Abstract

By analysis of the far-field cross-correlation function (CCF) of partially coherent optical beams, we demonstrate an implicit rule that the number of ring dislocations (dark zones) of the far-field CCF is equal to the original topological charge of an optical vortex rendered partially coherent. This novel link between an optical vortex and its correlation singularity may offer an efficient method for measuring the orbital angular momentum of partially coherent optical vortices in fields such as astrophysics and astronomy, as well as atmospheric laser communication.

© 2012 Optical Society of America

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  1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  2. H. He, M. Friese, and N. R. Heckenberg, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef]
  3. K. Dholakia and T. Čižmár, Nat. Photonics 5, 335 (2011).
    [CrossRef]
  4. A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
    [CrossRef]
  5. G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
    [CrossRef]
  6. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [CrossRef]
  7. I. B. Djordjevic, Opt. Express 19, 14277 (2011).
    [CrossRef]
  8. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
    [CrossRef]
  9. G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
    [CrossRef]
  10. C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
    [CrossRef]
  11. G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
    [CrossRef]
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    [CrossRef]
  13. C.-S. Guo, L.-L. Lu, and H.-T. Wang, Opt. Lett. 34, 3686 (2009).
    [CrossRef]
  14. C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
    [CrossRef]
  15. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
    [CrossRef]
  16. L. E. E. de Araujo and M. E. Anderson, Opt. Lett. 36, 787 (2011).
    [CrossRef]
  17. A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, Opt. Express 19, 5760 (2011).
    [CrossRef]
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    [CrossRef]
  19. Y. Liu, J. Pu, and B. Lü, Appl. Opt. 50, 4844 (2011).
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    [CrossRef]
  21. D. Palacios, I. Maleev, A. Marathay, and G. A. Swartzlander., Phys. Rev. Lett. 92, 143905 (2004).
    [CrossRef]
  22. Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
    [CrossRef]
  23. Y. Gu and G. Gbur, Opt. Commun. 283, 1209 (2010).
    [CrossRef]

2012 (2)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

2011 (6)

2010 (3)

Y. Gu and G. Gbur, Opt. Commun. 283, 1209 (2010).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

2009 (4)

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

C.-S. Guo, L.-L. Lu, and H.-T. Wang, Opt. Lett. 34, 3686 (2009).
[CrossRef]

2008 (2)

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
[CrossRef]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2004 (2)

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

D. Palacios, I. Maleev, A. Marathay, and G. A. Swartzlander., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

2003 (1)

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef]

1995 (1)

H. He, M. Friese, and N. R. Heckenberg, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

1992 (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Allen, L.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Anderson, M. E.

Anzolin, G.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
[CrossRef]

Barbieri, C.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
[CrossRef]

Baumgartl, J.

Beijersbergen, M.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Bianchini, A.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
[CrossRef]

Chavez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Cižmár, T.

K. Dholakia and T. Čižmár, Nat. Photonics 5, 335 (2011).
[CrossRef]

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

de Araujo, L. E. E.

Dholakia, K.

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

K. Dholakia and T. Čižmár, Nat. Photonics 5, 335 (2011).
[CrossRef]

A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, Opt. Express 19, 5760 (2011).
[CrossRef]

Djordjevic, I. B.

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Friese, M.

H. He, M. Friese, and N. R. Heckenberg, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Gbur, G.

Y. Gu and G. Gbur, Opt. Commun. 283, 1209 (2010).
[CrossRef]

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

Gu, Y.

Y. Gu and G. Gbur, Opt. Commun. 283, 1209 (2010).
[CrossRef]

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

Guo, C.-S.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

C.-S. Guo, L.-L. Lu, and H.-T. Wang, Opt. Lett. 34, 3686 (2009).
[CrossRef]

Han, Y.

He, H.

H. He, M. Friese, and N. R. Heckenberg, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, M. Friese, and N. R. Heckenberg, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Hradil, Z.

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Jennewein, T.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef]

Lavery, M. P. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Liu, Y.

Lu, L.-L.

Lü, B.

Maleev, I.

D. Palacios, I. Maleev, A. Marathay, and G. A. Swartzlander., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Marathay, A.

