Abstract

The manipulation of a Gaussian laser beam using conical diffraction in a high optical quality biaxial crystal of KGd(WO4)2 has been examined in detail with emphasis on the experimental techniques involved and intuitive explanations of the notable features. Two different optical arrangements were used to form the Pogendorff double-ring light pattern in the focal image plane. The formation of both diverging and non-diverging zeroth and first order Bessel beams was investigated. The various intensity distributions and polarization properties were measured and compared with the predictions of well-established theory.

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  1. W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Transactions of the Royal Irish Academy 17, 1–144 (1837).
  2. H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals” Phil. Mag. 1,112–120 and 207–210 (1833).
  3. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media 2nd Ed (Pergamon Press 1984) Chap. 11.
  4. M. Born, and E. Wolf, Principles of Optics 7th Ed (Cambridge University Press 1999) Chap. 15.
  5. J. G. Lunney and D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
    [CrossRef]
  6. A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).
  7. M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
    [CrossRef]
  8. M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
    [CrossRef]
  9. M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: Observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
    [CrossRef]
  10. M. V. Berry, M. R. Jeffrey, and M. J. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
    [CrossRef]
  11. L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (Bristol: Institute of physics publishing 2003).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. L. P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarization of a single photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517–2520 (2007).
    [CrossRef]
  16. 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]
  17. M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
    [CrossRef]

2007 (2)

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

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

2006 (3)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” N. J. Phys. 8(5), 75 (2006).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: Observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

J. G. Lunney and D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
[CrossRef]

2005 (1)

M. V. Berry, M. R. Jeffrey, and M. J. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[CrossRef]

2004 (1)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[CrossRef]

2002 (1)

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]

1999 (1)

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

1991 (1)

1987 (1)

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

1978 (1)

A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

1837 (1)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Transactions of the Royal Irish Academy 17, 1–144 (1837).

1833 (1)

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals” Phil. Mag. 1,112–120 and 207–210 (1833).

Aguiló, M.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Barnett, S. M.

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]

Belskii, A. M.

A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

Berry, M. V.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: Observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and M. J. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[CrossRef]

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[CrossRef]

Courtial, J.

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]

Deng, L. P.

Díaz, F.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Franke-Arnold, S.

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]

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” N. J. Phys. 8(5), 75 (2006).
[CrossRef]

Hamilton, W. R.

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Transactions of the Royal Irish Academy 17, 1–144 (1837).

Hermann, R. M.

Jeffrey, M. R.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: Observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and M. J. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[CrossRef]

Jennewein, T.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” N. J. Phys. 8(5), 75 (2006).
[CrossRef]

Khapaluyk, A. P.

A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

Leach, J.

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]

Lloyd, H.

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals” Phil. Mag. 1,112–120 and 207–210 (1833).

Lunney, J. G.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: Observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

J. G. Lunney and D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
[CrossRef]

Mansuripur, M. J.

M. V. Berry, M. R. Jeffrey, and M. J. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[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]

Nikolov, V.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Padgett, M. J.

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]

Pujol, M. C.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Rico, M.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Santos, X.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Solé, R.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Vaziri, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” N. J. Phys. 8(5), 75 (2006).
[CrossRef]

Wang, H.

Wang, K.

Weaire, D. W.

J. G. Lunney and D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
[CrossRef]

Weihs, G.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” N. J. Phys. 8(5), 75 (2006).
[CrossRef]

Wiggins, T. A.

Zaldo, C.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Zeilinger, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” N. J. Phys. 8(5), 75 (2006).
[CrossRef]

Appl. Phys. B (1)

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Santos, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68, 187–197 (1999).
[CrossRef]

Europhys. News (1)

J. G. Lunney and D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and M. J. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

N. J. Phys. (1)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” N. J. Phys. 8(5), 75 (2006).
[CrossRef]

Opt. Spectrosc. (1)

A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

Phil. Mag. (1)

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals” Phil. Mag. 1,112–120 and 207–210 (1833).

Phys. Rev. Lett. (2)

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]

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

Proc. R. Soc. A (1)

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: Observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

Prog. Opt. (1)

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

Transactions of the Royal Irish Academy (1)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Transactions of the Royal Irish Academy 17, 1–144 (1837).

Other (3)

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media 2nd Ed (Pergamon Press 1984) Chap. 11.

M. Born, and E. Wolf, Principles of Optics 7th Ed (Cambridge University Press 1999) Chap. 15.

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

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