Abstract

The recent demonstration that an optical vortex could be generated at x-ray wavelengths brings this interesting topological phenomenon into an entirely new regime with several possible applications. We examine the analytic propagation of an optical vortex generated in a synchrotron x-ray beam line. We compare the results obtained with the existing experimental data and further consider the generation and interpretation of mixed vortex-edge discontinuities which might be considered as non-integer charge vortices.

©2003 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  34. V. Pyragaite and A. Stabinis, “Free-space propagation of overlapping light vortex beams,” Opt. Commun. 213, 187–191 (2002).
    [Crossref]
  35. R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: canonical vs. non-canonical,” Opt. Commun. 215, 231–237 (2003).
    [Crossref]
  36. J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun. 175, 289–294 (2000).
    [Crossref]
  37. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
    [Crossref]
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  40. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 5th ed., (Academic Press,1994).

2003 (2)

R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: canonical vs. non-canonical,” Opt. Commun. 215, 231–237 (2003).
[Crossref]

D. Dragoman, “Unambiguous coherence retrieval from intensity measurements,” J. Opt. Soc. Am. A 20, 290–295 (2003).
[Crossref]

2002 (7)

G. S. Agarwal and J. Banerji, “Spatial coherence and information entropy in optical vortex fields,” Opt. Lett. 27, 800–802 (2002).
[Crossref]

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. C. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
[Crossref]

U. T. Schwarz, S. Sogomonian, and M. Maier, “Propagation dynamics of phase dislocations embedded in a Bessel light beam,” Opt. Commun. 208, 255–262 (2002).
[Crossref]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

V. Pyragaite and A. Stabinis, “Free-space propagation of overlapping light vortex beams,” Opt. Commun. 213, 187–191 (2002).
[Crossref]

Z. Bouchal, “Resistance of nondiffracting vortex beam against amplitude and phase pertubations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

M. D. Levenson, G. Dai, and T. Ebihara, “Vortex Mask: Making 80nm contacts with a twist!” Proc. SPIE 4889, 1293–1303 (2002).
[Crossref]

2001 (4)

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

D. V. Petrov, “Vortex-edge dislocation interaction in a linear medium,” Opt. Commun. 188, 307–312 (2001).
[Crossref]

G. A. Swartzlander, Jr., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).
[Crossref]

2000 (2)

D. Rozas and G. A. Swartzlander, Jr., “Observed rotational enhancement of nonlinear optical vorticies,” Opt. Lett. 25, 126–128 (2000).
[Crossref]

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun. 175, 289–294 (2000).
[Crossref]

1998 (1)

1997 (3)

1996 (3)

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

1995 (2)

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[Crossref]

M. Harris, “Light-field fluctuations in space and time,” Contemporary Phys. 36, 215–233 (1995).
[Crossref]

1993 (3)

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

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

I. V. Basistiy, V. Yu Bazhenov, M. S. Soskin, and M. V. Vasnetov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[Crossref]

1992 (2)

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[Crossref]

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] [PubMed]

1991 (1)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

1981 (1)

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

1974 (1)

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

1833 (1)

W. Whewell, “Essay towards a first approximation to a map of cotidal lines,” Phil. Trans. R. Soc. Lond. 123, 147–236 (1833).
[Crossref]

Agarwal, G. S.

Allen, L.

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

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

Allen, L. J.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

Allman, B. E.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Banerji, J.

Baranova, N. B.

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Basistiy, I. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[Crossref]

I. V. Basistiy, V. Yu Bazhenov, M. S. Soskin, and M. V. Vasnetov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[Crossref]

Battipede, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Bazhenov, V. Yu

I. V. Basistiy, V. Yu Bazhenov, M. S. Soskin, and M. V. Vasnetov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[Crossref]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[Crossref]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and 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, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate”, Opt. Commun.112, 321–327 (1994).
[Crossref]

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]

Bouchal, Z.

Z. Bouchal, “Resistance of nondiffracting vortex beam against amplitude and phase pertubations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

Brambilla, M.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Chang, J. S.

Chantler, C. T.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Chowdhury, S. R.

R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: canonical vs. non-canonical,” Opt. Commun. 215, 231–237 (2003).
[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 phaseplate”, Opt. Commun.112, 321–327 (1994).
[Crossref]

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Dai, G.

M. D. Levenson, G. Dai, and T. Ebihara, “Vortex Mask: Making 80nm contacts with a twist!” Proc. SPIE 4889, 1293–1303 (2002).
[Crossref]

Dragoman, D.

