Abstract

We present a novel method for the efficient generation of even, odd, and helical Mathieu–Gauss beams of arbitrary order and ellipticity by means of a phase-only spatial light modulator (SLM). Our method consists of displaying the phase of the desired beam in the SLM; the reconstructed field is obtained on-axis following a spatial filtering process with an annular aperture. The propagation invariance and topological properties of the generated beams are investigated numerically and experimentally.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
  2. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
    [CrossRef]
  3. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 657.
  4. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
    [CrossRef] [PubMed]
  5. Z. Bouchal and M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
    [CrossRef]
  6. 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]
  7. J. Turunen and A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993).
    [CrossRef]
  8. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
    [CrossRef]
  9. J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz—Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
    [CrossRef]
  10. M. A. Bandres and J. C. Gutiérrez-Vega, “Elliptical beams,” Opt. Express 16, 21087–21092 (2008).
    [CrossRef] [PubMed]
  11. Yaroslav V. Kartashov, Alexey A. Egorov, Victor A. Vysloukh, and Lluis Torner, “Shaping soliton properties in Mathieu lattices,” Opt. Lett. 31, 238–240 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. 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] [PubMed]
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    [CrossRef]
  15. 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] [PubMed]
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    [CrossRef]
  17. 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]
  18. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [CrossRef]
  19. 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] [PubMed]
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    [CrossRef] [PubMed]
  21. S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett. 26, 1803–1805 (2001).
    [CrossRef]
  22. C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express 14, 4182–4187 (2006).
    [CrossRef] [PubMed]
  23. A. Ruelas, S. Lopez-Aguayo, and J. C. Gutiérrez-Vega, “Stable solitons in elliptical photonic lattices,” Opt. Lett. 33, 2785–2787 (2008).
    [CrossRef] [PubMed]
  24. F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79, 053852 (2009).
    [CrossRef]
  25. B. M. Rodríguez-Lara and R. Jáuregui, “Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry,” Phys. Rev. A 78, 033813 (2008).
    [CrossRef]
  26. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
    [CrossRef]
  27. S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
    [CrossRef]
  28. C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  30. 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] [PubMed]
  31. 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] [PubMed]
  32. I. Ricardez-Vargas and K. Volke-Sepúlveda, “Experimental generation and dynamical reconfiguration of different circular optical lattices for applications in atom trapping,” J. Opt. Soc. Am. B 27, 948–955 (2010).
    [CrossRef]
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    [CrossRef]
  34. J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

2010 (1)

2009 (2)

2008 (3)

2007 (1)

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

2006 (5)

C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express 14, 4182–4187 (2006).
[CrossRef] [PubMed]

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[CrossRef]

Yaroslav V. Kartashov, Alexey A. Egorov, Victor A. Vysloukh, and Lluis Torner, “Shaping soliton properties in Mathieu lattices,” Opt. Lett. 31, 238–240 (2006).
[CrossRef] [PubMed]

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]

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] [PubMed]

2005 (2)

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

J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz—Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
[CrossRef]

2004 (1)

2003 (1)

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

2002 (3)

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (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 Quant. Semiclass. 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]

2001 (2)

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett. 26, 1803–1805 (2001).
[CrossRef]

2000 (1)

1999 (1)

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]

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] [PubMed]

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

1993 (2)

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

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] [PubMed]

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] [PubMed]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. 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] [PubMed]

Allison, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

Andersen, M. F.

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] [PubMed]

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 Quant. Semiclass. Opt. 4, S82–S88 (2002).
[CrossRef]

Arrizón, V.

Bandres, M. A.

Bandrés, M. A.

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[CrossRef]

Beijersbergen, M. W.

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] [PubMed]

Berry, M. V.

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

Bouchal, Z.

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

Chávez-Cerda, S.

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
[CrossRef] [PubMed]

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 Quant. Semiclass. 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]

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett. 26, 1803–1805 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

Clade, P.

