Abstract

Different configurations of optical lattices with circular cylindrical geometry have been recently studied in the context of atom trapping from a theoretical viewpoint, giving rise to a number of proposed applications. A common problem for testing theoretical predictions is the difficulty in the experimental realization of some of the necessary optical potentials. Here we discuss the experimental generation of four different circular optical lattices in an efficient and simple way using a single spatial light modulator. Our approach allows switching between different light configurations with a time resolution given by the response time of the light modulator.

© 2010 Optical Society of America

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  1. J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
    [CrossRef]
  2. P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At., Mol., Opt. Phys. 37, 95–139 (1996).
  3. G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, “Quantum logic gates in optical lattices,” Phys. Rev. Lett. 82, 1060–1063 (1999).
    [CrossRef]
  4. L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95, 063201 (2005).
    [CrossRef]
  5. B. M. Peden, R. Bhat, M. Kramer, and M. J. Holland, “Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices,” J. Phys. B 40, 3725–3744 (2007).
    [CrossRef]
  6. T. Wang and S. F. Yelin, “Fast mode of rotated atoms in one-dimensional lattice rings,” Phys. Rev. A 76, 033619 (2007).
    [CrossRef]
  7. 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. A 45, 8185–8189 (1992).
    [CrossRef]
  8. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef]
  9. 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, 826–829 (1995).
    [CrossRef]
  10. K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
    [CrossRef]
  11. J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
    [CrossRef]
  12. M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
    [CrossRef]
  13. C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
    [CrossRef]
  14. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
    [CrossRef]
  15. R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
    [CrossRef]
  16. H. L. Haroutyunyan and G. Nienhuis, “Diffraction by circular optical lattices,” Phys. Rev. A 70, 063408 (2004).
    [CrossRef]
  17. K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
    [CrossRef]
  18. A. Vasara, J. Turunen, and A. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef]
  19. J. A. Davis, J. Guertin, and D. M. Cottrell, “Diffraction-free beams generated with programmable spatial light modulators,” Appl. Opt. 32, 6368–6370 (1993).
    [CrossRef]
  20. Z. Bouchal and M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
    [CrossRef]
  21. R. Jáuregui, “Rotational effects of twisted light on atoms beyond the paraxial approximation,” Phys. Rev. A 70, 033415 (2004).
    [CrossRef]
  22. R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
    [CrossRef]
  23. K. Volke-Sepúlveda and E. Ley-Koo, “General construction and connections of vector propagation invariant optical fields: TE and TM modes and polarization states,” J. Opt. A, Pure Appl. Opt. 8, 867–877 (2006).
    [CrossRef]
  24. A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, “Experimental generation and analysis of first-order TE and TM Bessel modes in free space,” Opt. Lett. 31, 1732–1734 (2006).
    [CrossRef]
  25. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
    [CrossRef]
  26. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
    [CrossRef]
  27. J. Turunen and A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993).
    [CrossRef]
  28. A. Siegman, Lasers (University Science Books, 1986), pp. 626–652.
  29. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [CrossRef]
  30. K. T. Gahagan and G. A. Swartzlander, Jr., “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15, 524–534 (1998).
    [CrossRef]
  31. V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
    [CrossRef]
  32. T. Cizmar, V. Garcés-Chávez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
    [CrossRef]
  33. A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New J. Phys. 11, 043004 (2009).
    [CrossRef]
  34. M. Bhattacharya, “Lattice with a twist: helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
    [CrossRef]
  35. J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit by polarization gradients: simple theoretical models,” J. Opt. Soc. Am. B 6, 2023–2045 (1989).
    [CrossRef]
  36. U. Ruiz-Corona and V. Arrizon-Peña, “Characterization of twisted liquid crystal spatial light modulators,” Proc. SPIE 6422, 1–7 (2007).
  37. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  38. D. Ganic, X. Gan, and M. Gu, “Optical trapping force with annular and doughnut laser beams based on vectorial diffraction,” Opt. Express 13, 1260–1265 (2005).
    [CrossRef]
  39. J. A. Davis, E. Carcole, and Don M. Cottrell, “Nondiffracting interference patterns generated with programmable spatial light modulators,” Appl. Opt. 35, 599–602 (1996).
    [CrossRef]
  40. F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
    [CrossRef]
  41. V. Arrizón, D. Sánchez-de-la-Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett. 34, 1456–1458 (2009).
    [CrossRef]
  42. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 311–312.
  43. J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