Ebihara, T.

M. D. Levenson, G. Dai, and T. Ebihara, “Vortex Mask: Making 80nm contacts with a twist!” Proc. SPIE 4889, 1293–1303 (2002).
[Crossref]

Faulkner, H. M. L.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

Freund, I.

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun.159, 99–117(1999).
[Crossref]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 5th ed., (Academic Press,1994).

Gureyev, T. E.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Harris, M.

M. Harris, “Light-field fluctuations in space and time,” Contemporary Phys. 36, 215–233 (1995).
[Crossref]

Harvey, E. C.

Hayes, J. P.

Heckenberg, N. R.

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

Irving, T. H. K.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Jeon, J. H.

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 phaseplate”, Opt. Commun.112, 321–327 (1994).
[Crossref]

Lai, B.

Law, C. T.

Lee, J. H.

Levenson, M. D.

M. D. Levenson, G. Dai, and T. Ebihara, “Vortex Mask: Making 80nm contacts with a twist!” Proc. SPIE 4889, 1293–1303 (2002).
[Crossref]

Lin, J.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Lugiato, L. A.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Maier, M.

U. T. Schwarz, S. Sogomonian, and M. Maier, “Propagation dynamics of phase dislocations embedded in a Bessel light beam,” Opt. Commun. 208, 255–262 (2002).
[Crossref]

Mamayev, A. V.

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

Mancini, D. C.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Mancuso, A. P.

Marienko, I. G.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex” JETP Lett.71, 130–133 (2000).
[Crossref]

Masajada, J.

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun. 175, 289–294 (2000).
[Crossref]

McDuff, R.

McMahon, P. J.

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. C. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
[Crossref]

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

McNulty, I.

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. C. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
[Crossref]

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Moldovan, N.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Moon, H. J.

Nugent, K. A.

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. C. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
[Crossref]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

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]

Orlov, S.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Oxley, M. P.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

Padgett, M. J.

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Paganin, D.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Paterson, D.

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. C. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
[Crossref]

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Peele, A. G.

Penna, V.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Petrov, D. V.

D. V. Petrov, “Vortex-edge dislocation interaction in a linear medium,” Opt. Commun. 188, 307–312 (2001).
[Crossref]

Pilipetskii, N. F.

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

Prati, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Pyragaite, V.

V. Pyragaite and A. Stabinis, “Free-space propagation of overlapping light vortex beams,” Opt. Commun. 213, 187–191 (2002).
[Crossref]

Regelskis, K.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Retsch, C. C.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

Robertson, D. A.

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Rozas, D.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 5th ed., (Academic Press,1994).

Sacks, Z. S.

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, Jr., “Holographic formation of optical-vortex filaments,” J. Opt. Soc. Am. B 15, 2226–2234 (1998).
[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]

Schwarz, U. T.

U. T. Schwarz, S. Sogomonian, and M. Maier, “Propagation dynamics of phase dislocations embedded in a Bessel light beam,” Opt. Commun. 208, 255–262 (2002).
[Crossref]

Shkukov, V. V.

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers, (McGraw-Hill, 1971).

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Singh, R. P.

R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: canonical vs. non-canonical,” Opt. Commun. 215, 231–237 (2003).
[Crossref]

Smilgevicius, V.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Smith, C. P.

Smith, G. M.

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Sogomonian, S.

U. T. Schwarz, S. Sogomonian, and M. Maier, “Propagation dynamics of phase dislocations embedded in a Bessel light beam,” Opt. Commun. 208, 255–262 (2002).
[Crossref]

Soskin, M. S.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[Crossref]

I. V. Basistiy, V. Yu Bazhenov, M. S. Soskin, and M. V. Vasnetov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[Crossref]

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[Crossref]

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex” JETP Lett.71, 130–133 (2000).
[Crossref]

Stabinis, A.

V. Pyragaite and A. Stabinis, “Free-space propagation of overlapping light vortex beams,” Opt. Commun. 213, 187–191 (2002).
[Crossref]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Swartzlander, Jr., G. A.

Tamm, C.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Tran, C. Q.

Turnball, G. A.

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

van der Veen, H. E. L. O.

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

Vasnetov, M. V.

