Abstract

We have developed a mode transformer comprising two custom refractive optical elements which convert orbital angular momentum states into transverse momentum states. This transformation allows for an efficient measurement of the orbital angular momentum content of an input light beam. We characterise the channel capacity of the system for 50 input modes, giving a maximum value of 3.46 bits per photon. Using an electron multiplying CCD (EMCCD) camera with a laser source attenuated such that on average there is less than one photon present within the system per measurement period, we demonstrate that the elements are efficient for the use in single photon experiments.

© 2012 OSA

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  1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
    [CrossRef]
  3. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Phys. Rev. Lett. 88, 013601 (2001).
    [CrossRef]
  4. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
    [CrossRef] [PubMed]
  5. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [CrossRef] [PubMed]
  6. J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
    [CrossRef]
  7. J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
    [CrossRef] [PubMed]
  8. V. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wave-fronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  9. N. Heckenberg, R. McDuff, C. Smith, and A. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef] [PubMed]
  10. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316, (2001).
    [CrossRef] [PubMed]
  11. S. S. Oemrawsingh, J. de Jong, X. Ma, and A. Aiello. “High- dimensional mode analyzers for spatial quantum entanglement, Phys. Rev. A 73, 032339, (2006)
    [CrossRef]
  12. L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
    [CrossRef]
  13. J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
    [CrossRef] [PubMed]
  14. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
    [CrossRef]
  15. O. Bryngdahl, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64(8), 1092–1099 (1974).
    [CrossRef]
  16. W. Hossack, A. Darling, and A. Dahdour, “Coordinate transformations with multiple computer-generated optical-elements,” J. Mod. Opt. 34, 1235–1250 (1987).
    [CrossRef]
  17. Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real-time optical correlator using computer generated hologram,” Opt. Commun. 47(1), 8–11 (1983).
    [CrossRef]
  18. M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
    [CrossRef]
  19. G. C. G. Berkhout, M. P. J. Lavery, M. W. Beijersbergen, and M. J. Padgett, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett. 36, 1863–1865 (2011).
    [CrossRef] [PubMed]
  20. T.A. Dow, M.H. Miller, and P.J. Falter, “Application of a fast tool servo fordiamond turning of non-rotationally symmetric surfaces,” J. Precision Eng. 13, 243–250 (1991).
    [CrossRef]
  21. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379 (1948).
  22. M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
    [CrossRef]
  23. J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14, 11919–11924 (2006).
    [CrossRef] [PubMed]

2011

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, M. W. Beijersbergen, and M. J. Padgett, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett. 36, 1863–1865 (2011).
[CrossRef] [PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
[CrossRef]

2010

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[CrossRef]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

2008

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

2006

S. S. Oemrawsingh, J. de Jong, X. Ma, and A. Aiello. “High- dimensional mode analyzers for spatial quantum entanglement, Phys. Rev. A 73, 032339, (2006)
[CrossRef]

J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14, 11919–11924 (2006).
[CrossRef] [PubMed]

2004

2002

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef] [PubMed]

J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[CrossRef] [PubMed]

2001

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316, (2001).
[CrossRef] [PubMed]

1995

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

1992

N. Heckenberg, R. McDuff, C. Smith, and A. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

V. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wave-fronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

1991

T.A. Dow, M.H. Miller, and P.J. Falter, “Application of a fast tool servo fordiamond turning of non-rotationally symmetric surfaces,” J. Precision Eng. 13, 243–250 (1991).
[CrossRef]

1987

W. Hossack, A. Darling, and A. Dahdour, “Coordinate transformations with multiple computer-generated optical-elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[CrossRef]

1983

Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real-time optical correlator using computer generated hologram,” Opt. Commun. 47(1), 8–11 (1983).
[CrossRef]

1974

1948

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379 (1948).

Aiello, A.

S. S. Oemrawsingh, J. de Jong, X. Ma, and A. Aiello. “High- dimensional mode analyzers for spatial quantum entanglement, Phys. Rev. A 73, 032339, (2006)
[CrossRef]

Allen, L.

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Barnett, S.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

Bazhenov, V.

V. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wave-fronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, M. W. Beijersbergen, and M. J. Padgett, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett. 36, 1863–1865 (2011).
[CrossRef] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[CrossRef]

Berkhout, G. C. G.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, M. W. Beijersbergen, and M. J. Padgett, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett. 36, 1863–1865 (2011).
[CrossRef] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[CrossRef]

Boyd, R. W.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

Bryngdahl, O.

Courtial, J.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[CrossRef]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[CrossRef] [PubMed]

Dahdour, A.

W. Hossack, A. Darling, and A. Dahdour, “Coordinate transformations with multiple computer-generated optical-elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[CrossRef]

Darling, A.

W. Hossack, A. Darling, and A. Dahdour, “Coordinate transformations with multiple computer-generated optical-elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[CrossRef]

de Jong, J.

S. S. Oemrawsingh, J. de Jong, X. Ma, and A. Aiello. “High- dimensional mode analyzers for spatial quantum entanglement, Phys. Rev. A 73, 032339, (2006)
[CrossRef]

Dow, T.A.

T.A. Dow, M.H. Miller, and P.J. Falter, “Application of a fast tool servo fordiamond turning of non-rotationally symmetric surfaces,” J. Precision Eng. 13, 243–250 (1991).
[CrossRef]

Falter, P.J.

