Abstract

We demonstrate a general method for the first order compensation of singularity splitting in a vortex beam at a single plane. By superimposing multiple forked holograms on the SLM used to generate the vortex beam, we are able to compensate vortex splitting and generate beams with desired phase singularities of order = 0, 1, 2, and 3 in one plane. We then extend this method by application of a radial phase, in order to simultaneously compensate the observed vortex splitting at two planes (near and far field) for an = 2 beam.

© 2014 Optical Society of America

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  1. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
    [CrossRef]
  2. J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
    [CrossRef] [PubMed]
  3. A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
    [CrossRef] [PubMed]
  4. G. Molina-Terriza, A. Vaziri, R. Ursin, A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94(4), 040501 (2005).
    [CrossRef] [PubMed]
  5. M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597(2), 1266 (2003).
    [CrossRef]
  6. C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
    [CrossRef]
  7. F. Tamburini, B. Thidé, G. Molina-Terriza, G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
    [CrossRef]
  8. N. M. Elias, “Photon orbital angular momentum in astronomy,” Astron. Astrophys. 492, 883–922 (2008).
    [CrossRef]
  9. N. M. Elias, “Photon orbital angular momentum and torque metrics for single telescopes and interferometers,” Astron. Astrophys. 541, 101 (2012).
    [CrossRef]
  10. G. Foo, M. P. David, G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30(24), 3308–3310 (2005).
    [CrossRef]
  11. X. Zambrana-Puyalto, X. Vidal, G. Molina-Terriza, “Excitation of single multipolar modes with engineered cylindrically symmetric fields,” Opt. Express 20(22), 24536–24544 (2012).
    [CrossRef] [PubMed]
  12. I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159(1), 99–117 (1999).
    [CrossRef]
  13. F. Ricci, W. Löffler, M. P. van Exter, “Instability of higher-order optical vortices analyzed with a multi-pinhole interferometer,” Opt. Express 20(20), 22961–22975 (2012).
    [CrossRef] [PubMed]
  14. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
    [CrossRef]
  15. M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31(9), 1325–1327 (2006).
    [CrossRef] [PubMed]
  16. A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. 20(8), 1635–1643 (2003).
    [CrossRef]
  17. A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4), 237–247 (2004).
    [CrossRef]
  18. A. Wada, T. Ohtani, Y. Miyamoto, M. Takeda, “Propagation analysis of the Laguerre-Gaussian beam with astigmatism,” J. Opt. Soc. Am. 22(12), 2746–2755 (2005).
    [CrossRef]
  19. I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5), 422–428 (1993).
    [CrossRef]
  20. C. H. Schmitz, K. Uhrig, J. P. Spatz, J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
    [CrossRef] [PubMed]
  21. J. Carpenter, B. Thomsen, T. Wilkinson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett. 24(21), 1969–1972 (2012).
    [CrossRef]
  22. G. Molina-Terriza, J. P. Torres, 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]
  23. R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
    [CrossRef]
  24. J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
    [CrossRef]
  25. A. Kumar, P. Vaity, R. P. Singh, “Crafting the core asymmetry to lift the degeneracy of optical vortices,” Opt. Express 19(7), 6182–6190 (2011).
    [CrossRef] [PubMed]
  26. A. Kumar, P. Vaity, J. Bhatt, R. P. Singh, “Stability of higher order optical vortices produced by spatial light modulators,” J. Mod. Opt. 60, 1696–1700 (2013).
    [CrossRef]

2013

A. Kumar, P. Vaity, J. Bhatt, R. P. Singh, “Stability of higher order optical vortices produced by spatial light modulators,” J. Mod. Opt. 60, 1696–1700 (2013).
[CrossRef]

2012

F. Ricci, W. Löffler, M. P. van Exter, “Instability of higher-order optical vortices analyzed with a multi-pinhole interferometer,” Opt. Express 20(20), 22961–22975 (2012).
[CrossRef] [PubMed]

X. Zambrana-Puyalto, X. Vidal, G. Molina-Terriza, “Excitation of single multipolar modes with engineered cylindrically symmetric fields,” Opt. Express 20(22), 24536–24544 (2012).
[CrossRef] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

N. M. Elias, “Photon orbital angular momentum and torque metrics for single telescopes and interferometers,” Astron. Astrophys. 541, 101 (2012).
[CrossRef]

J. Carpenter, B. Thomsen, T. Wilkinson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett. 24(21), 1969–1972 (2012).
[CrossRef]

2011

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
[CrossRef]

F. Tamburini, B. Thidé, G. Molina-Terriza, G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[CrossRef]

A. Kumar, P. Vaity, R. P. Singh, “Crafting the core asymmetry to lift the degeneracy of optical vortices,” Opt. Express 19(7), 6182–6190 (2011).
[CrossRef] [PubMed]