I. V. Basistiy, V. Yu Bazhenov, M. S. Soskin, and M. V. Vasnetov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[Crossref]

Vasnetsov, M. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[Crossref]

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[Crossref]

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex” JETP Lett.71, 130–133 (2000).
[Crossref]

Weiss, C. O.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Whewell, W.

W. Whewell, “Essay towards a first approximation to a map of cotidal lines,” Phil. Trans. R. Soc. Lond. 123, 147–236 (1833).
[Crossref]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and 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, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate”, Opt. Commun.112, 321–327 (1994).
[Crossref]

Wolf, E.

E. Wolf, Progress in optics 42, (Elsevier, 2001),

Ya, B.

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

Zel’dovich,

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

Appl. Opt. (1)

Contemporary Phys. (1)

M. Harris, “Light-field fluctuations in space and time,” Contemporary Phys. 36, 215–233 (1995).
[Crossref]

J. Mod. Opt. (3)

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[Crossref]

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

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

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

Opt. Commun. (12)

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001).
[Crossref]

I. V. Basistiy, V. Yu Bazhenov, M. S. Soskin, and M. V. Vasnetov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[Crossref]

U. T. Schwarz, S. Sogomonian, and M. Maier, “Propagation dynamics of phase dislocations embedded in a Bessel light beam,” Opt. Commun. 208, 255–262 (2002).
[Crossref]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

V. Pyragaite and A. Stabinis, “Free-space propagation of overlapping light vortex beams,” Opt. Commun. 213, 187–191 (2002).
[Crossref]

R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: canonical vs. non-canonical,” Opt. Commun. 215, 231–237 (2003).
[Crossref]

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun. 175, 289–294 (2000).
[Crossref]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[Crossref]

D. V. Petrov, “Vortex-edge dislocation interaction in a linear medium,” Opt. Commun. 188, 307–312 (2001).
[Crossref]

Z. Bouchal, “Resistance of nondiffracting vortex beam against amplitude and phase pertubations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

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

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Opt. Lett. (5)

Phil. Trans. R. Soc. Lond. (1)

W. Whewell, “Essay towards a first approximation to a map of cotidal lines,” Phil. Trans. R. Soc. Lond. 123, 147–236 (1833).
[Crossref]

Phys. Rev. A (1)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns.m I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5117 (1991).
[Crossref] [PubMed]

Phys. Rev. E (1)

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

Phys. Rev. Lett. (2)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[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]

Pis’ma Zh. Eks. Teor. Fiz. (1)

N. B. Baranova, B. Ya, Zel’dovich, A. V. Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981).

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]

Proc. SPIE (1)

M. D. Levenson, G. Dai, and T. Ebihara, “Vortex Mask: Making 80nm contacts with a twist!” Proc. SPIE 4889, 1293–1303 (2002).
[Crossref]

Other (7)

M. S. Naschie, ed., “Special issue on nonlinear optical structures, patterns, chaos,” Chaos Solitons Fractals 4(8/9) (1994.).

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

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex” JETP Lett.71, 130–133 (2000).
[Crossref]

E. Wolf, Progress in optics 42, (Elsevier, 2001),

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun.159, 99–117(1999).
[Crossref]

A. E. Siegman, An Introduction to Lasers and Masers, (McGraw-Hill, 1971).

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 5th ed., (Academic Press,1994).

Supplementary Material (1)

» Media 1: MPG (1166 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Vortex detector plane intensity from Eq. (9). ω0=239.5 µm, z1=41.4 m, Z=5.8 m, λ=0.13 nm.

Fig. 2.
Fig. 2.

Interferograms of vortex phase structure produced analytically (a and b), numerically (c) and experimentally (d). From left to right, (a) Eq. (12), (b) Eq. (13), (c) Intensity distribution based on Eq. (10) method, (d) experimental result.

Fig. 3.
Fig. 3.

Interferograms of vortex phase structure for non-integer charge and a rotated phaseplate. From left to right; (a) Modified form of Eq. (13) with ν=0.5, (b) Eq. (14) with ν=0.5 and α=π/4, and (c) Eq. (14) with ν=0.5 and α=π/2.

Fig. 4.
Fig. 4.

(1.2 MB) Movie of evolution in the interferogram as the energy varies from 4.5 keV (charge=2.01) to 9 keV (charge=1).