T.A. Dow, M.H. Miller, and P.J. Falter, “Application of a fast tool servo fordiamond turning of non-rotationally symmetric surfaces,” J. Precision Eng. 13, 243–250 (1991).
[CrossRef]

Franke-Arnold, S.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[CrossRef] [PubMed]

Gibson, G.

Heckenberg, N.

Hossack, W.

W. Hossack, A. Darling, and A. Dahdour, “Coordinate transformations with multiple computer-generated optical-elements,” J. Mod. Opt. 34, 1235–1250 (1987).
[CrossRef]

Ireland, D. G.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

Jack, B.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

Jha, A. K.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

Karimi, E.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

Keen, S.

Komatsu, S.

Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real-time optical correlator using computer generated hologram,” Opt. Commun. 47(1), 8–11 (1983).
[CrossRef]

Kwiat, P. G.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

Lavery, M. P. J.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, M. W. Beijersbergen, and M. J. Padgett, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett. 36, 1863–1865 (2011).
[CrossRef] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[CrossRef]

Leach, J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14, 11919–11924 (2006).
[CrossRef] [PubMed]

J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[CrossRef] [PubMed]

Love, G. D.

Ma, X.

S. S. Oemrawsingh, J. de Jong, X. Ma, and A. Aiello. “High- dimensional mode analyzers for spatial quantum entanglement, Phys. Rev. A 73, 032339, (2006)
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316, (2001).
[CrossRef] [PubMed]

Marrucci, L.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

McDuff, R.

Miller, M.H.

T.A. Dow, M.H. Miller, and P.J. Falter, “Application of a fast tool servo fordiamond turning of non-rotationally symmetric surfaces,” J. Precision Eng. 13, 243–250 (1991).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

Oemrawsingh, S. S.

S. S. Oemrawsingh, J. de Jong, X. Ma, and A. Aiello. “High- dimensional mode analyzers for spatial quantum entanglement, Phys. Rev. A 73, 032339, (2006)
[CrossRef]

Ohzu, H.

Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real-time optical correlator using computer generated hologram,” Opt. Commun. 47(1), 8–11 (1983).
[CrossRef]

Padgett, M.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. Padgett, S. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[CrossRef] [PubMed]

Padgett, M. J.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13, 064006 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, M. W. Beijersbergen, and M. J. Padgett, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett. 36, 1863–1865 (2011).
[CrossRef] [PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[CrossRef]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14, 11919–11924 (2006).
[CrossRef] [PubMed]

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

Pas’ko, V.

Piccirillo, B

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

Romero, J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–655 (2010).
[CrossRef] [PubMed]

Saito, Y.

Y. Saito, S. Komatsu, and H. Ohzu, “Scale and rotation invariant real-time optical correlator using computer generated hologram,” Opt. Commun. 47(1), 8–11 (1983).
[CrossRef]

Santamato, E.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

Saunter, C.

Sciarrino, F.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379 (1948).

Slussarenko, S.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001, (2011).
[CrossRef]

Smith, C.

Soskin, M.

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Figures (4)

Fig. 1
Fig. 1

(a) Conversion of OAM states into transverse momentum states with refractive optical elements. An image of the beam was captured in several transverse planes and overlaid (in red) to give the image shown above. (b) A beam carrying OAM is prepared through the use of a -forked hologram, realised using a spatial light modulator (SLM) and then passed through the two elements, represented as the green rectangle, required to perform the transformation of both the phase and intensity of the beam.

Fig. 2
Fig. 2

Height profiles (a,c) and photos (b,d) of refractive elements 1 (top) and 2 (bottom). The aperture size is d = 8mm, focal length f = 300mm and the parameter b = 0.00477. The surfaces were made from PMMA (Poly methyl methacrylate), using a machined radius of 5.64 mm, angular spacing 1°, radial spacing of 5 μm, spindle speed of 500 RPM, roughing feedrate 5 mm/minute with a cut depth of 20 μm and finishing feedrate 1 mm/minute with a cut depth of 10 μm [20].

Fig. 3
Fig. 3

(a) Channel capacity for a N of LG modes, where N = 2,4,6,...,50. Detector noise was measured with no light incident on the camera, which was overcome by setting a threshold with a signal to noise ratio of 3000 to 1. (b) The ratio of energy measured in each of the detector regions showing the degree of cross talk.

Fig. 4
Fig. 4

Using a EMCCD camera in single photon counting mode, images were generated by summing over 16383 frames. Each pixel has a dark count rate, generating noise on every pixels in the camera. The images is shown are the raw captured images. The dark count rate was assessed by counting the photons over the same capture period with the camera shutter closed. A threshold was set with a value corresponding to the mean, plus one standard deviation of the dark count rate. The corresponding graph is a some of each column, in blue, and superimposed with the results when a Wiener Noise reduction filter is applied shown in red. Summing under the red curve gives us an approximation of the number of photons received at the camera plane.

Equations (2)

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Z 1 ( x , y ) = a f ( n 1 ) [ y arctan ( y x ) x ln ( x 2 + y 2 b ) + x 1 a ( 1 2 ( x 2 + y 2 ) ) lens term ] ,
Z 2 ( x , y ) = a b f ( n 1 ) [ exp ( u a ) cos ( v a ) 1 a b ( 1 2 ( u 2 + v 2 ) ) lens term ] ,

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