Abstract

We present a study of spatial structures created by superposition of spiral zone plates used for generating optical beams with phase singularities. Moiré fringes are observed that show topological defects similar to those appearing in interference patterns of optical vortices. A brief theoretical discussion is included that supports the similarities between the two phenomena. Our results may lead to interesting applications to digital information processing by optical means.

© 2003 Optical Society of America

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  1. M. Padgett, L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41, 275–285 (2000).
    [CrossRef]
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, 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]
  3. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinszteindunlop, “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]
  4. J. W. R. Tabosa, D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
    [CrossRef]
  5. K. Dholakia, N. B. Sympson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
    [CrossRef] [PubMed]
  6. J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
    [CrossRef]
  7. J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
    [CrossRef]
  8. D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, A. Z. Khoury, Phys. Rev. A art. no. 041801 (Rapid Comm.), (2002).
  9. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997).
    [CrossRef]
  10. D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
    [CrossRef]
  11. H. H. Arnaut, G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett. 85, 286–289 (2000).
    [CrossRef] [PubMed]
  12. A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
    [CrossRef]
  13. M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van de Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
    [CrossRef] [PubMed]
  14. J. N. Walford, K. A. Nugent, A. Roberts, R. E. Scholten, “High-resolution phase imaging of phase singularities in the focal region of a lens,” Opt. Lett. 27, 345–347 (2002).
    [CrossRef]
  15. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
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    [CrossRef]
  17. M. V. Berry, M. R. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime,” J. Phys. A 34, 8877–8888 (2001).
    [CrossRef]
  18. M. V. Berry, M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. London Ser. A 457, 2251–2263 (2001).
    [CrossRef]
  19. 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]
  20. G. F. Brand, “Phase singularities in beams,” Am. J. Phys. 67, 55–60 (1999).
    [CrossRef]
  21. E. Abramochkin, V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).
    [CrossRef]
  22. M. W. Beijersbergen, L. Allen, H. E. L. O. Wanderveen, J. P. Woerdman, “Astigmatic mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  23. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, Amsterdam, 1993).
  24. O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1989).
  25. J. W. Dally, W. F. Riley, Experimental Stress Analysis (McGraw-HillKogakusha, Tokyo, 1978).
  26. D. Post, B. Han, P. Ifiju, High Sensitivity Moiré Experimental Analysis for Mechanics (Springer-Verlag, New York, 1994).
  27. N. K. Mohan, “The influence of multiple-exposure recording on curvature pattern using multi-aperture speckle shear interferometry,” Opt. Commun. 186, 259–263 (2000).
    [CrossRef]
  28. J. Yang, D. Y. Fan, S. J. Wang, Y. Gu, “Moiré technique for spatial coherence measurements of soft-x-ray lasers,” J. Opt. Soc. Am. A 17, 790–793 (2000).
    [CrossRef]
  29. E. Fujiwara, S. Irie, T. Nemoto, S. Isoda, T. Kobayashi, “A scanning tunneling microscopy study on the monolayer epitaxy of [cyano(ethoxycarbonyl) methylene]-2-ylidene-4,5-dimethyl-1,3-dithiole on graphite and its dynamic feature,” Surf. Sci. 459, 390–400 (2000).
    [CrossRef]
  30. I. Amidror, R. D. Hersch, “Fourier-based analysis and synthesis of moirés in the superposition of geometrically transformed periodic structures,” J. Opt. Soc. Am. A 15, 1100–1113 (1998).
    [CrossRef]

2002

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, A. Z. Khoury, Phys. Rev. A art. no. 041801 (Rapid Comm.), (2002).

J. N. Walford, K. A. Nugent, A. Roberts, R. E. Scholten, “High-resolution phase imaging of phase singularities in the focal region of a lens,” Opt. Lett. 27, 345–347 (2002).
[CrossRef]

2001

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

M. V. Berry, M. R. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime,” J. Phys. A 34, 8877–8888 (2001).
[CrossRef]

M. V. Berry, M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. London Ser. A 457, 2251–2263 (2001).
[CrossRef]

2000

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van de Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

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

J. Yang, D. Y. Fan, S. J. Wang, Y. Gu, “Moiré technique for spatial coherence measurements of soft-x-ray lasers,” J. Opt. Soc. Am. A 17, 790–793 (2000).
[CrossRef]

H. H. Arnaut, G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett. 85, 286–289 (2000).
[CrossRef] [PubMed]

N. K. Mohan, “The influence of multiple-exposure recording on curvature pattern using multi-aperture speckle shear interferometry,” Opt. Commun. 186, 259–263 (2000).
[CrossRef]

E. Fujiwara, S. Irie, T. Nemoto, S. Isoda, T. Kobayashi, “A scanning tunneling microscopy study on the monolayer epitaxy of [cyano(ethoxycarbonyl) methylene]-2-ylidene-4,5-dimethyl-1,3-dithiole on graphite and its dynamic feature,” Surf. Sci. 459, 390–400 (2000).
[CrossRef]