Equations (27)

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

u ( r , θ , 0 ) = 2 π ω 0 exp [ r 2 ω 0 2 ] ,
z 3 π 4 λ ( r r ) max 4 ,
u ( ρ , ϕ , z 1 ) = i λz 2 π 1 ω ( z 1 ) exp [ ρ 2 ω ( z 1 ) 2 ] exp [ i k 2 ρ 2 R ( z 1 ) ] exp [ i ( k z 1 Ψ ( z 1 ) ) ] ,
ω ( z ) = ω 0 [ 1 + ( z z R ) 2 ] 1 2 ; z R = π ω 0 2 λ ;
Ψ ( z ) = atan ( z z R ) ; and R ( z ) = z [ 1 + ( z R z ) 2 ] .
u ( ρ , ϕ , z 1 ) = A m ( ρ , z 1 ) exp [ i Φ ( ρ , z 1 ) ] exp [ imϕ ] ,
A m ( ρ , z 1 ) = i λ z 1 2 π 1 ω ( z 1 ) exp [ ρ 2 ω ( z 1 ) 2 ] ; and
Φ ( ρ , z 1 ) = k 2 ρ 2 R ( z 1 ) + k z 1 Ψ ( z 1 ) .
u ( R , Θ , Z ) = i λZ exp [ λZ R 2 ] 0 0 2 π u ( ρ , ϕ , z 1 ) ρ exp [ λZ ρ 2 ] ×
exp [ i k Z ρ R cos ( ϕ Θ ) ] d ρ d ϕ ,
J m ( α ) = 1 2 π 0 2 π exp [ im ( θ π 2 ) ] exp [ i α cos θ ] d θ ;
u ( R , Θ , Z ) = i λZ exp [ im ( Θ + π 2 ) ] exp [ λZ R 2 ] 0 ρ A m ( ρ , z 1 ) exp [ λZ ρ 2 ] ×
exp [ i Φ ( ρ , z 1 ) ] J m ( Rkρ Z ) d ρ .
u ( R , Θ , Z ) = A ( Z ) exp [ A ( Z ) R 2 ] exp [ im Θ ] exp [ i Φ ( Z ) ] exp [ i Φ ˝ ( Z ) R 2 ] ×
R [ I 1 2 ( m 1 ) ( γ 2 8 β ) I 1 2 ( m + 1 ) ( γ 2 8 β ) ] ,
A ( Z ) = π 2 π λZ 1 λ z 1 2 π 1 ω ( z 1 ) k 8 Z [ 1 ω ( z 1 ) 4 + ( π λ ) 2 { 1 R ( z 1 ) 1 Z } 2 ] 3 4 ;
A ( Z ) = ( k Z ) 2 1 8 1 ω ( z 1 ) 2 1 [ 1 ω ( z 1 ) 4 + ( π λ ) 2 ( 1 R ( z 1 ) 1 Z ) 2 ] ;
Φ ( Z ) = π m π 2 + k z 1 Ψ ( z 1 ) 3 2 atan [ ( π λ ) ω ( z 1 ) 2 ( 1 R ( z 1 ) 1 Z ) ] ;
Φ ˝ ( Z ) = k 2 Z + ( k Z ) 2 1 8 π λ ( 1 R ( z 1 ) 1 Z ) 1 [ 1 ω ( z 1 ) 4 + ( π λ ) 2 ( 1 R ( z 1 ) 1 Z ) 2 ] ;
γ = Rk Z ; and β = 1 ω ( z 1 ) 2 + i π λ ( 1 R ( z 1 ) 1 Z ) .
I ( R , Θ , Z ) = u ( R , Θ , Z ) 2 .
a ( x , y , z ) = F 1 { exp i 2 π z 1 k x 2 k y 2 F { a ( x , y , z = 0 ) } } .
I = A v 2 + A cyl 2 + 2 A v A cyl cos θ i nterf ,
θ interf = { m Θ + Φ ( Z ) + Φ ˝ ( Z ) R 2 + atan ( I 1 2 ( m 1 ) ( γ 2 8 β ) I 1 2 ( m + 1 ) ( γ 2 8 β ) )
+ k ( R cos Θ x offs ) 2 + ( Z z offs ) 2 + m atan ( R sin Θ x offs ) } ,
θ interf = ( m atan ( y x ) + kZ + k ( x x offs ) 2 + ( Z z offs ) 2 + m atan ( y x offs ) ) .
θ interf = ( ν atan ( y cos α x sin α x cos α + y sin α ) + kZ + k ( x x offs ) 2 + ( Z z offs ) 2 + ν atan ( y cos α x sin α x offs ) ) ,

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