Abstract

We demonstrate the efficient sorter of Bessel beams separating both the azimuthal and radial components. This is based upon the recently reported transformation of angular to transverse momentum states. We separately identify over forty azimuthal and radial components, with a radial spacing of 1588 m−1, and outline how the device could be used to identify the two spatial dimensions simultaneously.

© 2013 OSA

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  1. M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transferof orbital angular momentum,” Opt. Commun.96(1-3), 123–132 (1993).
    [CrossRef]
  2. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177(1-6), 297–301 (2000).
    [CrossRef]
  3. 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]
  4. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
    [CrossRef] [PubMed]
  5. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
    [CrossRef] [PubMed]
  6. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88(1), 013601 (2002).
    [CrossRef] [PubMed]
  7. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett.89(24), 240401 (2002).
    [CrossRef] [PubMed]
  8. J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys.4(4), 282–286 (2008).
    [CrossRef]
  9. 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,” Science329(5992), 662–665 (2010).
    [CrossRef] [PubMed]
  10. Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys.6, 131 (2004).
    [CrossRef]
  11. R. Celechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys.9(9), 328 (2007).
    [CrossRef]
  12. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
  13. J. Turunen, A. Vasara, and A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt.27(19), 3959–3962 (1988).
    [CrossRef] [PubMed]
  14. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A6(11), 1748–1754 (1989).
    [CrossRef] [PubMed]
  15. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A6(1), 150–152 (1989).
    [CrossRef]
  16. R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
    [CrossRef]
  17. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
    [CrossRef]
  18. I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun.282(6), 1078–1082 (2009).
    [CrossRef]
  19. M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express20(21), 23589–23597 (2012).
    [CrossRef] [PubMed]
  20. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004).
    [CrossRef] [PubMed]
  21. S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
    [CrossRef]
  22. J. Leach, M. J. Padgett, S. M. 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]
  23. M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (2011).
    [CrossRef]
  24. A. F. Abouraddy, T. M. Yarnall, and B. E. A. Saleh, “Angular and radial mode analyzer for optical beams,” Opt. Lett.36(23), 4683–4685 (2011).
    [CrossRef] [PubMed]
  25. I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express20(10), 10996–11004 (2012).
    [CrossRef] [PubMed]
  26. 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] [PubMed]
  27. 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(6), 064006 (2011).
    [CrossRef]
  28. G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett.36(10), 1863–1865 (2011).
    [CrossRef] [PubMed]
  29. M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20(3), 2110–2115 (2012).
    [CrossRef] [PubMed]
  30. C. López-Mariscal and K. Helmerson; “Shaped nondiffracting beams,” Opt. Lett.35(8), 1215–1217 (2010).
    [CrossRef] [PubMed]
  31. R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt.59(3), 259–267 (2012).
    [CrossRef]
  32. M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

2012 (4)

2011 (4)

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett.36(10), 1863–1865 (2011).
[CrossRef] [PubMed]

A. F. Abouraddy, T. M. Yarnall, and B. E. A. Saleh, “Angular and radial mode analyzer for optical beams,” Opt. Lett.36(23), 4683–4685 (2011).
[CrossRef] [PubMed]

M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (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(6), 064006 (2011).
[CrossRef]

2010 (3)

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] [PubMed]

C. López-Mariscal and K. Helmerson; “Shaped nondiffracting beams,” Opt. Lett.35(8), 1215–1217 (2010).
[CrossRef] [PubMed]

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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

2009 (1)

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun.282(6), 1078–1082 (2009).
[CrossRef]

2008 (1)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys.4(4), 282–286 (2008).
[CrossRef]

2007 (1)

R. Celechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys.9(9), 328 (2007).
[CrossRef]

2004 (2)

2002 (3)

J. Leach, M. J. Padgett, S. M. 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]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88(1), 013601 (2002).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett.89(24), 240401 (2002).
[CrossRef] [PubMed]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

2000 (2)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177(1-6), 297–301 (2000).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[CrossRef]

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

1996 (1)

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
[CrossRef]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transferof orbital angular momentum,” Opt. Commun.96(1-3), 123–132 (1993).
[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]

1989 (2)

1988 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Abouraddy, A. F.

Agnew, M.

