Abstract

We propose using a solitary kinoform-type spiral phase plate structure to generate an array of vortices located in a single beam. Kinoform-type spiral surfaces allow each wavelength component of the phase modulation value to be wrapped back to its 2π equivalent for optical vortices of high charge. This allows the surface-relief profiles of high-charge vortices to be microfabricated with the same physical height as spiral phase plates of unity-charged optical vortices. The m-charged optical vortex obtained interacts with the inherent coherent background, which changes the propagation dynamics of the optical vortex and splits the initial m charge into |m| unity-charged optical vortices within the same beam. Compared to a hologram, a multistart spiral phase plate is more efficient in the use of available spatial frequencies and beam energy and also is computationally less demanding. Furthermore, using microfabrication techniques will allow for greater achievable tolerances in terms of smaller feature sizes.

© 2006 Optical Society of America

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  1. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
    [CrossRef]
  2. N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, and B. Ya. Zel'dovich, "Wavefront dislocations: topological limitations for adaptive systems with phase conjugation," J. Opt. Soc. Am. 73, 525-528 (1983).
    [CrossRef]
  3. A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
    [CrossRef]
  4. M. Harris, C. A. Hill, and J. M. Vaughan, "Optical helices and spiral interference fringes," Opt. Commun. 106, 161-166 (1994).
    [CrossRef]
  5. D. Y. Tang, N. R. Heckenberg, and C. O. Weiss, "Phase dependent helical pattern formation in a laser," Opt. Commun. 114, 95-100 (1995).
    [CrossRef]
  6. G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
    [CrossRef] [PubMed]
  7. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
    [CrossRef]
  8. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604-612 (1993).
    [CrossRef]
  9. L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, "Atom dynamics in multiple Laguerre-Gaussian beams," Phys. Rev. A 54, 4259-4270 (1996).
    [CrossRef] [PubMed]
  10. K. T. Gahagan and G. A. Swartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996).
    [CrossRef] [PubMed]
  11. G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).
  12. 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]
  13. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1996).
    [CrossRef]
  14. M. J. Padgett and L. Allen, "Orbital angular momentum exchange in cylindrical-lens mode converters," J. Opt. B Quantum Semiclass. Opt. 4, S17-S19 (2002).
    [CrossRef]
  15. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
    [CrossRef]
  16. J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
    [CrossRef] [PubMed]
  17. J. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef] [PubMed]
  18. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-327 (1994).
    [CrossRef]
  19. S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
    [CrossRef]
  20. G.-H. Kim, J.-H. Jeon, K.-H. Ko, H.-J. Moon, J.-H. Lee, and J. S. Chang, "Optical vortices produced with a nonspiral phase plate," Appl. Opt. 36, 8614-8621 (1997).
    [CrossRef]
  21. W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
    [CrossRef]
  22. T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
    [CrossRef]
  23. K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, "Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses," Opt. Express 12, 3548-3553 (2004).
    [CrossRef] [PubMed]
  24. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
    [CrossRef]
  25. D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3064 (1997).
    [CrossRef]
  26. I. D. Maleev and G. A. Swartzlander, Jr., "Composite optical vortices," J. Opt. Soc. Am. B 20, 1169-1176 (2003).
    [CrossRef]
  27. D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
    [CrossRef]
  28. D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics; Design Fabrication and Test (SPIE Press, 2003).

2004 (4)

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, "Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses," Opt. Express 12, 3548-3553 (2004).
[CrossRef] [PubMed]

2003 (4)

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

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

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics; Design Fabrication and Test (SPIE Press, 2003).

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

2002 (1)

M. J. Padgett and L. Allen, "Orbital angular momentum exchange in cylindrical-lens mode converters," J. Opt. B Quantum Semiclass. Opt. 4, S17-S19 (2002).
[CrossRef]

1997 (4)

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

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

D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3064 (1997).
[CrossRef]

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

1996 (3)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1996).
[CrossRef]

K. T. Gahagan and G. A. Swartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996).
[CrossRef] [PubMed]

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, "Atom dynamics in multiple Laguerre-Gaussian beams," Phys. Rev. A 54, 4259-4270 (1996).
[CrossRef] [PubMed]

1995 (3)

G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).

D. Y. Tang, N. R. Heckenberg, and C. O. Weiss, "Phase dependent helical pattern formation in a laser," Opt. Commun. 114, 95-100 (1995).
[CrossRef]

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

1994 (2)

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

M. Harris, C. A. Hill, and J. M. Vaughan, "Optical helices and spiral interference fringes," Opt. Commun. 106, 161-166 (1994).
[CrossRef]

1993 (2)

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

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604-612 (1993).
[CrossRef]

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]

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

1991 (1)

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

1983 (1)

1974 (1)

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

Allen, L.