2009 (3)

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New J. Phys. 11, 043004 (2009).
[CrossRef]

V. Arrizón, D. Sánchez-de-la-Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett. 34, 1456–1458 (2009).
[CrossRef]

2007 (7)

M. Bhattacharya, “Lattice with a twist: helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
[CrossRef]

U. Ruiz-Corona and V. Arrizon-Peña, “Characterization of twisted liquid crystal spatial light modulators,” Proc. SPIE 6422, 1–7 (2007).

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

B. M. Peden, R. Bhat, M. Kramer, and M. J. Holland, “Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices,” J. Phys. B 40, 3725–3744 (2007).
[CrossRef]

T. Wang and S. F. Yelin, “Fast mode of rotated atoms in one-dimensional lattice rings,” Phys. Rev. A 76, 033619 (2007).
[CrossRef]

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[CrossRef]

2006 (3)

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

K. Volke-Sepúlveda and E. Ley-Koo, “General construction and connections of vector propagation invariant optical fields: TE and TM modes and polarization states,” J. Opt. A, Pure Appl. Opt. 8, 867–877 (2006).
[CrossRef]

A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, “Experimental generation and analysis of first-order TE and TM Bessel modes in free space,” Opt. Lett. 31, 1732–1734 (2006).
[CrossRef]

2005 (5)

D. Ganic, X. Gan, and M. Gu, “Optical trapping force with annular and doughnut laser beams based on vectorial diffraction,” Opt. Express 13, 1260–1265 (2005).
[CrossRef]

T. Cizmar, V. Garcés-Chávez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[CrossRef]

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[CrossRef]

2004 (2)

H. L. Haroutyunyan and G. Nienhuis, “Diffraction by circular optical lattices,” Phys. Rev. A 70, 063408 (2004).
[CrossRef]

R. Jáuregui, “Rotational effects of twisted light on atoms beyond the paraxial approximation,” Phys. Rev. A 70, 033415 (2004).
[CrossRef]

2003 (1)

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

2002 (2)

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
[CrossRef]

1999 (2)

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, “Quantum logic gates in optical lattices,” Phys. Rev. Lett. 82, 1060–1063 (1999).
[CrossRef]

1998 (1)

1996 (2)

1995 (2)

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, 826–829 (1995).
[CrossRef]

Z. Bouchal and M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (4)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

J. Turunen and A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993).
[CrossRef]

J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
[CrossRef]

J. A. Davis, J. Guertin, and D. M. Cottrell, “Diffraction-free beams generated with programmable spatial light modulators,” Appl. Opt. 32, 6368–6370 (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. A 45, 8185–8189 (1992).
[CrossRef]

1989 (2)

1987 (2)

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

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

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Allen, L.

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. A 45, 8185–8189 (1992).
[CrossRef]

Amico, L.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[CrossRef]

Andersen, M. F.

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Arlt, J.

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
[CrossRef]

Arrizón, V.

Arrizon-Peña, V.

U. Ruiz-Corona and V. Arrizon-Peña, “Characterization of twisted liquid crystal spatial light modulators,” Proc. SPIE 6422, 1–7 (2007).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[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. A 45, 8185–8189 (1992).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Bhat, R.

B. M. Peden, R. Bhat, M. Kramer, and M. J. Holland, “Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices,” J. Phys. B 40, 3725–3744 (2007).
[CrossRef]

Bhattacharya, M.

M. Bhattacharya, “Lattice with a twist: helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 311–312.

Bouchal, Z.

Z. Bouchal and M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

Brennen, G. K.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, “Quantum logic gates in optical lattices,” Phys. Rev. Lett. 82, 1060–1063 (1999).
[CrossRef]

Carcole, E.

