Abstract

We establish a correlation rule of which the value of the topological charge obtained in intensity correlation between two coherence vortices is such that this value is bounded by the topological charge of each coherence vortex. The original phase information is scrambled in each speckle pattern and unveiled using numerical intensity correlation. According to this rule, it is also possible to obtain a coherence vortex stable, an integer vortex, even when each incoherent vortex beam is instable, non-integer vortex.

© 2012 OSA

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl Opt.6(2), 259–268 (2004).
    [CrossRef]
  3. J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys.6, 71 (2004).
    [CrossRef]
  4. A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, “Visualization of the birth of an optical vortex using diffraction from a triangular aperture,” Opt. Express19(7), 5760–5771 (2011).
    [CrossRef] [PubMed]
  5. H. C. Huang, Y. T. Lin, and M. F. Shih, “Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach-Zehnder interferometers,” Opt. Commun.285(4), 383–388 (2012).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge; New York, 1995).
  7. F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt.45(3), 539–554 (1998).
    [CrossRef]
  8. J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett.26(7), 405–407 (2001).
    [CrossRef] [PubMed]
  9. G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett.28(11), 878–880 (2003).
    [CrossRef] [PubMed]
  10. G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun.222(1-6), 117–125 (2003).
    [CrossRef]
  11. I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation vortices in partially coherent light: theory,” J. Opt. Soc. Am. B21(11), 1895–1900 (2004).
    [CrossRef]
  12. D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett.92(14), 143905 (2004).
    [CrossRef] [PubMed]
  13. W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
    [CrossRef] [PubMed]
  14. H. D. Pires, J. Woudenberg, and M. P. van Exter, “Measurements of spatial coherence of partially coherent light with and without orbital angular momentum,” J. Opt. Soc. Am. A27(12), 2630–2637 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Observation of interference pattern in the intensity correlation of a non-local object using a Hanbury Brown and Twiss-type experiment,” Europhys. Lett.82(3), 34004 (2008).
    [CrossRef]
  17. I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
    [CrossRef]
  18. Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics4(10), 721–726 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
  21. P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, “Engineering a square truncated lattice with light’s orbital angular momentum,” Opt. Express19(21), 20616–20621 (2011).
    [CrossRef] [PubMed]
  22. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3(5), 305–310 (2007).
    [CrossRef]
  23. S. Straupe and S. Kulik, “Quantum optics the quest for higher dimensionality,” Nat. Photonics4(9), 585–586 (2010).
    [CrossRef]

2012 (1)

H. C. Huang, Y. T. Lin, and M. F. Shih, “Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach-Zehnder interferometers,” Opt. Commun.285(4), 383–388 (2012).
[CrossRef]

2011 (2)

2010 (4)

H. D. Pires, J. Woudenberg, and M. P. van Exter, “Measurements of spatial coherence of partially coherent light with and without orbital angular momentum,” J. Opt. Soc. Am. A27(12), 2630–2637 (2010).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics4(10), 721–726 (2010).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105(5), 053904 (2010).
[CrossRef] [PubMed]

S. Straupe and S. Kulik, “Quantum optics the quest for higher dimensionality,” Nat. Photonics4(9), 585–586 (2010).
[CrossRef]

2009 (1)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett.95(13), 131110 (2009).
[CrossRef]

2008 (2)

I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Observation of interference pattern in the intensity correlation of a non-local object using a Hanbury Brown and Twiss-type experiment,” Europhys. Lett.82(3), 34004 (2008).
[CrossRef]

I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
[CrossRef]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3(5), 305–310 (2007).
[CrossRef]

2006 (1)

W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
[CrossRef] [PubMed]

2004 (4)

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett.92(14), 143905 (2004).
[CrossRef] [PubMed]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl Opt.6(2), 259–268 (2004).
[CrossRef]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys.6, 71 (2004).
[CrossRef]

I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation vortices in partially coherent light: theory,” J. Opt. Soc. Am. B21(11), 1895–1900 (2004).
[CrossRef]

2003 (2)

2001 (1)

1998 (1)

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt.45(3), 539–554 (1998).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

1971 (1)

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Baumgartl, J.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl Opt.6(2), 259–268 (2004).
[CrossRef]

Bogatyryova, G. V.

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt.45(3), 539–554 (1998).
[CrossRef]

Bromberg, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics4(10), 721–726 (2010).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett.95(13), 131110 (2009).
[CrossRef]

Caetano, D. P.

I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
[CrossRef]

I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Observation of interference pattern in the intensity correlation of a non-local object using a Hanbury Brown and Twiss-type experiment,” Europhys. Lett.82(3), 34004 (2008).
[CrossRef]

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105(5), 053904 (2010).
[CrossRef] [PubMed]

Dholakia, K.

