett, L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41, 275–285 (2000).
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, “An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes,” Am. J. Phys. 64, 77–82 (1996).
[CrossRef]

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

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

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, Vol. XXXIX, E. Wolf, ed. (North-Holland, Amsterdam, 1999) pp. 291–372.

Pismen, L. M.

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
[CrossRef]

Recolons, J.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902-1–4 (2001).
[CrossRef]

Rozas, D.

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

H. He, M. Friese, N. R. Heckenberg, 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]

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]

Siegman, A. E.

Simpson, N.

M. Padgett, J. Arlt, N. Simpson, “An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes,” Am. J. Phys. 64, 77–82 (1996).
[CrossRef]

Simpson, N. B.

Soskin, M. S.

A. Ya. Beksaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Lett. 75, 127–130 (2002).
[CrossRef]

M. S. Soskin, M. V. Vasnetsov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (North-Holland, Amsterdam, 2001), pp. 219–276.

Swartzlander, G. A.

Tikhonenko, V.

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
[CrossRef]

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]

Torner, L.

G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902-1–4 (2001).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902-1–4 (2001).
[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 orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Vasnetsov, M. V.

A. Ya. Beksaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Lett. 75, 127–130 (2002).
[CrossRef]

M. S. Soskin, M. V. Vasnetsov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (North-Holland, Amsterdam, 2001), pp. 219–276.

Vaziri, A.

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

Weber, H.

N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).

Weighs, G.

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

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” 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 orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Wright, E. M.

Zeilinger, A.

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

Am. J. Phys. (1)

M. Padgett, J. Arlt, N. Simpson, “An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes,” Am. J. Phys. 64, 77–82 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

Contemp. Phys. (1)

M. Padgett, L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41, 275–285 (2000).
[CrossRef]

J. Mod. Opt. (2)

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

JETP Lett. (1)

A. Ya. Beksaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Lett. 75, 127–130 (2002).
[CrossRef]

Nature (1)

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

Opt. Commun. (4)

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198–206 (1998).
[CrossRef]

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

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

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1997).
[CrossRef]

Opt. Lett. (3)

Opt. Photon. News (1)

Y. S. Kivshar, A. Ostrovskaya, “Optical vortices: folding and twisting waves of light,” Opt. Photon. News, December2001 pp. 24–29.

Phys. Rev. Lett. (3)

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]

H. He, M. Friese, N. R. Heckenberg, 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]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 023902-1–4 (2001).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

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

Other (4)

M. S. Soskin, M. V. Vasnetsov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (North-Holland, Amsterdam, 2001), pp. 219–276.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, Vol. XXXIX, E. Wolf, ed. (North-Holland, Amsterdam, 1999) pp. 291–372.

N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).

J. A. Arnaud, “Hamiltonian theory of beam mode propagation,” in Progress in Optics, Vol. XI, E. Wolf, ed. (North-Holland, Amsterdam, 1973), pp. 247–304.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Optical scheme of the experiment. CGH, computer-generated hologram; A, aperture; CL, cylindrical lens.

Fig. 2
Fig. 2

Trajectory of a noncanonical vortex. Theoretical (top) and experimental (bottom).

Fig. 3
Fig. 3

Shape of the vortex after passing through the CL (focal length 70 mm) at distances 2.5 cm, 12.5 cm, and 22.5 cm (left to right). Theoretical (top), and experimental (bottom) without any image processing.

Equations (12)

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

r2γ2=ABCDr1γ1,
AxxAxyAyxAyy.
ADT-BCT=I,
ABT=BAT,
CDT=DCT.
E2(x2, y2)=-i exp(ikL)λdet B×E1(x1, y1)expik2(r1TAB-1r1+r2TDB-1r2-2r1B-1r2)dx1dy1.
E1(x1, y1)=(x1+iy1)expik2r1TQ1-1r1,
Q1-1=1/qxx,11/xy,11/qyx,11/qyy,1.
E2(x2, y2)=(F1+iF2)expik2r2TQ2-1r2,
F=(AB-1+Q1-1)-1B-1r2.
Q2-1=(C+DQ1-1)(A+BQ1-1)-1
M(θ)=10L0010L00100001×10dn1cos2 θd2n1sin 2θ01-d2n1sin 2θdn1cos2 θ-Dy sin2 θDy2sin 2θ10Dy2sin 2θ-Dy cos2 θ01=1-LDy sin2 θLDy2sin 2θL+dn1cos2 θd2n1sin 2θDy2L sin 2θ1-LDy cos2 θ-d2n1sin 2θL+dn1cos2 θ-Dy sin2 θDy2sin 2θ10Dy2sin 2θ-Dy cos2 θ01.

Metrics