2008

N. M. Elias, “Photon orbital angular momentum in astronomy,” Astron. Astrophys. 492, 883–922 (2008).
[CrossRef]

2007

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

2006

2005

G. Foo, M. P. David, G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30(24), 3308–3310 (2005).
[CrossRef]

A. Wada, T. Ohtani, Y. Miyamoto, M. Takeda, “Propagation analysis of the Laguerre-Gaussian beam with astigmatism,” J. Opt. Soc. Am. 22(12), 2746–2755 (2005).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94(4), 040501 (2005).
[CrossRef] [PubMed]

2004

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4), 237–247 (2004).
[CrossRef]

2003

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597(2), 1266 (2003).
[CrossRef]

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. 20(8), 1635–1643 (2003).
[CrossRef]

2002

G. Molina-Terriza, J. P. Torres, 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]

2001

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

1999

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159(1), 99–117 (1999).
[CrossRef]

1997

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[CrossRef]

1993

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5), 422–428 (1993).
[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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

Anzolin, G.

F. Tamburini, B. Thidé, G. Molina-Terriza, G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[CrossRef]

Barbieri, C.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5), 422–428 (1993).
[CrossRef]

Bazhenov, V. Y.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5), 422–428 (1993).
[CrossRef]

Bekshaev, A. Y.

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4), 237–247 (2004).
[CrossRef]

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. 20(8), 1635–1643 (2003).
[CrossRef]

Bhatt, J.

A. Kumar, P. Vaity, J. Bhatt, R. P. Singh, “Stability of higher order optical vortices produced by spatial light modulators,” J. Mod. Opt. 60, 1696–1700 (2013).
[CrossRef]

Bowman, R.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
[CrossRef]

Carpenter, J.

J. Carpenter, B. Thomsen, T. Wilkinson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett. 24(21), 1969–1972 (2012).
[CrossRef]

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Curtis, J. E.

D’Ambrosio, V.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
[CrossRef]

D’Onofrio, M.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Da Deppo, V.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

David, M. P.

Dennis, M. R.

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31(9), 1325–1327 (2006).
[CrossRef] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Di Trapani, P.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
[CrossRef]

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

Dravins, D.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Elias, N. M.

N. M. Elias, “Photon orbital angular momentum and torque metrics for single telescopes and interferometers,” Astron. Astrophys. 541, 101 (2012).
[CrossRef]

N. M. Elias, “Photon orbital angular momentum in astronomy,” Astron. Astrophys. 492, 883–922 (2008).
[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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

Foo, G.

Fornasier, S.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Fosbury, R. A. E.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Freund, I.

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159(1), 99–117 (1999).
[CrossRef]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[CrossRef]

Grier, D. G.

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

Harwit, M.

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597(2), 1266 (2003).
[CrossRef]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

Jedrkiewicz, O.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
[CrossRef]

Kumar, A.

A. Kumar, P. Vaity, J. Bhatt, R. P. Singh, “Stability of higher order optical vortices produced by spatial light modulators,” J. Mod. Opt. 60, 1696–1700 (2013).
[CrossRef]

A. Kumar, P. Vaity, R. P. Singh, “Crafting the core asymmetry to lift the degeneracy of optical vortices,” Opt. Express 19(7), 6182–6190 (2011).
[CrossRef] [PubMed]

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Löffler, W.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[CrossRef]

Miyamoto, Y.

A. Wada, T. Ohtani, Y. Miyamoto, M. Takeda, “Propagation analysis of the Laguerre-Gaussian beam with astigmatism,” J. Opt. Soc. Am. 22(12), 2746–2755 (2005).
[CrossRef]

Molina-Terriza, G.

X. Zambrana-Puyalto, X. Vidal, G. Molina-Terriza, “Excitation of single multipolar modes with engineered cylindrically symmetric fields,” Opt. Express 20(22), 24536–24544 (2012).
[CrossRef] [PubMed]

F. Tamburini, B. Thidé, G. Molina-Terriza, G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94(4), 040501 (2005).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, 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]

Naletto, G.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Nilsson, R.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Occhipinti, T.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Ohtani, T.

A. Wada, T. Ohtani, Y. Miyamoto, M. Takeda, “Propagation analysis of the Laguerre-Gaussian beam with astigmatism,” J. Opt. Soc. Am. 22(12), 2746–2755 (2005).
[CrossRef]

Padgett, M. J.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

Ricci, F.

Rubino, E.

R. Bowman, V. D’Ambrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, M. J. Padgett, “Optimisation of a low cost SLM for diffraction efficiency and ghost order diffraction,” Eur. Phys. J. Spec. Top. 199(1), 149–158 (2011).
[CrossRef]

Schmitz, C. H.