Duan, Z. H.

W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
[CrossRef] [PubMed]

Fel’de, C. V.

Fonseca, E. J. S.

P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, “Engineering a square truncated lattice with light’s orbital angular momentum,” Opt. Express19(21), 20616–20621 (2011).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105(5), 053904 (2010).
[CrossRef] [PubMed]

I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Observation of interference pattern in the intensity correlation of a non-local object using a Hanbury Brown and Twiss-type experiment,” Europhys. Lett.82(3), 34004 (2008).
[CrossRef]

I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
[CrossRef]

Gbur, G.

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun.222(1-6), 117–125 (2003).
[CrossRef]

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt.45(3), 539–554 (1998).
[CrossRef]

Hanson, S. G.

W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
[CrossRef] [PubMed]

Hickmann, J. M.

P. H. F. Mesquita, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, “Engineering a square truncated lattice with light’s orbital angular momentum,” Opt. Express19(21), 20616–20621 (2011).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105(5), 053904 (2010).
[CrossRef] [PubMed]

I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Observation of interference pattern in the intensity correlation of a non-local object using a Hanbury Brown and Twiss-type experiment,” Europhys. Lett.82(3), 34004 (2008).
[CrossRef]

I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
[CrossRef]

Huang, H. C.

H. C. Huang, Y. T. Lin, and M. F. Shih, “Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach-Zehnder interferometers,” Opt. Commun.285(4), 383–388 (2012).
[CrossRef]

Jesus-Silva, A. J.

Jones, A. L.

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett.95(13), 131110 (2009).
[CrossRef]

Kirk, J. P.

Kulik, S.

S. Straupe and S. Kulik, “Quantum optics the quest for higher dimensionality,” Nat. Photonics4(9), 585–586 (2010).
[CrossRef]

Lahini, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics4(10), 721–726 (2010).
[CrossRef]

Leach, J.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys.6, 71 (2004).
[CrossRef]

Lin, Y. T.

H. C. Huang, Y. T. Lin, and M. F. Shih, “Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach-Zehnder interferometers,” Opt. Commun.285(4), 383–388 (2012).
[CrossRef]

Maleev, I. D.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett.92(14), 143905 (2004).
[CrossRef] [PubMed]

I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation vortices in partially coherent light: theory,” J. Opt. Soc. Am. B21(11), 1895–1900 (2004).
[CrossRef]

Marathay, A. S.

I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation vortices in partially coherent light: theory,” J. Opt. Soc. Am. B21(11), 1895–1900 (2004).
[CrossRef]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett.92(14), 143905 (2004).
[CrossRef] [PubMed]

Mesquita, P. H. F.

Miyamoto, Y.

W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
[CrossRef] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3(5), 305–310 (2007).
[CrossRef]

Mourka, A.

Movilla, J. M.

Olindo, C.

I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
[CrossRef]

Padgett, M. J.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys.6, 71 (2004).
[CrossRef]

Palacios, D. M.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett.92(14), 143905 (2004).
[CrossRef] [PubMed]

I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation vortices in partially coherent light: theory,” J. Opt. Soc. Am. B21(11), 1895–1900 (2004).
[CrossRef]

Pires, H. D.

Polyanskii, P. V.

Ponomarenko, S. A.

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt.45(3), 539–554 (1998).
[CrossRef]

Serna, J.

Shanor, C.

Shih, M. F.

H. C. Huang, Y. T. Lin, and M. F. Shih, “Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach-Zehnder interferometers,” Opt. Commun.285(4), 383–388 (2012).
[CrossRef]

Silberberg, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics4(10), 721–726 (2010).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett.95(13), 131110 (2009).
[CrossRef]

Small, E.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics4(10), 721–726 (2010).
[CrossRef]

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105(5), 053904 (2010).
[CrossRef] [PubMed]

Soskin, M. S.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Straupe, S.

S. Straupe and S. Kulik, “Quantum optics the quest for higher dimensionality,” Nat. Photonics4(9), 585–586 (2010).
[CrossRef]

Swartzlander, G. A.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett.92(14), 143905 (2004).
[CrossRef] [PubMed]

I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation vortices in partially coherent light: theory,” J. Opt. Soc. Am. B21(11), 1895–1900 (2004).
[CrossRef]

Takeda, M.

W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
[CrossRef] [PubMed]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3(5), 305–310 (2007).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3(5), 305–310 (2007).
[CrossRef]

van Exter, M. P.

Vicalvi, S.