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transferof orbital angular momentum,” Opt. Commun.96(1-3), 123–132 (1993).
[CrossRef]

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]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177(1-6), 297–301 (2000).
[CrossRef]

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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. 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]

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(4), 282–286 (2008).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett.36(10), 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] [PubMed]

M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transferof orbital angular momentum,” Opt. Commun.96(1-3), 123–132 (1993).
[CrossRef]

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]

Berkhout, G. C. G.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20(3), 2110–2115 (2012).
[CrossRef] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett.36(10), 1863–1865 (2011).
[CrossRef] [PubMed]

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(6), 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] [PubMed]

Boothroyd, S. A.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
[CrossRef]

Bouchal, Z.

R. Celechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys.9(9), 328 (2007).
[CrossRef]

Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys.6, 131 (2004).
[CrossRef]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

Boyd, R. W.

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express20(21), 23589–23597 (2012).
[CrossRef] [PubMed]

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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

Celechovský, R.

R. Celechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys.9(9), 328 (2007).
[CrossRef]

Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys.6, 131 (2004).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

Chrostowski, J.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
[CrossRef]

Courtial, J.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20(3), 2110–2115 (2012).
[CrossRef] [PubMed]

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(6), 064006 (2011).
[CrossRef]

M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (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] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. 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]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

Dholakia, K.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177(1-6), 297–301 (2000).
[CrossRef]

Dudley, A.

I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express20(10), 10996–11004 (2012).
[CrossRef] [PubMed]

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt.59(3), 259–267 (2012).
[CrossRef]

M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (2011).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Forbes, A.

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express20(21), 23589–23597 (2012).
[CrossRef] [PubMed]

I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express20(10), 10996–11004 (2012).
[CrossRef] [PubMed]

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt.59(3), 259–267 (2012).
[CrossRef]

M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (2011).
[CrossRef]

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun.282(6), 1078–1082 (2009).
[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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. 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]

Friberg, A. T.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Gibson, G.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Helmerson, K.

Indebetouw, G.

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,” Science329(5992), 662–665 (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,” Science329(5992), 662–665 (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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[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(4), 282–286 (2008).
[CrossRef]

Laakkonen, P.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[CrossRef]

Lavery, M.

M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (2011).
[CrossRef]

Lavery, M. P. J.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20(3), 2110–2115 (2012).
[CrossRef] [PubMed]

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(6), 064006 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett.36(10), 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] [PubMed]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

Leach, J.

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express20(21), 23589–23597 (2012).
[CrossRef] [PubMed]

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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. 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]

Litvin, I.

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun.282(6), 1078–1082 (2009).
[CrossRef]

Litvin, I. A.

Lopez-Mariscal, C.

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt.59(3), 259–267 (2012).
[CrossRef]

López-Mariscal, C.

Love, G. D.

MacDonald, R. P.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

McLaren, M.

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express20(21), 23589–23597 (2012).
[CrossRef] [PubMed]

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun.282(6), 1078–1082 (2009).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88(1), 013601 (2002).
[CrossRef] [PubMed]

Okamoto, T.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
[CrossRef]

Padgett, M.

M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (2011).
[CrossRef]

Padgett, M. J.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20(3), 2110–2115 (2012).
[CrossRef] [PubMed]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express20(21), 23589–23597 (2012).
[CrossRef] [PubMed]

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(6), 064006 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, “Measuring orbital angular momentum superpositions of light by mode transformation,” Opt. Lett.36(10), 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] [PubMed]

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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. 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]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

Pas’ko, V.

Robertson, D. J.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express20(3), 2110–2115 (2012).
[CrossRef] [PubMed]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

Rop, R.

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt.59(3), 259–267 (2012).
[CrossRef]

Roux, F. S.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Saleh, B. E. A.

Skidanov, R. V.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[CrossRef]

Sponselli, A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

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]

Steinhoff, N. K.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

Syrett, B. A.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88(1), 013601 (2002).
[CrossRef] [PubMed]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88(1), 013601 (2002).
[CrossRef] [PubMed]

Turunen, J.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[CrossRef]

A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A6(11), 1748–1754 (1989).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, and A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt.27(19), 3959–3962 (1988).
[CrossRef] [PubMed]

Tyler, G. A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

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

M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transferof orbital angular momentum,” Opt. Commun.96(1-3), 123–132 (1993).
[CrossRef]

Vasara, A.

Vasnetsov, M.

