Abstract

Internal conical diffraction produces a superposition of orthogonally polarised zero- and first-order Bessel like beams from an incident circularly polarised Gaussian beam. For right-circularly polarised light, the first-order beam has an optical vortex of charge −1. Upon propagation of the first-order beam through a second biaxial crystal, a process which is termed cascade conical refraction, the generated beam is a superposition of orthogonally polarised fields of charge 0 and −1 or 0 and −2. This spin to orbital angular momentum conversion provides a new method for the generation and annihilation of optical vortices in an all-optical arrangement that is solely dependent on the incident polarisation and vortex handedness.

© 2011 OSA

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    [CrossRef]
  3. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
    [CrossRef]
  4. R. L. Eriksen, P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array,” Appl. Opt. 42(25), 5107–5111 (2003).
    [CrossRef] [PubMed]
  5. C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43(12), 2397–2399 (2004).
    [CrossRef] [PubMed]
  6. C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
    [CrossRef] [PubMed]
  7. E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).
  8. S. Straupe and S. Kulik, “Quantum optics: The quest for higher dimensionality,” Nat. Photonics 4(9), 585–586 (2010).
    [CrossRef]
  9. C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
    [CrossRef] [PubMed]
  10. M. V. Berry, M. J. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A: Pure App. Opt. 7, 685–690 (2005).
    [CrossRef]
  11. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
    [CrossRef]
  12. T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
    [CrossRef]
  13. M. Berry, “Conical diffraction asymptotics: Fine structure of Poggendorff rings and axial spike,” J. Opt. A: Pure Appl. Opt. 6, 289–300 (2004).
    [CrossRef]
  14. A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
    [CrossRef] [PubMed]
  15. M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt. 12(7), 075704 (2010).
    [CrossRef]
  16. D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
    [CrossRef] [PubMed]
  17. A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
    [CrossRef] [PubMed]
  18. S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
    [CrossRef] [PubMed]
  19. E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
    [CrossRef]
  20. L.-P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarisation of single-photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517–2520 (2007).
    [CrossRef]
  21. L. Chen and W. She, “Increasing Shannon dimensionality by hyperentanglement of spin and fractional orbital angular momentum,” Opt. Lett. 34(12), 1855–1857 (2009).
    [CrossRef] [PubMed]

2010 (6)

S. Straupe and S. Kulik, “Quantum optics: The quest for higher dimensionality,” Nat. Photonics 4(9), 585–586 (2010).
[CrossRef]

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
[CrossRef] [PubMed]

M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt. 12(7), 075704 (2010).
[CrossRef]

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[CrossRef]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

2009 (3)

L. Chen and W. She, “Increasing Shannon dimensionality by hyperentanglement of spin and fractional orbital angular momentum,” Opt. Lett. 34(12), 1855–1857 (2009).
[CrossRef] [PubMed]

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).

2008 (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[CrossRef]

2007 (1)

L.-P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarisation of single-photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517–2520 (2007).
[CrossRef]

2006 (1)

C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
[CrossRef] [PubMed]

2005 (2)

M. V. Berry, M. J. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A: Pure App. Opt. 7, 685–690 (2005).
[CrossRef]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

2004 (2)

M. Berry, “Conical diffraction asymptotics: Fine structure of Poggendorff rings and axial spike,” J. Opt. A: Pure Appl. Opt. 6, 289–300 (2004).
[CrossRef]

C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43(12), 2397–2399 (2004).
[CrossRef] [PubMed]

2003 (2)

R. L. Eriksen, P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array,” Appl. Opt. 42(25), 5107–5111 (2003).
[CrossRef] [PubMed]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[CrossRef] [PubMed]

2001 (1)

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Abdolvand, A.

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
[CrossRef] [PubMed]

Aiello, A.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[CrossRef]

Berry, M.

M. Berry, “Conical diffraction asymptotics: Fine structure of Poggendorff rings and axial spike,” J. Opt. A: Pure Appl. Opt. 6, 289–300 (2004).
[CrossRef]

Berry, M. V.

M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt. 12(7), 075704 (2010).
[CrossRef]

M. V. Berry, M. J. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A: Pure App. Opt. 7, 685–690 (2005).
[CrossRef]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Chen, L.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

L. Chen and W. She, “Increasing Shannon dimensionality by hyperentanglement of spin and fractional orbital angular momentum,” Opt. Lett. 34(12), 1855–1857 (2009).
[CrossRef] [PubMed]

Curtis, J. E.

C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
[CrossRef] [PubMed]

Daria, V. R.

R. L. Eriksen, P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array,” Appl. Opt. 42(25), 5107–5111 (2003).
[CrossRef] [PubMed]

Deng, L.-P.