Cataliotti, F.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[CrossRef]

Caves, C. M.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, “Quantum logic gates in optical lattices,” Phys. Rev. Lett. 82, 1060–1063 (1999).
[CrossRef]

Chávez-Cerda, S.

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Cizmar, T.

T. Cizmar, V. Garcés-Chávez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Clade, P.

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Cline, R. A.

J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Cohen-Tannoudji, C.

Cottrell, D. M.

Cottrell, Don M.

Dalibard, J.

Davidson, N.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[CrossRef]

Davis, J. A.

Deutsch, I. H.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, “Quantum logic gates in optical lattices,” Phys. Rev. Lett. 82, 1060–1063 (1999).
[CrossRef]

P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At., Mol., Opt. Phys. 37, 95–139 (1996).

Dholakia, K.

T. Cizmar, V. Garcés-Chávez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Firstenberg, O.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[CrossRef]

Flores-Pérez, A.

A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New J. Phys. 11, 043004 (2009).
[CrossRef]

A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, “Experimental generation and analysis of first-order TE and TM Bessel modes in free space,” Opt. Lett. 31, 1732–1734 (2006).
[CrossRef]

Friberg, A.

Friberg, A. T.

J. Turunen and A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993).
[CrossRef]

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, 826–829 (1995).
[CrossRef]

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Gahagan, K. T.

Gan, X.

Ganic, D.

Garcés-Chávez, V.

T. Cizmar, V. Garcés-Chávez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Gu, M.

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Guertin, J.

Hacyan, S.

R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[CrossRef]

Haroutyunyan, H. L.

H. L. Haroutyunyan and G. Nienhuis, “Diffraction by circular optical lattices,” Phys. Rev. A 70, 063408 (2004).
[CrossRef]

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, 826–829 (1995).
[CrossRef]

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, 826–829 (1995).
[CrossRef]

Heinzen, D. J.

J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
[CrossRef]

Helmerson, K.

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Hernández-Hernández, J.

Holland, M. J.

B. M. Peden, R. Bhat, M. Kramer, and M. J. Holland, “Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices,” J. Phys. B 40, 3725–3744 (2007).
[CrossRef]

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

Jáuregui, R.

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, “Experimental generation and analysis of first-order TE and TM Bessel modes in free space,” Opt. Lett. 31, 1732–1734 (2006).
[CrossRef]

R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[CrossRef]

R. Jáuregui, “Rotational effects of twisted light on atoms beyond the paraxial approximation,” Phys. Rev. A 70, 033415 (2004).
[CrossRef]

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Jessen, P. S.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, “Quantum logic gates in optical lattices,” Phys. Rev. Lett. 82, 1060–1063 (1999).
[CrossRef]

P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At., Mol., Opt. Phys. 37, 95–139 (1996).

Kramer, M.

B. M. Peden, R. Bhat, M. Kramer, and M. J. Holland, “Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices,” J. Phys. B 40, 3725–3744 (2007).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Ley-Koo, E.

K. Volke-Sepúlveda and E. Ley-Koo, “General construction and connections of vector propagation invariant optical fields: TE and TM modes and polarization states,” J. Opt. A, Pure Appl. Opt. 8, 867–877 (2006).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Méndez, G.

Miceli, J. J.

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

Miller, J. D.

J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
[CrossRef]

Natarajan, V.

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Nienhuis, G.

H. L. Haroutyunyan and G. Nienhuis, “Diffraction by circular optical lattices,” Phys. Rev. A 70, 063408 (2004).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Olivik, M.

Z. Bouchal and M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

Osterloh, A.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Peden, B. M.

B. M. Peden, R. Bhat, M. Kramer, and M. J. Holland, “Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices,” J. Phys. B 40, 3725–3744 (2007).
[CrossRef]

Petrov, D. V.

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

Phillips, W. D.

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Pugatch, R.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[CrossRef]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Ron, A.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[CrossRef]

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, 826–829 (1995).
[CrossRef]

Ruiz, U.

Ruiz-Corona, U.