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt.45(3), 539–554 (1998).
[CrossRef]

Vidal, I.

I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
[CrossRef]

I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Observation of interference pattern in the intensity correlation of a non-local object using a Hanbury Brown and Twiss-type experiment,” Europhys. Lett.82(3), 34004 (2008).
[CrossRef]

Visser, T. D.

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun.222(1-6), 117–125 (2003).
[CrossRef]

Wang, W.

W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
[CrossRef] [PubMed]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Wolf, E.

Woudenberg, J.

Wright, E. M.

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys.6, 71 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett.95(13), 131110 (2009).
[CrossRef]

Europhys. Lett. (1)

I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Observation of interference pattern in the intensity correlation of a non-local object using a Hanbury Brown and Twiss-type experiment,” Europhys. Lett.82(3), 34004 (2008).
[CrossRef]

J. Mod. Opt. (1)

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt.45(3), 539–554 (1998).
[CrossRef]

J. Opt. A, Pure Appl Opt. (1)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl Opt.6(2), 259–268 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Nat. Photonics (2)

S. Straupe and S. Kulik, “Quantum optics the quest for higher dimensionality,” Nat. Photonics4(9), 585–586 (2010).
[CrossRef]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics4(10), 721–726 (2010).
[CrossRef]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3(5), 305–310 (2007).
[CrossRef]

New J. Phys. (1)

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys.6, 71 (2004).
[CrossRef]

Opt. Commun. (2)

H. C. Huang, Y. T. Lin, and M. F. Shih, “Measuring the fractional orbital angular momentum of a vortex light beam by cascaded Mach-Zehnder interferometers,” Opt. Commun.285(4), 383–388 (2012).
[CrossRef]

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun.222(1-6), 117–125 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

I. Vidal, D. P. Caetano, C. Olindo, E. J. S. Fonseca, and J. M. Hickmann, “Second-order interference with orthogonally polarized pseudothermal beams,” Phys. Rev. A78(5), 053815 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett.105(5), 053904 (2010).
[CrossRef] [PubMed]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett.92(14), 143905 (2004).
[CrossRef] [PubMed]

W. Wang, Z. H. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: Local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett.96(7), 073902 (2006).
[CrossRef] [PubMed]

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge; New York, 1995).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Speckles patterns recorded in single shot mode using a CCD camera. Line (A) shows images of LG beams with m1 = 4 and m2 = 0.5 after diffracting by GGD without A1 and A2 apertures in the beam path. Line (B) shows images of LG beams with m1 = 2.5 and m2 = - 0.5 after diffracting by GGD with A1 and A2 in the beams path, respectively.

Fig. 3
Fig. 3

Numerical intensity correlation averaged over 100 realization (First column), theoretical results of amplitude (second column) and phase (third column) of coherence function, Eq. (6). All results were obtained without considering A1 and A2 apertures.

Fig. 4
Fig. 4

Numerical intensity correlation averaged over 100 realization (First column), theoretical results of amplitude (second column) and phase (third column) of coherence function, Eq. (6). All results were obtained considering a distributed object (A1 and A2 apertures).

Equations (6)

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E m ( r,ϕ )= E 0 | r w 0 | | m | exp( r 2 / w 0 2 )exp( imϕ ),
I 1 ( r 1 ) I 2 ( r 2 ) = E 1 ( r 1 ) E 2 ( r 2 ) E 1 ( r 1 ) E 2 ( r 2 ) = I 1 ( r 1 ) I 2 ( r 2 ) + | Γ( r 1 , r 2 ) | 2 ,
Γ( r 1 , r 2 )= E 1 ( r 1 ) E 2 ( r 2 ) .
Γ m 1 , m 2 ( r 1 , r 2 )= E 0 2 w 0 ( | m 1 |+| m 2 | ) r 1 | m 1 | r 2 | m 2 | exp( i m Γ ϕ Γ ) ×exp[ ( r 1 2 + r 2 2 ) / w 0 2 ]C( | r 1 r 2 | ),
Γ ˜ m 1 , m 2 ( k 1 , k 2 )= A 1 ( r 1 ) A 2 ( r 2 ) Γ m 1 , m 2 ( r 1 , r 2 ) exp( i k 2 r 2 i k 1 r 1 )d r 1 d r 2 ,
Γ ˜ m 1 , m 2 = E 0 2 w 0 ( | m 1 |+| m 2 | ) A 1 ( r 1 ) A 2 ( r 1 ) r 1 | m 1 |+| m 2 | e [ i( m 1 m 2 ) ϕ 1 ] e [ 2 r 1 2 / w 0 2 ] e [ 2i k r 1 ] d r 1 ,

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