Abstract

Phase singularities are a ubiquitous feature of waves of all forms and represent a fundamental aspect of wave topology. An optical vortex phase singularity occurs when there is a spiral phase ramp about a point phase singularity. We report an experimental observation of an optical vortex in a field consisting of 9-keV x-ray photons. The vortex is created with an x-ray optical structure that imparts a spiral phase distribution to the incident wave field and is observed by use of diffraction about a wire to create a division-of-wave-front interferometer.

© 2002 Optical Society of America

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  1. M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 1980), Vol. XVIII, pp. 257–346.
    [CrossRef]
  2. D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1998).
    [CrossRef]
  3. M. Born and E. Wolf, in Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 256–257 and 449–453.
    [CrossRef]
  4. D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997), and references therein.
    [CrossRef]
  5. S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
    [CrossRef]
  6. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
    [CrossRef] [PubMed]
  7. L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
    [CrossRef]
  8. Z. S. Sacks, D. Rozas, and G. A. Swartzlander, J. Opt. Soc. Am. B 15, 2226 (1998).
    [CrossRef]
  9. P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
    [CrossRef]
  10. V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Piz’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].
  11. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef]
  12. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
    [CrossRef]
  13. E. C. Harvey and P. T. Rumsby, Proc. SPIE 3223, 26 (1997).
    [CrossRef]
  14. D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
    [CrossRef]
  15. D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
    [CrossRef]
  16. G. A. Swartzlander, Opt. Lett. 26, 497 (2001).
    [CrossRef]

2002 (1)

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

2001 (3)

G. A. Swartzlander, Opt. Lett. 26, 497 (2001).
[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
[CrossRef]

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

1998 (2)

1997 (2)

1996 (2)

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1992 (1)

1990 (1)

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Piz’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

1989 (1)

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[CrossRef]

Allen, L. J.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
[CrossRef]

Allman, B. E.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Piz’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Berry, M. V.

M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 1980), Vol. XVIII, pp. 257–346.
[CrossRef]

Born, M.

M. Born and E. Wolf, in Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 256–257 and 449–453.
[CrossRef]

Chantler, C. T.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Chávez-Cerda, S.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[CrossRef]

Faulkner, H. M. L.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
[CrossRef]

Gil, L.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[CrossRef]

Gureyev, T. E.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Harvey, E. C.

E. C. Harvey and P. T. Rumsby, Proc. SPIE 3223, 26 (1997).
[CrossRef]

Heckenberg, N. R.

Irving, T. H. K.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Law, C. T.

Lin, J.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

MacMahon, P. J.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Mancini, D. C.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

McDonald, G. S.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

McDuff, R.

McNulty, I.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Moldovan, N.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

New, G. H. C.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Nugent, K. A.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
[CrossRef]

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1998).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Oxley, M. P.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
[CrossRef]

Paganin, D.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
[CrossRef]

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1998).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Palacios, D.

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

Paterson, D.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Retsch, C. C.

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[CrossRef]

Rozas, D.

Rumsby, P. T.

E. C. Harvey and P. T. Rumsby, Proc. SPIE 3223, 26 (1997).
[CrossRef]

Sacks, Z. S.

Smith, C. P.

Soskin, M. S.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Piz’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Swartzlander, G. A.

Upstill, C.

M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 1980), Vol. XVIII, pp. 257–346.
[CrossRef]

Vasnetsov, M. V.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Piz’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, in Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 256–257 and 449–453.
[CrossRef]

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

Opt. Commun. (4)

D. Paterson, B. E. Allman, P. J. MacMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
[CrossRef]

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. E (1)

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, Phys. Rev. E 63, 037602 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1998).
[CrossRef]

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

Piz’ma Zh. Eksp. Teor. Fiz. (1)

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Piz’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Proc. SPIE (1)

E. C. Harvey and P. T. Rumsby, Proc. SPIE 3223, 26 (1997).
[CrossRef]

Other (2)

M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 1980), Vol. XVIII, pp. 257–346.
[CrossRef]

M. Born and E. Wolf, in Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 256–257 and 449–453.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Optical microscope image, showing a spiral phase plate as manufactured. The image is focused on the deepest step, so the top layer is slightly out of focus.

Fig. 2
Fig. 2

Image of the x-ray intensity at a propagation distance of 5.8 m from the spiral phase plate. Structure from the nonuniform illuminating field has been removed through division of the original data by the corresponding image with the phase plate removed. The spiral structure can be seen, as can a strong diffraction edge that is due to the slope in the large step joining the top and the bottom of the spiral. A faint ring can be observed about the central dark core region. Inset, average of the horizontal and vertical profiles through the core as shown.

Fig. 3
Fig. 3

Fresnel near-field diffraction image produced by the spiral phase plate and a wire, showing interference between the vortex input beam and the diffracted field from the wire. Inset, an otherwise identical image, except that the phase plate has been removed. The standard Fresnel diffraction pattern for a wire is clearly observed.

Fig. 4
Fig. 4

Two of a sequence of images showing the scan of an edge across a vortex core. The arrows indicating the position of the forked fringe are aligned such that the movement of the edge can be seen, as can the fact that the position of the vortex core (at the fork) remains stationary.

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