Abstract

The Young’s double-slit experiment is one of the most popular stories in the history of physics. This paper, like many others, has emerged from the Young’s idea. It investigates the diffraction of the plane or spherical wave produced by three or four small holes in an opaque screen. It was noticed that the interference field contained a lattice of optical vortices which were equivalent to those produced in optical vortex interferometer. The vortex lattice generated by the three holes possessed some unique properties from which the analytical formulae for vortex points position were derived. We also pointed out the differences between our case and the double-slit experiment. Finally, some remarks on possible applications of our arrangement are discussed briefly. These theoretical considerations are illustrated with the use of experimental results.

© 2007 Optical Society of America

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References

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  1. T. Young, "Experimental demonstration of the General Law of the Interference of Light," Philos. Trans. R. Soc. London 94, (1804).
  2. R. Welti, "Light transmission through two slits: the Young experiment revisited," J. Opt. A: Pure Appl. Opt. 8, 606-609 (2006).
    [CrossRef]
  3. C. Jönsson, "Electron diffraction at multiple slits," Am. J. Phys. 42, 4-11 (1974).
    [CrossRef]
  4. A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
    [CrossRef]
  5. O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 66, 2689-2692 (1991).
    [CrossRef] [PubMed]
  6. W. Schöllkopf and J. Toennies, "The nondestructive mass selection of small van der Waals clusters," Science 226, 1345-1348 (1994).
    [CrossRef]
  7. C. K. Hong and T. G. Noh, "Two-photon double slit interference experiment," J. Opt. Soc. Am. B 15, 1192-1197 (1997).
    [CrossRef]
  8. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-189 (1974).
    [CrossRef]
  9. J. F. Nye, Natural focusing and fine structure of light (IoP, Bristol and Philadelphia, 1999).
  10. M. Vasnetsov, K. Staliunas, eds., Optical vortices (Nova Science Publishers, 1999).
  11. L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (IoP, Bristol, Philadelphia, 2003).
    [CrossRef]
  12. L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, chapter IV (1999).
    [CrossRef]
  13. M. S. Soskin and M. V. Vasnetsov, "Singular Optics," Prog. Opt. 42, chapter IV (2001).
  14. J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
    [CrossRef]
  15. J. Masajada, A. Popiołek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as a phase markers," Opt. Commun. 207, 85-93 (2002).
    [CrossRef]
  16. J. Masajada, A. Popiołek Masajada, E. Frączek and W. Frączek, "Vortex points localization problem in optical vortices interferometr," Opt. Commun. 234, 23-28 (2004).
    [CrossRef]
  17. J. Masajada, "Small rotation-angle measurement with optical vortex interferometer," Opt. Commun. 234, 373-381 (2004).
    [CrossRef]
  18. A. Popiołek-Masajada, M Borwińska and W Frączek, "Testing a new method for small-angle rotation measurements with Optical Vortices Interferometer," Meas. Sci. Technol. 17, 653-658 (2006).
    [CrossRef]
  19. M. Borwińska, A. Popiołek-Masajada and B. Dubik, "Reconstruction of the plane wave tilt and its orientation using Optical Vortex Interferometer," Opt. Eng. (to be published).
  20. J. Masajada, "The interferometry based on regular net of optical vortices," Opt. Appl. to be published in vol. 37, (2007).
  21. J. Masajada, "The optical vortex interferometer, theory, technology, and applications," Proc. SPIE 6254, 62540C1-10 (2006).
  22. P. Kurzynowski, A. Woźniak and E. Frączek, "Optical vortices generation using the Wollaston prism," Appl. Opt. 45, 7898-7903 (2006).
    [CrossRef] [PubMed]
  23. P. Kurzynowski and M. Borwińska, "Generation of the vortex type markers in a one wave setup," Appl. Opt. 46, 676-679 (2007).
    [CrossRef] [PubMed]
  24. K. O’Holleran, M. J. Padgett, and M. R. Dennis, "Topology of optical vortex lines formed by the interference of three, four and five plane waves," Opt. Express 14, 3039 - 3044 (2006).
    [CrossRef] [PubMed]
  25. J. Courtial, R. Zambrini, M. Dennis, and M. Vasnetsov, "Angular momentum of optical vortex arrays", Opt. Express 14, 938-949 (2006)
    [CrossRef] [PubMed]
  26. W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
    [CrossRef]
  27. J. Primot and L. Sogno, "Achromatic three-wave (or more) lateral shearing interferometer," J. Opt. Soc. Am. A 12, 2679-2685 (1995).
    [CrossRef]
  28. J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
    [CrossRef]
  29. N. Guerineau and J. Primot, "Nondiffracting array generation using an N-wave interferometer," J. Opt. Soc. Am. A 16, 293-298 (1999).
    [CrossRef]
  30. S. Velghe, J. Primot, N. Guerineau, M. Cohen and B. Wattellier, "Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers," Opt. Lett. 30, 245-247 (2005).
    [CrossRef] [PubMed]
  31. A. S. Patra and A. Khare, "Interferometric array generation," Opt. Laser Techn. 38, 37-45 (2006).
    [CrossRef]
  32. W. Singer, M. Totzeck and H. Gross, Handbook of Optical System, (Wiley-VCH, Berlin, 2005) Vol. 2
  33. W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, M. Takeda and S. Hanson, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express 14, 120-127 (2006).
    [CrossRef] [PubMed]