M. J. Padgett and L. Allen, "Orbital angular momentum exchange in cylindrical-lens mode converters," J. Opt. B Quantum Semiclass. Opt. 4, S17-S19 (2002).
[CrossRef]

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, "Atom dynamics in multiple Laguerre-Gaussian beams," Phys. Rev. A 54, 4259-4270 (1996).
[CrossRef] [PubMed]

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]

Babiker, M.

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, "Atom dynamics in multiple Laguerre-Gaussian beams," Phys. Rev. A 54, 4259-4270 (1996).
[CrossRef] [PubMed]

Baranova, N. B.

Basistiy, I. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604-612 (1993).
[CrossRef]

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

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and 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, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-327 (1994).
[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]

Berry, M. V.

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

Chang, J. S.

Cheong, W. C.

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

Coerwinkel, R. P. C.

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

Curtis, J.

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

Curtis, J. E.

Dholakia, K.

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

Drugan, D. L.

G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).

Elie, E. R.

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

Freeman, M. O.

G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1996).
[CrossRef]

Fujii, M.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Gahagan, K. T.

Gorshkov, V. N.

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

Grier, D. G.

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

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

Hallak, N.

G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).

Harris, M.

M. Harris, C. A. Hill, and J. M. Vaughan, "Optical helices and spiral interference fringes," Opt. Commun. 106, 161-166 (1994).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1996).
[CrossRef]

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

Heckenberg, N. R.

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

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1996).
[CrossRef]

D. Y. Tang, N. R. Heckenberg, and C. O. Weiss, "Phase dependent helical pattern formation in a laser," Opt. Commun. 114, 95-100 (1995).
[CrossRef]

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

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

Hill, C. A.

M. Harris, C. A. Hill, and J. M. Vaughan, "Optical helices and spiral interference fringes," Opt. Commun. 106, 161-166 (1994).
[CrossRef]

Hooft, G. W't

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

Iketaki, Y.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Jeon, J.-H.

Kathman, A. D.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics; Design Fabrication and Test (SPIE Press, 2003).

Kim, G.-H.

Ko, K.-H.

Kristensen, M.

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

Lai, W. K.

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, "Atom dynamics in multiple Laguerre-Gaussian beams," Phys. Rev. A 54, 4259-4270 (1996).
[CrossRef] [PubMed]

Law, C. T.

D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3064 (1997).
[CrossRef]

G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).

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

Lee, J.-H.

Lee, W. M.

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

Lembessis, V. E.

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, "Atom dynamics in multiple Laguerre-Gaussian beams," Phys. Rev. A 54, 4259-4270 (1996).
[CrossRef] [PubMed]

Loosterboer, J. G. K.

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

Maleev, I. D.

Malos, J. T.

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

Mamaev, A. V.

McDuff, R.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

Miyaji, G.

Miyanaga, N.

Moon, H.-J.

Nakatsuka, M.

Nye, J. F.

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

Oemrawsingh, S. S. R.

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

O'Shea, D. C.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics; Design Fabrication and Test (SPIE Press, 2003).

Padgett, M. J.

M. J. Padgett and L. Allen, "Orbital angular momentum exchange in cylindrical-lens mode converters," J. Opt. B Quantum Semiclass. Opt. 4, S17-S19 (2002).
[CrossRef]

Pilipetskii, N. F.

Prather, D. W.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics; Design Fabrication and Test (SPIE Press, 2003).

Rozas, D.

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

D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3064 (1997).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1996).
[CrossRef]

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

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

Sacks, Z. S.

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

Shkunov, V. V.

Smith, C. P.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

Soskin, M. S.

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

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

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604-612 (1993).
[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]

Sueda, K.

Suleski, T. J.

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics; Design Fabrication and Test (SPIE Press, 2003).

Swartzlander, G. A.

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

D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3064 (1997).
[CrossRef]

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

K. T. Gahagan and G. A. Swartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).

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

Tamm, Chr.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

Tang, D. Y.

D. Y. Tang, N. R. Heckenberg, and C. O. Weiss, "Phase dependent helical pattern formation in a laser," Opt. Commun. 114, 95-100 (1995).
[CrossRef]

Toyama, N.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Vasnetsov, M. V.

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

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

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604-612 (1993).
[CrossRef]

Vaughan, J. M.

M. Harris, C. A. Hill, and J. M. Vaughan, "Optical helices and spiral interference fringes," Opt. Commun. 106, 161-166 (1994).
[CrossRef]

Verstegen, E. J. K.