1999

J. W. R. Tabosa, D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

G. F. Brand, “Phase singularities in beams,” Am. J. Phys. 67, 55–60 (1999).
[CrossRef]

1998

D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

I. Amidror, R. D. Hersch, “Fourier-based analysis and synthesis of moirés in the superposition of geometrically transformed periodic structures,” J. Opt. Soc. Am. A 15, 1100–1113 (1998).
[CrossRef]

1997

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

1996

K. Dholakia, N. B. Sympson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

1995

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinszteindunlop, “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

S. M. Barnett, L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

1993

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

1992

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]

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

1991

E. Abramochkin, V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).
[CrossRef]

Abramochkin, E.

E. Abramochkin, V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).
[CrossRef]

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, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

K. Dholakia, N. B. Sympson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

S. M. Barnett, L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

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

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

Almeida, M. P.

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, A. Z. Khoury, Phys. Rev. A art. no. 041801 (Rapid Comm.), (2002).

Amidror, I.

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

Arnaut, H. H.

H. H. Arnaut, G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett. 85, 286–289 (2000).
[CrossRef] [PubMed]

Balistreri, M. L. M.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van de Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Barbosa, G. A.

H. H. Arnaut, G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett. 85, 286–289 (2000).
[CrossRef] [PubMed]

Barnett, S. M.

S. M. Barnett, L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

Beijersbergen, M. W.

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

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

M. V. Berry, M. R. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime,” J. Phys. A 34, 8877–8888 (2001).
[CrossRef]

M. V. Berry, M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. London Ser. A 457, 2251–2263 (2001).
[CrossRef]

Boschi, D.

D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997).
[CrossRef]

Branca, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Brand, G. F.

G. F. Brand, “Phase singularities in beams,” Am. J. Phys. 67, 55–60 (1999).
[CrossRef]

Caetano, D. P.

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, A. Z. Khoury, Phys. Rev. A art. no. 041801 (Rapid Comm.), (2002).

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

Coutinho dos Santos, B.

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, A. Z. Khoury, Phys. Rev. A art. no. 041801 (Rapid Comm.), (2002).

Dally, J. W.

J. W. Dally, W. F. Riley, Experimental Stress Analysis (McGraw-HillKogakusha, Tokyo, 1978).

De Martini, F.

D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Dennis, M. R.

M. V. Berry, M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. London Ser. A 457, 2251–2263 (2001).
[CrossRef]

M. V. Berry, M. R. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime,” J. Phys. A 34, 8877–8888 (2001).
[CrossRef]

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

K. Dholakia, N. B. Sympson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997).
[CrossRef]

Fan, D. Y.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinszteindunlop, “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]

Fujiwara, E.

E. Fujiwara, S. Irie, T. Nemoto, S. Isoda, T. Kobayashi, “A scanning tunneling microscopy study on the monolayer epitaxy of [cyano(ethoxycarbonyl) methylene]-2-ylidene-4,5-dimethyl-1,3-dithiole on graphite and its dynamic feature,” Surf. Sci. 459, 390–400 (2000).
[CrossRef]

Glatt, I.

O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1989).

Gu, Y.

Han, B.

D. Post, B. Han, P. Ifiju, High Sensitivity Moiré Experimental Analysis for Mechanics (Springer-Verlag, New York, 1994).

Hardy, L.

D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinszteindunlop, “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. E. J. Friese, N. R. Heckenberg, H. Rubinszteindunlop, “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]

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]

Hersch, R. D.

Huguenin, J. A. O.

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, A. Z. Khoury, Phys. Rev. A art. no. 041801 (Rapid Comm.), (2002).

Ifiju, P.

D. Post, B. Han, P. Ifiju, High Sensitivity Moiré Experimental Analysis for Mechanics (Springer-Verlag, New York, 1994).

Irie, S.

E. Fujiwara, S. Irie, T. Nemoto, S. Isoda, T. Kobayashi, “A scanning tunneling microscopy study on the monolayer epitaxy of [cyano(ethoxycarbonyl) methylene]-2-ylidene-4,5-dimethyl-1,3-dithiole on graphite and its dynamic feature,” Surf. Sci. 459, 390–400 (2000).
[CrossRef]

Isoda, S.

E. Fujiwara, S. Irie, T. Nemoto, S. Isoda, T. Kobayashi, “A scanning tunneling microscopy study on the monolayer epitaxy of [cyano(ethoxycarbonyl) methylene]-2-ylidene-4,5-dimethyl-1,3-dithiole on graphite and its dynamic feature,” Surf. Sci. 459, 390–400 (2000).
[CrossRef]

Kafri, O.