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett.89(24), 240401 (2002).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys.4(4), 282–286 (2008).
[CrossRef]

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett.89(24), 240401 (2002).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Wilner, A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transferof orbital angular momentum,” Opt. Commun.96(1-3), 123–132 (1993).
[CrossRef]

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]

Yao, A. 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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

Yarnall, T. M.

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett.89(24), 240401 (2002).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Mod. Opt. (1)

R. Rop, A. Dudley, C. Lopez-Mariscal, and A. Forbes, “Measuring the rotation rates of superpositions of higher-order Bessel beams,” J. Mod. Opt.59(3), 259–267 (2012).
[CrossRef]

J. Opt. (1)

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(6), 064006 (2011).
[CrossRef]

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

Nat. Phys. (1)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys.4(4), 282–286 (2008).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

New J. Phys. (4)

Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys.6, 131 (2004).
[CrossRef]

R. Celechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys.9(9), 328 (2007).
[CrossRef]

M. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys.13(9), 093014 (2011).
[CrossRef]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. Wilner, and M. J. Padgett, “Efficient measurement of orbital angular momentum over 50 states,” New J. Phys.in press.

Opt. Commun. (6)

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, and B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun.122(4-6), 169–177 (1996).
[CrossRef]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun.282(6), 1078–1082 (2009).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, “Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element,” Opt. Commun.175(4-6), 301–308 (2000).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transferof orbital angular momentum,” Opt. Commun.96(1-3), 123–132 (1993).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177(1-6), 297–301 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (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]

Phys. Rev. Lett. (6)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett.88(1), 013601 (2002).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett.89(24), 240401 (2002).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. 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]

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] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Science (1)

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,” Science329(5992), 662–665 (2010).
[CrossRef] [PubMed]

Supplementary Material (1)

» Media 1: MOV (3254 KB)     

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Figures (7)

Fig. 1
Fig. 1

(a): The annular rings of two Bessel beams are mapped to transverse momentum modes in (b). Cylindrical lenses (CL) arranged in a 4-f configuration map the transverse momentum modes to unique x- and y-coordinates in column (c).

Fig. 2
Fig. 2

(a) Schematic of the experimental setup for identifying the azimuthal and radial components of Bessel beams. L, lens (fL1 = 15 mm, fL2 = 125 mm, fL3 = 500 mm, fL4 = 500 mm); SLM, spatial light modulator; M, mirror; R, aspheric optical element; CL, cylindrical lens (fCL1 = 50 mm,(orientated to focus the y-axis), fCL2 = 100 mm (orientated to focus the x-axis), fCL3 = 50 mm (orientated to focus the y-axis)); CCD, CCD camera. (b) The phase profile of the annular ring with a zoomed-in insert of the alternating phase values.

Fig. 3
Fig. 3

(a) The Bessel beam and (b) lateral spot for kr = 2.62 × 104 m−1 and l = 5. Theoretical results are given as inserts.

Fig. 4
Fig. 4

(a) The position of the spot produced at the plane of the CCD as a function of l. Accompanying theoretical Bessel beams are given as inserts. (b) Relative fractions of the intensity at each detector position for l = 20 to + 20 (kr = 2.62 × 104 m−1). The strong diagonal and weak off-diagonal terms imply a highly accurate and precise mode sorter.

Fig. 5
Fig. 5

(a) The Bessel beam and (b) unraveled transverse momentum mode for l = + 1 and kr = 0.72 × 104 m−1. Theoretical results are given as inserts.

Fig. 6
Fig. 6

(a) The position of the transformed line produced at the plane of the CCD as a function of R. Accompanying theoretical Bessel beams are given as inserts. (b) Relative fractions of the intensity at each detector position for kr = 0.23 × 104 m−1 to 6.43 × 104 m−1 (l = + 1).

Fig. 7
Fig. 7

(a) Super-imposed Bessel beams and (b) the lateral spots produced at the plane of the CCD. Theoretical results are given as inserts.

Equations (8)

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

u(r,θ,z=0)= J l ( k r r)exp(ilθ).
[ u(r,θ) ]={ exp(ilθ) Rr 0 elsewhere .
v= d 2π arctan( y x ),
u= d 2π ln( x 2 + y 2 b )= d 2π ln( k r f kb ),
Δu= d 2π Δ k r k r ,
Δ k r 2π d k r δ.
Δ H = λfl d .
Δ V = d 2π ln( k r f kb ).

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