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

Wang, H.

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

Watanabe, T.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Watanabe, Y.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Weiss, C. O.

D. Y. Tang, N. R. Heckenberg, and C. O. Weiss, "Phase dependent helical pattern formation in a laser," Opt. Commun. 114, 95-100 (1995).
[CrossRef]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

White, A. G.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

Woerdman, J. P.

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

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

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

Yuan, X.-C.

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

Zel'dovich, B. Ya.

Zhang, L. S.

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. C. Cheong, W. M. Lee, X.-C. Yuan, K. Dholakia, L. S. Zhang, and H. Wang, "Direct electron beam writing of continuous spiral phase plates in SU-8 with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004).
[CrossRef]

J. Mod. Opt. (2)

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

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, "Interferometric measurements of phase singularities in the output of a visible laser," J. Mod. Opt. 38, 2531-2541 (1991).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

S. S. R. Oemrawsingh, E. R. Elie, J. P. Woerdman, E. J. K. Verstegen, J. G. K. Loosterboer, and G. W't Hooft, "Half-integral spiral phase plates for optical wavelengths," J. Opt. A Pure Appl. Opt. 6, S288-S290 (2004).
[CrossRef]

J. Opt. B Quantum Semiclass. Opt. (1)

M. J. Padgett and L. Allen, "Orbital angular momentum exchange in cylindrical-lens mode converters," J. Opt. B Quantum Semiclass. Opt. 4, S17-S19 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Laser Phys. (1)

G. A. Swartzlander, Jr., D. L. Drugan, N. Hallak, M. O. Freeman, and C. T. Law, "Optical transistor effect using an optical vortex soliton," Laser Phys. 5, 704-709 (1995).

Opt. Commun. (5)

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

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604-612 (1993).
[CrossRef]

M. Harris, C. A. Hill, and J. M. Vaughan, "Optical helices and spiral interference fringes," Opt. Commun. 106, 161-166 (1994).
[CrossRef]

D. Y. Tang, N. R. Heckenberg, and C. O. Weiss, "Phase dependent helical pattern formation in a laser," Opt. Commun. 114, 95-100 (1995).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (3)

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

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, "Atom dynamics in multiple Laguerre-Gaussian beams," Phys. Rev. A 54, 4259-4270 (1996).
[CrossRef] [PubMed]

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]

Phys. Rev. Lett. (4)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1996).
[CrossRef]

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

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

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

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

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

Rev. Sci. Instrum. (1)

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131-5135 (2004).
[CrossRef]

Other (1)

D. C. O'Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics; Design Fabrication and Test (SPIE Press, 2003).

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Figures (8)

Fig. 1
Fig. 1

Phase element structures: (a) phase ramp providing a total of 8π phase retardations, (b) equivalent blazed, structure, (c) modeled structure of an l = 4 conventional SPP, (d) equivalent l = 4 kinoform structure.

Fig. 2
Fig. 2

(a) Far-field distributions obtained from a conventional m = 1 SPP with N quantization levels. (b) Diffraction efficiency for a specific number of quantization levels.

Fig. 3
Fig. 3

(a) Far-field distributions obtained from kinoform m = 4 SPP with N quantization levels. (b) Diffraction efficiency for a specific number of quantization levels.

Fig. 4
Fig. 4

(a) Far-field distributions obtained from a conventional m = 4 SPP with N quantization levels. (b) Diffraction efficiency for a specific number of quantization levels.

Fig. 5
Fig. 5

(a) Prototype microfabricated kinoform structure at 50× under a scanning-electron microscope. Color variations reveal six quantization levels in profile height. (b) Single quadrant of the final kinoform structure with 18 level quantization levels. The cross marks the location of the kinoform center.

Fig. 6
Fig. 6

(a) Calculated intensity distribution at 0.5 Zr obtained by passing a Gaussian beam through the kinoform's SPP structure. (b) Calculated interferogram, showing a charge 4 vortex within the beam.

Fig. 7
Fig. 7

Degeneration of an m-charged vortex into |m| single-charge vortices within the same beam during coaxial superposition with a small coherent background. Calculated intensity profiles at (a) 0.5 and (c) 1.1 Zr. Calculated fringe pattern during interference with a plane wave at (b) 0.5 and (d) 1.1 Zr.

Fig. 8
Fig. 8

Experimental results: Observed intensity profiles at (a) 10, (b) 20, and (c) 30 cm. (d) Interferogram of multiple vortices in a single beam and plane wave at 30 cm; positions of the phase singularities are represented by crosses.

Equations (2)

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t = t s θ 2 π + t 0 ,
m = t s Δ n / λ ,

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