2007 (1)

2006 (7)

2005 (2)

W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

S. Velghe, J. Primot, N. Guerineau, M. Cohen and B. Wattellier, "Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers," Opt. Lett. 30, 245-247 (2005).
[CrossRef] [PubMed]

2004 (2)

J. Masajada, A. Popiołek Masajada, E. Frączek and W. Frączek, "Vortex points localization problem in optical vortices interferometr," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

J. Masajada, "Small rotation-angle measurement with optical vortex interferometer," Opt. Commun. 234, 373-381 (2004).
[CrossRef]

2002 (1)

J. Masajada, A. Popiołek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as a phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

2001 (1)

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

1999 (1)

N. Guerineau and J. Primot, "Nondiffracting array generation using an N-wave interferometer," J. Opt. Soc. Am. A 16, 293-298 (1999).
[CrossRef]

1997 (1)

1996 (1)

J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
[CrossRef]

1995 (1)

1994 (1)

W. Schöllkopf and J. Toennies, "The nondestructive mass selection of small van der Waals clusters," Science 226, 1345-1348 (1994).
[CrossRef]

1991 (1)

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 66, 2689-2692 (1991).
[CrossRef] [PubMed]

1988 (1)

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
[CrossRef]

1974 (2)

C. Jönsson, "Electron diffraction at multiple slits," Am. J. Phys. 42, 4-11 (1974).
[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-189 (1974).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-189 (1974).
[CrossRef]

Bhattacharaya, S.

J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
[CrossRef]

Borwinska, M

A. Popiołek-Masajada, M Borwińska and W Frączek, "Testing a new method for small-angle rotation measurements with Optical Vortices Interferometer," Meas. Sci. Technol. 17, 653-658 (2006).
[CrossRef]

Borwinska, M.

P. Kurzynowski and M. Borwińska, "Generation of the vortex type markers in a one wave setup," Appl. Opt. 46, 676-679 (2007).
[CrossRef] [PubMed]

M. Borwińska, A. Popiołek-Masajada and B. Dubik, "Reconstruction of the plane wave tilt and its orientation using Optical Vortex Interferometer," Opt. Eng. (to be published).

Carnal, O.

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 66, 2689-2692 (1991).
[CrossRef] [PubMed]

Cohen, M.

Courtial, J.

Darlin, J. S.

J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
[CrossRef]

Dennis, M.

Dennis, M. R.

Dubik, B.

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

M. Borwińska, A. Popiołek-Masajada and B. Dubik, "Reconstruction of the plane wave tilt and its orientation using Optical Vortex Interferometer," Opt. Eng. (to be published).

Fraczek, E.

P. Kurzynowski, A. Woźniak and E. Frączek, "Optical vortices generation using the Wollaston prism," Appl. Opt. 45, 7898-7903 (2006).
[CrossRef] [PubMed]

J. Masajada, A. Popiołek Masajada, E. Frączek and W. Frączek, "Vortex points localization problem in optical vortices interferometr," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

Fraczek, W

A. Popiołek-Masajada, M Borwińska and W Frączek, "Testing a new method for small-angle rotation measurements with Optical Vortices Interferometer," Meas. Sci. Technol. 17, 653-658 (2006).
[CrossRef]

Fraczek, W.