O. Kafri, I. Glatt, The Physics of Moiré Metrology (Wiley, New York, 1989).

Khoury, A. Z.

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, A. Z. Khoury, Phys. Rev. A art. no. 041801 (Rapid Comm.), (2002).

Kobayashi, T.

E. Fujiwara, S. Irie, T. Nemoto, S. Isoda, T. Kobayashi, “A scanning tunneling microscopy study on the monolayer epitaxy of [cyano(ethoxycarbonyl) methylene]-2-ylidene-4,5-dimethyl-1,3-dithiole on graphite and its dynamic feature,” Surf. Sci. 459, 390–400 (2000).
[CrossRef]

Korterik, J. P.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van de Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Kuipers, L.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van de Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Mair, A.

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

Mattle, K.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997).
[CrossRef]

McDuff, R.

Mohan, N. K.

N. K. Mohan, “The influence of multiple-exposure recording on curvature pattern using multi-aperture speckle shear interferometry,” Opt. Commun. 186, 259–263 (2000).
[CrossRef]

Nemoto, T.

E. Fujiwara, S. Irie, T. Nemoto, S. Isoda, T. Kobayashi, “A scanning tunneling microscopy study on the monolayer epitaxy of [cyano(ethoxycarbonyl) methylene]-2-ylidene-4,5-dimethyl-1,3-dithiole on graphite and its dynamic feature,” Surf. Sci. 459, 390–400 (2000).
[CrossRef]

Nugent, K. A.

Padgett, M.

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

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

K. Dholakia, N. B. Sympson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

Pan, J. W.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997).
[CrossRef]

Patorski, K.

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, Amsterdam, 1993).

Petrov, D. V.

J. W. R. Tabosa, D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

Popescu, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Post, D.

D. Post, B. Han, P. Ifiju, High Sensitivity Moiré Experimental Analysis for Mechanics (Springer-Verlag, New York, 1994).

Riley, W. F.

J. W. Dally, W. F. Riley, Experimental Stress Analysis (McGraw-HillKogakusha, Tokyo, 1978).

Roberts, A.

Rubinszteindunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinszteindunlop, “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]

Scholten, R. E.

Smith, C. P.

Souto Ribeiro, P. H.

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Figures (5)

Fig. 1
Fig. 1

Zone plates for (a) m=0 (FZP), (b) m=1, and (c) m=2.

Fig. 2
Fig. 2

Experimental setup for interferometric measurements. H, hologram; L, lens; M, mirror; BS, beam splitter; DP, Dove prism, D=fH+fL. (a) Setup used for self-interference of an m=1 optical vortex and for interference between m=1 and m=-1. (b) setup used for interference between m=0 and m=1.

Fig. 3
Fig. 3

Interference patterns between two optical vortices with (a) m1=m2=1, (b) m1=1 and m2=0, (c) m1=1 and m2=-1, and analogous moiré fringes for superposition of two spiral zone plates: (d) m1=m2=1, (e) m1=1 and m2=0, (f) m1=1 and m2=-1.

Fig. 4
Fig. 4

Interference patterns between a divergent optical vortex and a collimated one for (a) m1=m2=1, (b) m1=1 and m2=0, (c) m1=1 and m2=-1, and analogous moiré fringes for spiral zone plates with different radial scales: (d) m1=m2=1, (e) m1=1 and m2=0, (f) m1=1 and m2=-1.

Fig. 5
Fig. 5

Moiré fringes between spiral zone plates with (a) m1=m2=2, (b) m1=2 and m2=-2, and moiré fringes for spiral zone plates with different radial scales: (c) m1=m2=2, (d) m1=2 and m2=-2.

Equations (12)

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ψmp=Cmpw(z)r2w(z)|m|Lp|m|2r2w2(z)exp-r2w2(z) ×expikr22R(z)-(2p+|m|+1)tan-1zzR+mϕ.
p(x)=n=-cn exp(2iπνnx).
t(r, ϕ)=t1(r, ϕ)t2(r, ϕ).
g(r, ϕ)=αr2+mϕ,
ti(r, ϕ)=n=-cn(i)exp[2iπngi(r, ϕ)],
t1(r, ϕ)t2(r, ϕ)=n,l=-cn(1)cl(2)exp{2iπ[ng1(r, ϕ)+lg2(r, ϕ)]}.
fk1,k2(r, ϕ)=m=-cmk1(1)cmk2(2)exp[2iπmgk1,k2(r, ϕ)],
g1(r, ϕ)=α[(x+/2)2+y2]+m1ϕ, g2(r, ϕ)=α[(x-/2)2+y2]+m2ϕ,
g1,-1(r, ϕ)=2αx+Δmϕ=2αr cos ϕ+Δmϕ,
g1(r, ϕ)=α1r2+m1ϕ,
g2(r, ϕ)=α2r2+m2ϕ.
g1,-1(r, ϕ)=Δαr2+Δmϕ,

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