Singh, R. P.

A. Kumar, P. Vaity, J. Bhatt, R. P. Singh, “Stability of higher order optical vortices produced by spatial light modulators,” J. Mod. Opt. 60, 1696–1700 (2013).
[CrossRef]

A. Kumar, P. Vaity, R. P. Singh, “Crafting the core asymmetry to lift the degeneracy of optical vortices,” Opt. Express 19(7), 6182–6190 (2011).
[CrossRef] [PubMed]

Soskin, M. S.

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4), 237–247 (2004).
[CrossRef]

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. 20(8), 1635–1643 (2003).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[CrossRef]

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5), 422–428 (1993).
[CrossRef]

Spatz, J. P.

Swartzlander, G. A.

Takeda, M.

A. Wada, T. Ohtani, Y. Miyamoto, M. Takeda, “Propagation analysis of the Laguerre-Gaussian beam with astigmatism,” J. Opt. Soc. Am. 22(12), 2746–2755 (2005).
[CrossRef]

Tamburini, F.

F. Tamburini, B. Thidé, G. Molina-Terriza, G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[CrossRef]

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Thidé, B.

F. Tamburini, B. Thidé, G. Molina-Terriza, G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[CrossRef]

Thomsen, B.

J. Carpenter, B. Thomsen, T. Wilkinson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett. 24(21), 1969–1972 (2012).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, 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, 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]

Tur, M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

Uhrig, K.

Ursin, R.

G. Molina-Terriza, A. Vaziri, R. Ursin, A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94(4), 040501 (2005).
[CrossRef] [PubMed]

Uthas, H.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

Vaity, P.

A. Kumar, P. Vaity, J. Bhatt, R. P. Singh, “Stability of higher order optical vortices produced by spatial light modulators,” J. Mod. Opt. 60, 1696–1700 (2013).
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Vasnetsov, M. V.

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4), 237–247 (2004).
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A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. 20(8), 1635–1643 (2003).
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M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
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[CrossRef]

Vaziri, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94(4), 040501 (2005).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

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Wada, A.

A. Wada, T. Ohtani, Y. Miyamoto, M. Takeda, “Propagation analysis of the Laguerre-Gaussian beam with astigmatism,” J. Opt. Soc. Am. 22(12), 2746–2755 (2005).
[CrossRef]

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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

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A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

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J. Carpenter, B. Thomsen, T. Wilkinson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett. 24(21), 1969–1972 (2012).
[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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (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, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

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Zeilinger, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94(4), 040501 (2005).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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IEEE Photon. Technol. Lett.

J. Carpenter, B. Thomsen, T. Wilkinson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett. 24(21), 1969–1972 (2012).
[CrossRef]

J. Mod. Opt.

C. Barbieri, D. Dravins, T. Occhipinti, F. Tamburini, G. Naletto, V. Da Deppo, S. Fornasier, M. D’Onofrio, R. A. E. Fosbury, R. Nilsson, H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes,” J. Mod. Opt. 54(2–3), 191–197 (2007).
[CrossRef]

A. Kumar, P. Vaity, J. Bhatt, R. P. Singh, “Stability of higher order optical vortices produced by spatial light modulators,” J. Mod. Opt. 60, 1696–1700 (2013).
[CrossRef]

J. Opt. Soc. Am.

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. 20(8), 1635–1643 (2003).
[CrossRef]

A. Wada, T. Ohtani, Y. Miyamoto, M. Takeda, “Propagation analysis of the Laguerre-Gaussian beam with astigmatism,” J. Opt. Soc. Am. 22(12), 2746–2755 (2005).
[CrossRef]

Nat. Photonics

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[CrossRef]

Nat. Phys.

F. Tamburini, B. Thidé, G. Molina-Terriza, G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[CrossRef]

Nature

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

New J. Phys.

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
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Opt. Commun.

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159(1), 99–117 (1999).
[CrossRef]

A. Y. Bekshaev, M. S. Soskin, M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4), 237–247 (2004).
[CrossRef]

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5), 422–428 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[CrossRef]

Phys. Rev. Lett.

G. Molina-Terriza, A. Vaziri, R. Ursin, A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94(4), 040501 (2005).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, 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]

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Figures (7)

Fig. 1
Fig. 1

(a) OAM spectrum calculated for = 2, ℓ′ = 0, α′ = 0.19, ϑ′ = 4.5 radians. (b) Phase hologram for beam of = 2. (c) Phase hologram for beam of = 2, and ℓ′ and weighting and relative phase corresponding to (a). The center of both holograms in (b) and (c) are expanded to highlight the differences.