J. Masajada, A. Popiołek Masajada, E. Frączek and W. Frączek, "Vortex points localization problem in optical vortices interferometr," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

Gähler, R.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
[CrossRef]

Guerineau, N.

Hanson, S.

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, M. Takeda and S. Hanson, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express 14, 120-127 (2006).
[CrossRef] [PubMed]

W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

Hong, C. K.

Ishii, N.

W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

Ishijima, R.

Jönsson, C.

C. Jönsson, "Electron diffraction at multiple slits," Am. J. Phys. 42, 4-11 (1974).
[CrossRef]

Khare, A.

A. S. Patra and A. Khare, "Interferometric array generation," Opt. Laser Techn. 38, 37-45 (2006).
[CrossRef]

Kothiyal, M. P.

J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
[CrossRef]

Kurzynowski, P.

Mampe, W.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
[CrossRef]

Masajada, J.

J. Masajada, A. Popiołek Masajada, E. Frączek and W. Frączek, "Vortex points localization problem in optical vortices interferometr," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

J. Masajada, "Small rotation-angle measurement with optical vortex interferometer," Opt. Commun. 234, 373-381 (2004).
[CrossRef]

J. Masajada, A. Popiołek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as a phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

Miyamoto, Y.

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, M. Takeda and S. Hanson, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express 14, 120-127 (2006).
[CrossRef] [PubMed]

W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

Mlynek, J.

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 66, 2689-2692 (1991).
[CrossRef] [PubMed]

Noh, T. G.

Nye, J. F.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-189 (1974).
[CrossRef]

O’Holleran, K.

Padgett, M. J.

Patra, A. S.

A. S. Patra and A. Khare, "Interferometric array generation," Opt. Laser Techn. 38, 37-45 (2006).
[CrossRef]

Popiolek Masajada, A.

J. Masajada, A. Popiołek Masajada, E. Frączek and W. Frączek, "Vortex points localization problem in optical vortices interferometr," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

Popiolek-Masajada, A.

A. Popiołek-Masajada, M Borwińska and W Frączek, "Testing a new method for small-angle rotation measurements with Optical Vortices Interferometer," Meas. Sci. Technol. 17, 653-658 (2006).
[CrossRef]

J. Masajada, A. Popiołek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as a phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

M. Borwińska, A. Popiołek-Masajada and B. Dubik, "Reconstruction of the plane wave tilt and its orientation using Optical Vortex Interferometer," Opt. Eng. (to be published).

Primot, J.

Schöllkopf, W.

W. Schöllkopf and J. Toennies, "The nondestructive mass selection of small van der Waals clusters," Science 226, 1345-1348 (1994).
[CrossRef]

Senthilkumaran, P.

J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
[CrossRef]

Shull, C. G.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
[CrossRef]

Sirohi, R. S.

J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
[CrossRef]

Sogno, L.

Takeda, M.

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, M. Takeda and S. Hanson, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express 14, 120-127 (2006).
[CrossRef] [PubMed]

W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

Toennies, J.

W. Schöllkopf and J. Toennies, "The nondestructive mass selection of small van der Waals clusters," Science 226, 1345-1348 (1994).
[CrossRef]

Treimer, W.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
[CrossRef]

Vasnetsov, M.

Velghe, S.

Wada, A.

Wang, W.

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, M. Takeda and S. Hanson, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express 14, 120-127 (2006).
[CrossRef] [PubMed]

W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

Wattellier, B.

Welti, R.

R. Welti, "Light transmission through two slits: the Young experiment revisited," J. Opt. A: Pure Appl. Opt. 8, 606-609 (2006).
[CrossRef]

Wieliczka, D.

J. Masajada, A. Popiołek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as a phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

Wozniak, A.

Yokozeki, T.

Young, T.

T. Young, "Experimental demonstration of the General Law of the Interference of Light," Philos. Trans. R. Soc. London 94, (1804).

Zambrini, R.