L.-P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarisation of single-photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517–2520 (2007).
[CrossRef]

Donegan, J. F.

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

Eastham, P. R.

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

Eliel, E. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

Eriksen, R. L.

R. L. Eriksen, P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array,” Appl. Opt. 42(25), 5107–5111 (2003).
[CrossRef] [PubMed]

Franke-Arnold, S.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[CrossRef]

Glückstad, J.

R. L. Eriksen, P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array,” Appl. Opt. 42(25), 5107–5111 (2003).
[CrossRef] [PubMed]

Hershcovitz, O.

C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43(12), 2397–2399 (2004).
[CrossRef] [PubMed]

Hogervorst, W.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Hooft, G. W.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

Jeffrey, M. J.

M. V. Berry, M. J. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A: Pure App. Opt. 7, 685–690 (2005).
[CrossRef]

Jennewein, T.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[CrossRef] [PubMed]

Kalkandjiev, T. K.

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
[CrossRef] [PubMed]

Karimi, E.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).

Kazak, N. S.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Khilo, N. A.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

King, T. A.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Kulik, S.

S. Straupe and S. Kulik, “Quantum optics: The quest for higher dimensionality,” Nat. Photonics 4(9), 585–586 (2010).
[CrossRef]

Leach, J.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

Lipson, S. G.

C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43(12), 2397–2399 (2004).
[CrossRef] [PubMed]

Lunney, J. G.

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

Ma, X.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

Mansuripur, M.

M. V. Berry, M. J. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A: Pure App. Opt. 7, 685–690 (2005).
[CrossRef]

Marrucci, L.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).

Moed, S.

C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43(12), 2397–2399 (2004).
[CrossRef] [PubMed]

Nagali, E.

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).

O’Dwyer, D. P.

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

Oemrawsingh, S. S. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[CrossRef]

Padgett, M. J.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

Pan, J. W.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[CrossRef] [PubMed]

Peet, V.

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[CrossRef]

Phelan, C. F.

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

Piccirillo, B.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).

Rafailov, E. U.

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
[CrossRef] [PubMed]

Rakovich, Y. P.

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

Rodrigo, P. J.

R. L. Eriksen, P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array,” Appl. Opt. 42(25), 5107–5111 (2003).
[CrossRef] [PubMed]

Rotschild, C.

C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S. G. Lipson, “Adjustable spiral phase plate,” Appl. Opt. 43(12), 2397–2399 (2004).
[CrossRef] [PubMed]

Ryzhevich, A. A.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Santamato, E.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).

Schmitz, C. H. J.

C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
[CrossRef] [PubMed]

She, W.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

L. Chen and W. She, “Increasing Shannon dimensionality by hyperentanglement of spin and fractional orbital angular momentum,” Opt. Lett. 34(12), 1855–1857 (2009).
[CrossRef] [PubMed]

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E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

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C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
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S. Straupe and S. Kulik, “Quantum optics: The quest for higher dimensionality,” Nat. Photonics 4(9), 585–586 (2010).
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C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
[CrossRef] [PubMed]

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A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[CrossRef] [PubMed]

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S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

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L.-P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarisation of single-photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517–2520 (2007).
[CrossRef]

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L.-P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarisation of single-photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517–2520 (2007).
[CrossRef]

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A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[CrossRef] [PubMed]

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A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
[CrossRef] [PubMed]

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S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

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A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
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Appl. Opt. (3)

R. L. Eriksen, P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array,” Appl. Opt. 42(25), 5107–5111 (2003).
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[CrossRef] [PubMed]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eignmodes of light by thermally tuned q-plates,” Appl. Opt. 94, 231124 (2009).

J. Opt. (2)

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[CrossRef]

M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt. 12(7), 075704 (2010).
[CrossRef]

J. Opt. A: Pure App. Opt. (1)

M. V. Berry, M. J. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A: Pure App. Opt. 7, 685–690 (2005).
[CrossRef]

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

M. Berry, “Conical diffraction asymptotics: Fine structure of Poggendorff rings and axial spike,” J. Opt. A: Pure Appl. Opt. 6, 289–300 (2004).
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J. Opt. Soc. Am. B (1)

L.-P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarisation of single-photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517–2520 (2007).
[CrossRef]

Laser Photon. Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[CrossRef]

Nat. Photonics (1)

S. Straupe and S. Kulik, “Quantum optics: The quest for higher dimensionality,” Nat. Photonics 4(9), 585–586 (2010).
[CrossRef]

Opt. Commun. (1)

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Opt. Express (4)

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
[CrossRef] [PubMed]

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express 18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
[CrossRef] [PubMed]

Opt. Lett. (1)

L. Chen and W. She, “Increasing Shannon dimensionality by hyperentanglement of spin and fractional orbital angular momentum,” Opt. Lett. 34(12), 1855–1857 (2009).
[CrossRef] [PubMed]

Phys. Rev. (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Phys. Rev. A (1)

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[CrossRef] [PubMed]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[CrossRef] [PubMed]

Other (1)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (Bristol: Institute of Physics Publishing, (2003).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the cascade conical refraction process. Outputs A,B,C and D are discussed in the text.