D. Palacios, I. Maleev, A. Marathay, and G. A. Swartzlander., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Mari, E.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

Mazilu, M.

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Mourka, A.

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, Opt. Express 19, 5760 (2011).
[CrossRef]

Padgett, M. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Palacios, D.

D. Palacios, I. Maleev, A. Marathay, and G. A. Swartzlander., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Pan, J. W.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef]

Prasciolu, M.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

Pu, J.

Rehácek, J.

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Romanato, F.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

Shanor, C.

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Sponselli, A.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Swartzlander, G. A.

D. Palacios, I. Maleev, A. Marathay, and G. A. Swartzlander., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Tamburini, F.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Tur, M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Umbriaco, G.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
[CrossRef]

Vaziri, A.

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef]

Vettenburg, T.

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

Villoresi, P.

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

Wang, H.-T.

Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Wei, G.-X.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Weihs, G.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef]

Willner, A. E.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Wright, E. M.

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, Opt. Express 19, 5760 (2011).
[CrossRef]

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yue, S.-J.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Zeilinger, A.

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef]

Zhao, G.

A&A (1)

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, A&A 488, 1159 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Earth Moon Planet (1)

C. Barbieri, F. Tamburini, G. Anzolin, A. Bianchini, E. Mari, A. Sponselli, G. Umbriaco, M. Prasciolu, F. Romanato, and P. Villoresi, Earth Moon Planet 105, 283 (2009).
[CrossRef]

Nat. Photonics (2)

K. Dholakia and T. Čižmár, Nat. Photonics 5, 335 (2011).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Opt. Commun. (2)

Y. Gu and G. Gbur, Opt. Commun. 282, 709 (2009).
[CrossRef]

Y. Gu and G. Gbur, Opt. Commun. 283, 1209 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Phys. Rev. Lett. (7)

H. He, M. Friese, and N. R. Heckenberg, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef]

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

D. Palacios, I. Maleev, A. Marathay, and G. A. Swartzlander., Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Far-field intensity (a)–(c) and cross-correlation functions (CCFs) (d)–(f) for m = 3 for coherence lengths L c .

Fig. 2.
Fig. 2.

One-dimensional far-field CCFs influenced by coherence lengths L c , where m = 1 .

Fig. 3.
Fig. 3.

Cross-correlation functions (CCFs) in the far-field plane for different topological charges, where L c = w 0 . (a)  m = 1 , (b)  m = 2 , (c)  m = 4 , (d)  m = 5 .

Equations (8)

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Γ ( ρ⃗ 1 , ρ⃗ 2 , 0 ) = E 0 ( ρ⃗ 1 · ρ⃗ 2 ) m exp ( | ρ⃗ 1 ρ⃗ 2 | 2 L c 2 ) exp ( ρ 1 2 + ρ 2 2 w 0 2 ) exp ( i m ( ϕ 2 ϕ 1 ) ) ,
Γ ( ρ⃗ 1 , ρ⃗ 2 , z ) = ( 1 λ z ) 2 d ρ⃗ 1 d ρ⃗ 2 Γ ( ρ⃗ 1 , ρ⃗ 2 , 0 ) exp ( 2 π i λ z ( ρ⃗ 1 · ρ⃗ 1 ρ⃗ 2 · ρ⃗ 2 ) ) ,
χ c ( x , y ) = ( 2 z 2 β k 2 ( x 2 + y 2 ) ( k 2 w 0 4 T c 4 + 4 z 2 α 2 ) ) k 2 w 0 8 T c 2 β 3 exp ( 2 k 2 α w 0 2 ( x 2 + y 2 ) β ) ,
α = w 0 2 + T c 2 ,
β = 4 z 2 α + k 2 w 0 4 T c 2 .
P i j = d x 1 d x 2 x 1 i x 2 j exp ( b 1 x 1 2 + c 1 x 1 + b 2 x 2 2 + c 2 x 2 + a x 1 x 2 ) .
P 00 = 2 π 4 b 1 b 2 a 2 exp ( b 1 c 2 2 + b 2 c 1 2 c 1 c 2 a 4 b 1 b 2 a 2 ) ,
P i j = i j P 00 ( c 1 ) i ( c 2 ) j ,

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