Zeilinger, A.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
[CrossRef]

Am. J. Phys. (1)

C. Jönsson, "Electron diffraction at multiple slits," Am. J. Phys. 42, 4-11 (1974).
[CrossRef]

Appl. Opt. (2)

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

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

J. Opt. A: Pure Appl. Opt. (1)

R. Welti, "Light transmission through two slits: the Young experiment revisited," J. Opt. A: Pure Appl. Opt. 8, 606-609 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

N. Guerineau and J. Primot, "Nondiffracting array generation using an N-wave interferometer," J. Opt. Soc. Am. A 16, 293-298 (1999).
[CrossRef]

Meas. Sci. Technol. (1)

A. Popiołek-Masajada, M Borwińska and W Frączek, "Testing a new method for small-angle rotation measurements with Optical Vortices Interferometer," Meas. Sci. Technol. 17, 653-658 (2006).
[CrossRef]

Opt. Commun. (5)

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

J. Masajada, A. Popiołek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as a phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

J. S. Darlin, P. Senthilkumaran, S. Bhattacharaya, M. P. Kothiyal and R. S. Sirohi, "Fabrication of an array illuminator using tandem Michelson interferometers," Opt. Commun. 123, 1-4 (1996).
[CrossRef]

J. Masajada, "Small rotation-angle measurement with optical vortex interferometer," Opt. Commun. 234, 373-381 (2004).
[CrossRef]

W. Wang, N. Ishii, S. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

Opt. Eng. (1)

M. Borwińska, A. Popiołek-Masajada and B. Dubik, "Reconstruction of the plane wave tilt and its orientation using Optical Vortex Interferometer," Opt. Eng. (to be published).

Opt. Express (3)

Opt. Laser Techn. (1)

A. S. Patra and A. Khare, "Interferometric array generation," Opt. Laser Techn. 38, 37-45 (2006).
[CrossRef]

Opt. Lett. (1)

Opt., Commun. (1)

J. Masajada, A. Popiołek Masajada, E. Frączek and W. Frączek, "Vortex points localization problem in optical vortices interferometr," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 66, 2689-2692 (1991).
[CrossRef] [PubMed]

Proc. Roy. Soc. Lond. A (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-189 (1974).
[CrossRef]

Rev. Mod. Phys. (1)

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, "Single and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067-1073 (1988).
[CrossRef]

Science (1)

W. Schöllkopf and J. Toennies, "The nondestructive mass selection of small van der Waals clusters," Science 226, 1345-1348 (1994).
[CrossRef]

Other (9)

J. Masajada, "The interferometry based on regular net of optical vortices," Opt. Appl. to be published in vol. 37, (2007).

J. Masajada, "The optical vortex interferometer, theory, technology, and applications," Proc. SPIE 6254, 62540C1-10 (2006).

T. Young, "Experimental demonstration of the General Law of the Interference of Light," Philos. Trans. R. Soc. London 94, (1804).

J. F. Nye, Natural focusing and fine structure of light (IoP, Bristol and Philadelphia, 1999).

M. Vasnetsov, K. Staliunas, eds., Optical vortices (Nova Science Publishers, 1999).

L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (IoP, Bristol, Philadelphia, 2003).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, chapter IV (1999).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, "Singular Optics," Prog. Opt. 42, chapter IV (2001).

W. Singer, M. Totzeck and H. Gross, Handbook of Optical System, (Wiley-VCH, Berlin, 2005) Vol. 2

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Figures (13)

Fig. 1.
Fig. 1.

The basic optical setup of the optical vortex interferometer.

Fig. 2.
Fig. 2.

The example of the equiphase line plot (for the vortex lattice generated by three plane waves' interference). The lattice was computer generated.

Fig 3.
Fig 3.

The comparison between the experiment and the results of far field computations. The circles correspond to the computed positions of the vortex points. The crosses mark the vortex points localized in the interferogram. Both figures differ in the arrangement of the three holes as shown under each interferogram. The plates were inspected under microscopy while applying to the calculations.

Fig. 4.
Fig. 4.

The interference pattern obtained by adding the light emerging from the plate with three holes together with an additional plane wave. The fork like fringes indicates the presence of optical vortices. The vortex points localized on this interferogram are marked with crosses.

Fig. 5
Fig. 5

The position of vortex points calculated for the plate shown in Fig. 3(a) using far (pluses) and near (circles) field diffractions integral (numerical integration). The positions of the three vortex points were adjusted manually to show the difference between the lattice determined by both methods.

Fig. 6.
Fig. 6.

The scheme for the parabolic approximation.

