Abstract

We report on the generation of high-order optical vortices by spiral phase mirrors (SPMs). The mirrors are produced by direct machining with a diamond tool and are shown to produce high-quality optical vortices with topological charges ranging from 1 to upwards of 100 at a wavelength of 532 nm. The direct machining technique is flexible and offers the promise of high-precision, large-diameter SPMs that are compatible with high optical powers.

© 2012 Optical Society of America

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    [CrossRef]
  2. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
    [CrossRef]
  3. D. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
    [CrossRef]
  4. T. Kuga, Y. Torii, N. Shiokawa, and T. Hirano, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008

2007

2006

K. J. Moh, X.-C. Yuan, W. C. Cheong, L. S. Zhang, J. Lin, B. P. S. Ahluwalia, and H. Wang, “High-power efficient multiple optical vortices in a single beam generated by a kinoform-type spiral phase plate,” Appl. Opt. 45, 1153–1161 (2006).
[CrossRef]

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14, 3792–3805 (2006).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97, 053901 (2006).
[CrossRef]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[CrossRef]

2005

2003

J. Curtis and D. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003).
[CrossRef]

D. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

2002

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

2001

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

1997

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

1994

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

1992

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

1989

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Abraham, E. R. I.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Ahluwalia, B. P. S.

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Beijersbergen, M.

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

Bernet, S.

Cheong, W. C.

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Coerwinkel, R.

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

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Curtis, J.

Foo, G.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97, 053901 (2006).
[CrossRef]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Fürhapter, S.

Gil, L.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Grier, D.

D. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

J. Curtis and D. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003).
[CrossRef]

Gruzberg, I.

Heckenberg, N. R.

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

Hell, S. W.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[CrossRef]

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Hirano, T.

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

Jahn, R.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[CrossRef]

Jesacher, A.

Johnson, E. G.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97, 053901 (2006).
[CrossRef]

Karimi, E.

Kennedy, S. A.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Khonina, S. N.

Kotlyar, V. V.

Kovalev, A. A.

Kristensen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. 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, and T. Hirano, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Lee, J. H.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97, 053901 (2006).
[CrossRef]

Lin, J.

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]

Marrucci, L.

Maurer, C.

McDuff, R.

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

Moh, K. J.

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Piccirillo, B.

Porterfield, J. Z.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Ritsch-Marte, M.

Rizzoli, S. O.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[CrossRef]

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Santamato, E.

Shiokawa, N.

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

Skidanov, R. V.

Smith, C. P.

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

Sundbeck, S.

Swartzlander, G. A.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97, 053901 (2006).
[CrossRef]

Szabo, M. J.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Teslow, H.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Torii, Y.

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

Turunen, J.

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[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]

Wang, H.

Weihs, G.

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

Westphal, V.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[CrossRef]

White, A. G.

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

Willig, K. I.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[CrossRef]

Woerdman, J.

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

Yuan, X.-C.

Zeilinger, 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]

Zhang, L. S.

Zito, G.

Appl. Opt.

Laser Photon. Rev.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[CrossRef]

Nature

D. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[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]

Opt. Commun.

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

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Opt. Express

Opt. Lett

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

Opt. Lett.

Phys. Rev. A

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre–Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Phys. Rev. Lett.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph,” Phys. Rev. Lett. 97, 053901 (2006).
[CrossRef]

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

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

SEM image of the central region of a charge 100 SPM. Inset, the edge of one of the steps.

Fig. 2.
Fig. 2.

(a) Calculated intensity of the mode produced by illuminating a charge 15 SPM with a collimated TEM00. The propagation distance is normalized to the Rayleigh length, z0, and the width to the beam waist, ω0.( b, c) Measured (solid red trace) and calculated (dashed blue trace) radial intensity profiles after propagation and at the location of the SPM, respectively.

Fig. 3.
Fig. 3.

Left panel, comparison of the calculated and observed intensity and phase of a charge 15 optical vortex. Right panel, the same data converted to polar coordinates. The phase fitting fails in the center of the vortex where there is little optical power.

Fig. 4.
Fig. 4.

(a) Measured (solid red) and calculated (long-dashed blue) radial intensity profiles for a charge 1 optical vortex. (b) For comparison, a charge 1 Laguerre–Gaussian mode is also shown (short-dashed green). (c) The phase of the charge 1 vortex, imaged in the near field. (d) Measured (solid red) and calculated (dashed blue) intensity profiles for a charge 100 optical vortex, which is shown in (e). (f) Measured phase of the vortex in the same plane as the intensity measurement.

Fig. 5.
Fig. 5.

(a) Intensity profile of the charge 100 optical vortex, imaged in the plane featuring the narrowest ring width. (b) The same profile, integrated over the azimuthal coordinate and shown on a Log10 scale. (c) Intensity profile of a charge 1000 optical vortex. (d) Vortex produced by a charge 15 SPM with a 2/3π period modulation of the phase ramp.

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