Fig. 2
Fig. 2

Optical setup for cascade conical diffraction, including a Mach-Zehnder interferometer. The cascade element is removed to enable the imaging of the profiles from the first crystal. BS - beam splitters, M - Mirrors, WP1/2/3/4 are λ/4 plates, LP1/2 are linear polarisers. λ/2 plate is used to rotate the Gaussian reference arm polarisation to match the polarisation of the conical field.

Fig. 3
Fig. 3

Far-field intensity patterns of separated conically diffracting beam described by a Bessel function after first biaxial crystal. (a) (i) zero-order conically diffracting Bessel beam (ii) collinear interference pattern with a Gaussian beam (iii) wedge interference pattern. (b) first-order diffracting Bessel beam (ii) collinear interference pattern with a Gaussian beam (iii) wedge interference pattern showing first order edge dislocation. All images are 1.32 mm x 1.32 mm in size.

Fig. 4
Fig. 4

ℓ = −1 component of Path A and Path C from Fig. 1.(i) intensity profile (ii) collinear interference with a Gaussian beam (iii) wedge interference with a Gaussian beam.

Fig. 5
Fig. 5

ℓ = −2 component of Path B from Fig. 1. (i) intensity profile (ii) collinear interference with a Gaussian beam (iii) wedge interference with a Gaussian beam

Fig. 6
Fig. 6

ℓ = 0 component of Path D from Fig. 1. (i) Intensity profile (ii) collinear interference with a Gaussian beam (iii) wedge interference with a Gaussian beam

Fig. 7
Fig. 7

Measured (dashed) and calculated (solid) radial intensity profiles of (a) B12 , (b) B22 and (c) B02 beams generated in a two crystal cascade internal conical diffraction process. Calculated images of the intensity distribution are also shown.

Equations (16)

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E ( R , Z ) = k 2 π e i k ( P R 1 2 Z P 2 ) × [ cos ( k P R 0 ) I i sin ( k P R 0 ) M ( θ P ) ] a ( P ) d P
M ( θ P ) = ( cos θ P sin θ P sin θ P cos θ P )
M ( θ P ) = ( 0 e i θ P e i θ P 0 )
E ( R , Z ) = B 0 ( R , R 0 , Z ) e + ( ) + B 1 ( R , R 0 , Z ) e + ( ) i θ e ( + )
B 0 ( R , R 0 , Z ) = k 0 P cos ( k P R 0 ) a ( P ) J 0 ( k P R ) e 1 2 i k P 2 Z d P ,
B 1 ( R , R 0 , Z ) = k 0 P sin ( k P R 0 ) a ( P ) J 1 ( k P R ) e 1 2 i k P 2 Z d P ,
a ( P ) = i e 1 2 i k P 2 Z sin ( k P R 0 ) M ( θ P ) a i n ( P ) e = i e 1 2 i k P 2 Z sin ( k P R 0 ) e i θ P a i n ( P ) e +
E ( R , θ , Z ) = B 12 e i θ e + + B 02 e
B 02 = k 2 0 P ( cos ( 2 k P R 0 ) 1 ) a i n ( P ) J 0 ( k P R ) e 1 2 i k P 2 Z 2 d P
B 12 = k 2 0 P sin ( 2 k P R 0 ) a i n ( P ) J 1 ( k P R ) e 1 2 i k P 2 Z 2 d P
a ( P ) = i e 1 2 i k Z P 2 sin ( k P R 0 ) e i θ P a i n ( P ) e ,
E ( R , θ , Z ) = B 12 e i θ e + B 22 e 2 i θ e + ,
B 22 = k 2 0 P ( 1 cos ( 2 k P R 0 ) ) a i n ( P ) J 2 ( k P R ) e 1 2 i k P 2 Z 2 d P
a ( P ) = a ( P ) e i n θ p e + ( )
E ( R , θ , Z ) = i n e i n θ e + ( ) k 0 P J n ( k P R ) a ( P ) d P
e 1 2 i k P 2 Z { cos ( k P R 0 ) a ( P ) e i n θ p e + ( ) i sin ( k P R 0 ) e i θ P a ( P ) e i ( n + ( ) 1 ) θ p e + ( ) }

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