Fig. 7.
Fig. 7.

(a). The position of the vortex points for the plate shown in Fig. 3(a), calculated using parabolic (crosses) and near (circles) field approximation, (b) comparison between computations using parabolic field approximation and experimental results.

Fig. 8.
Fig. 8.

The interference pattern produced by the four holes in the arrangement shown below each interferogram. The vortex points (marked as crosses) were localized by using minima method. Contrary to the three-holes case both lattice shown in these interferograms are irregular.

Fig. 9.
Fig. 9.

The vortex lattice without (circles) and with (pluses) wedge. The plate shown in Fig. 3(a) was used. Due to wave tilt the lattice was shifted as a rigid body (experiment).

Fig. 10.
Fig. 10.

The spherical wave incident on the plate; here drawn in cross section. Since the holes are small we can assume that each hole is illuminated by the plane wave tangent to the given spherical wave at the hole center.

Fig. 11.
Fig. 11.

When the plate is illuminated by the spherical waves the somb functions representing the holes are mutually shifted in frequency domain. Here, for simplicity somb function representing wave A and one of the other two waves are plotted. For this reason in a given direction each hole contributes to a different amplitude, which complicates remarkably the conditions for vortex points positions.

Fig. 12
Fig. 12

The vortex lattice shift due to small plate shift in the direction perpendicular to the optical axis. Figure 12(a) shows two vortex lattices (circles-no shift, x-after the test was shifted). Each lattice can be divided into two sublattices which differ in the topological charge (the red signs plus and minus are marked next to the vortices). The plus sublattices overlaps – they have the same geometry. The minus sublattices are mutually shifted. This is in agreement with our conclusions drawn from the theory. Figures 12(b) and 12(c) show the corresponding interferograms (before and after the plate shift).

Fig. 13
Fig. 13

The same experiment as in Fig. 13, but with four holes. This setup is much more sensitive than the previous one, but the analysis is much more complicated. The relevant methods are not ready yet.

Equations (21)

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U ( f x , f y ) = Ω exp { i π f p 2 z } somb ( R f p ) ×
[ 1 + exp { 2 πi ( T Bx f x + T B y f y ) } + exp { 2 π i ( T Cx f x + T By f y ) } ] .
Ω = exp { i k z } 2 i λ z .
somb ( x ) = 2 J 1 ( x ) x .
ψ A = 0 ; ψ B = 2 3 π + 2 π m ; ψ c = 4 3 π + 2 π n ,
ψ A = 0 ; ψ B = 4 3 π + 2 π m ; ψ c = 2 3 π + 2 π n .
2 π ( T Bx f x + T By f y ) = 2 3 π + 2 π m ,
2 π ( T Cx f x + T Cy f y ) = 4 3 π + 2 π n ,
2 π ( T Bx f x + T By f y ) = 4 3 π + 2 π m ,
2 π ( T Cx f x + T Cy f y ) = 2 3 π + 2 π n .
f x = 1 3 T By ( 2 + 3 n ) T Cy ( 1 + 3 m ) T By T Cx T Bx T Cy ,
f y = 1 3 T Bx ( 2 + 3 n ) T Cx ( 1 + 3 m ) T By T Cx T Bx T Cy ,
f x = 1 3 T Cy ( 2 + 3 m ) T By ( 1 + 3 n ) T By T Cx T Bx T Cy ,
f y = 1 3 T Bx ( 1 + 3 n ) T Cx ( 2 + 3 m ) T By T Cx T Bx T Cy .
r q = z + 1 2 ( x q x ) 2 + ( y q y ) 2 z .
k ( r b r a ) + δ b = ψ b + 2 π m ,
k ( r c r a ) + δ c = ψ c + 2 π n .
x = 1 2 y c ( H b + 2 m λ z ) y b ( H c + 2 n λ z ) x b y c y b x c ,
y = 1 2 x c ( H b + 2 m λ z ) x b ( H c + 2 n λ z ) x b y c y b x c ,
H q = 2 z ( ψ q δ q k ) x q 2 y q 2 .
U ( f x , f y ) = Ω exp { i π f′ p 2 z } somb ( f′ p ) ( 1 + exp { 2 πi ( T Bx f x + T B y f y ) } + exp { 2 πi ( T Cx f x + T By f y ) } ) .

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