Fig. 2
Fig. 2

Experimental setup used to generate a beam with arbitrary OAM, , and subsequently compensate the observed separation of nulls in the near and far-field. The lens system consisting of lenses L3 and L4 magnifies and images the far-field spot onto the CCD. A typical image is given by inset (a). Lenses L3 and L5 magnify and image the near-field i.e. the plane at the SLM onto the CCD. A typical image is shown in inset (b). Note that the entire beam profile in (b) cannot be observed with the CCD. The focal lengths of the lenses are as follows: L1 = 25.4 mm, L2 = 75 mm, L3 = 500 mm, L4 = 35 mm, L5 = 125 mm. HWP = Half wave plate, SLM = spatial light modulator, BS = beam splitter, ND = neutral density filter, SF = spatial filter, CCD = charge-coupled device, HeNe = Helium-Neon laser.

Fig. 3
Fig. 3

(a)–(d) Far-field images of beams with OAM = 0, 1, 2 and 3 in the absence of any compensation. The configuration of lenses for these images was L3 and L4 (Fig. 2). (e)–(f) Near-field images of the same beams are given for = 0, 1, 2 and 3. The configuration used for these images was L3 and L5 (see Fig. 2). From these images (a)–(d) and (e)–(h), we can see that the effect of aberrations on a vortex beam is to induce a splitting of the central singularity and a deformation of the intensity profile. This is consistent with the existence of another mode with 1 = − 2. In all images a logarithmic intensity scale is used. The physical scale used in all images is the same 490px×490px (3mm×3mm).

Fig. 4
Fig. 4

Calculated far-field images of a beam with OAM = 0 (a) and = 0 + 1 = −2 (b) and experimentally measured far-field images of our = 0 beam uncompensated (c) and with compensation (d). Calculated images have identical scaling in z. In all images a logarithmic scale is used.

Fig. 5
Fig. 5

To construct the phase hologram used to generate two collinear beams with OAM = 2 and ℓ′ = 0, we calculate the complex amplitude of each individual beam, add them and extract the resulting phase profile (ψSLM). Parameters α′ and ϑ′ control the relative weighting and phase between the beams. When illuminated with a Gaussian beam, the output is a ℓ′ = 0 and a = 2 beam. Although not additive, displayed are the holograms associated with the ℓ′ = 0 component, = 2 component and the final hologram used to create the two collinear beams.

Fig. 6
Fig. 6

Far-field images of beams with OAM quantum numbers of = 0, 1, 2 and 3 (a)–(d) with compensation applied as detailed in the text. The deformation of the intensity profiles are decreased compared to Figs. 3(a) and 3(b). Vortex splitting associated with = 3 and 4 (c,d) has been reduced relative to Fig. 3. Near-field images of the same beams are given for = 0, 1, 2 and 3 (e)–(f). In all images a logarithmic scale is used.

Fig. 7
Fig. 7

Far-field (a) and near-field (b) images of a beam with OAM = 2 in the absence of any compensation. Far-field (c) and near-field (d) images of an = 2 beam compensated by the removal of the 1 component by destructive interference with a collinear beam of ℓ′. Far-field (e) and near-field (f) images of a = 2 beam with the same compensation as applied in (c),(d) but with a radial phase (Eq. (10)) applied to the ℓ′ = 0 compensation component. For the radial phase, r0 = 10 pixels (90 μm). The result of this additional radial phase is that the separation of the vortices in the near-field has been reduced from (c) to (e). In all images a logarithmic scale is used.

Equations (10)

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

U ( ρ , ϕ , z ) = C ( ρ , z ) × exp ( i ϕ )
E = C ( ρ , z ) exp ( i ϕ ) + n = 1 C n ( ρ , z ) exp ( i ( n ϕ + ϑ n ) ) ,
E C ( ρ , z ) exp ( i ϕ ) + C 1 ( ρ , z ) exp ( i ( 1 ϕ + ϑ 1 ) + C ( ρ , z ) exp ( i ( ϕ + ϑ ) )
Ψ SLM = arg [ exp ( i [ ϕ ] ) + α exp ( i [ ϕ + ϑ ] ) ]
E ( ρ , ϕ , z ) = G ( ρ , z ) exp [ i arctan ( sin ( ϕ ) + α sin ( ϕ + ϑ ) cos ( ϕ ) + α cos ( ϕ + ϑ ) ) ]
C ( ρ , z ) = 0 2 π E ( ρ , ϕ , z ) exp ( i ϕ ) d ϕ
F ( k x , k y ) = f ( x , y ) e i ( k x x + k y y ) d x d y
F ( 0 , 0 ) = f ( x , y ) d x d y
Ψ SLM = arg [ exp ( i [ ϕ ] ) + α exp ( i [ ϕ + ϑ + ψ r ( r ) ] ) ]
ψ r = { 0 if r r 0 π if r > r 0

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