U. Ruiz-Corona and V. Arrizon-Peña, “Characterization of twisted liquid crystal spatial light modulators,” Proc. SPIE 6422, 1–7 (2007).

Ryu, C.

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Sánchez-de-la-Llave, D.

Santillán, A. O.

A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New J. Phys. 11, 043004 (2009).
[CrossRef]

Shuker, M.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[CrossRef]

Sibbett, W.

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Siegman, A.

A. Siegman, Lasers (University Science Books, 1986), pp. 626–652.

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. A 45, 8185–8189 (1992).
[CrossRef]

Swartzlander, G. A.

Tabosa, J. W. R.

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

Turunen, J.

J. Turunen and A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993).
[CrossRef]

A. Vasara, J. Turunen, and A. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
[CrossRef]

Vasara, A.

Vaziri, A.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Volke-Sepúlveda, K.

A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New J. Phys. 11, 043004 (2009).
[CrossRef]

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, “Experimental generation and analysis of first-order TE and TM Bessel modes in free space,” Opt. Lett. 31, 1732–1734 (2006).
[CrossRef]

K. Volke-Sepúlveda and E. Ley-Koo, “General construction and connections of vector propagation invariant optical fields: TE and TM modes and polarization states,” J. Opt. A, Pure Appl. Opt. 8, 867–877 (2006).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Wang, T.

T. Wang and S. F. Yelin, “Fast mode of rotated atoms in one-dimensional lattice rings,” Phys. Rev. A 76, 033619 (2007).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[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. A 45, 8185–8189 (1992).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 311–312.

Yelin, S. F.

T. Wang and S. F. Yelin, “Fast mode of rotated atoms in one-dimensional lattice rings,” Phys. Rev. A 76, 033619 (2007).
[CrossRef]

Zemanek, P.

T. Cizmar, V. Garcés-Chávez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Adv. At., Mol., Opt. Phys. (1)

P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At., Mol., Opt. Phys. 37, 95–139 (1996).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

T. Cizmar, V. Garcés-Chávez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

J. Mod. Opt. (3)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

Z. Bouchal and M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

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

K. Volke-Sepúlveda and E. Ley-Koo, “General construction and connections of vector propagation invariant optical fields: TE and TM modes and polarization states,” J. Opt. A, Pure Appl. Opt. 8, 867–877 (2006).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S88 (2002).
[CrossRef]

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

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

J. Phys. B (2)

B. M. Peden, R. Bhat, M. Kramer, and M. J. Holland, “Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices,” J. Phys. B 40, 3725–3744 (2007).
[CrossRef]

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

New J. Phys. (2)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New J. Phys. 11, 043004 (2009).
[CrossRef]

Opt. Commun. (3)

M. Bhattacharya, “Lattice with a twist: helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (7)

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

H. L. Haroutyunyan and G. Nienhuis, “Diffraction by circular optical lattices,” Phys. Rev. A 70, 063408 (2004).
[CrossRef]

R. Jáuregui, “Rotational effects of twisted light on atoms beyond the paraxial approximation,” Phys. Rev. A 70, 033415 (2004).
[CrossRef]

R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[CrossRef]

J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
[CrossRef]

T. Wang and S. F. Yelin, “Fast mode of rotated atoms in one-dimensional lattice rings,” Phys. Rev. A 76, 033619 (2007).
[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. A 45, 8185–8189 (1992).
[CrossRef]

Phys. Rev. Lett. (8)

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

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, 826–829 (1995).
[CrossRef]

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

C. Ryu, M. F. Andersen, P. Clade, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[CrossRef]

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, “Quantum logic gates in optical lattices,” Phys. Rev. Lett. 82, 1060–1063 (1999).
[CrossRef]

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95, 063201 (2005).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Proc. SPIE (1)

U. Ruiz-Corona and V. Arrizon-Peña, “Characterization of twisted liquid crystal spatial light modulators,” Proc. SPIE 6422, 1–7 (2007).

Pure Appl. Opt. (1)

J. Turunen and A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993).
[CrossRef]

Other (2)

A. Siegman, Lasers (University Science Books, 1986), pp. 626–652.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 311–312.

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