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] [PubMed]

Cottrell, D. M.

Courtial, J.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

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] [PubMed]

Davis, J. A.

Dholakia, K.

C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express 14, 4182–4187 (2006).
[CrossRef] [PubMed]

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 Quant. Semiclass. 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] [PubMed]

Eberly, J. H.

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

Egorov, Alexey A.

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 657.

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] [PubMed]

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] [PubMed]

Garcés-Chávez, V.

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 Quant. Semiclass. 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]

Guattari, G.

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

Guertin, J.

Gutiérrez-Vega, J. C.

A. Ruelas, S. Lopez-Aguayo, and J. C. Gutiérrez-Vega, “Stable solitons in elliptical photonic lattices,” Opt. Lett. 33, 2785–2787 (2008).
[CrossRef] [PubMed]

M. A. Bandres and J. C. Gutiérrez-Vega, “Elliptical beams,” Opt. Express 16, 21087–21092 (2008).
[CrossRef] [PubMed]

C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express 14, 4182–4187 (2006).
[CrossRef] [PubMed]

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[CrossRef]

J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz—Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
[CrossRef]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
[CrossRef] [PubMed]

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett. 26, 1803–1805 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[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] [PubMed]

Heckenberg, N. R.

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

Helmerson, K.

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] [PubMed]

Hu, B.

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79, 053852 (2009).
[CrossRef]

Indebetouw, G.

Iturbe-Castillo, M. D.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

Jáuregui, R.

B. M. Rodríguez-Lara and R. Jáuregui, “Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry,” Phys. Rev. A 78, 033813 (2008).
[CrossRef]

Kartashov, Yaroslav V.

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]

Lopez-Aguayo, S.

López-Mariscal, C.

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[CrossRef]

C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express 14, 4182–4187 (2006).
[CrossRef] [PubMed]

MacVicar, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[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] [PubMed]

Mihalache, D.

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79, 053852 (2009).
[CrossRef]

Milne, G.

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 657.

Natarajan, V.

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] [PubMed]

New, G. H. C.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett. 26, 1803–1805 (2001).
[CrossRef]

Nye, J. F.

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

O’Neil, A. T.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

Olivik, M.

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

Padgett, M. J.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

Padovani, C.

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

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] [PubMed]

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] [PubMed]

Ramírez, G. A.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Ricardez-Vargas, I.

Rodríguez-Dagnino, R. M.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Rodríguez-Lara, B. M.

B. M. Rodríguez-Lara and R. Jáuregui, “Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry,” Phys. Rev. A 78, 033813 (2008).
[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] [PubMed]

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] [PubMed]

Ruelas, A.

Ruiz, U.

Ryu, C.

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] [PubMed]

Sánchez-de-la-Llave, D.

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] [PubMed]

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]

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] [PubMed]

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]

Tepichín, E.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Torner, Lluis

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] [PubMed]

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] [PubMed]

Volke-Sepúlveda, K.

I. Ricardez-Vargas and K. Volke-Sepúlveda, “Experimental generation and dynamical reconfiguration of different circular optical lattices for applications in atom trapping,” J. Opt. Soc. Am. B 27, 948–955 (2010).
[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 Quant. Semiclass. 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]

Vysloukh, Victor A.

Woerdman, J. P.

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] [PubMed]

Ye, F.

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79, 053852 (2009).
[CrossRef]

Appl. Opt. (1)

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. (2)

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 Quant. Semiclass. Opt. (2)

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 Quant. Semiclass. Opt. 4, S82–S88 (2002).
[CrossRef]

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B Quant. Semiclass. Opt. 4, S52–S57 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Opt. Commun. (2)

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

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

Opt. Eng. (1)

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. A (4)

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]

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79, 053852 (2009).
[CrossRef]

B. M. Rodríguez-Lara and R. Jáuregui, “Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry,” Phys. Rev. A 78, 033813 (2008).
[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] [PubMed]

Phys. Rev. Lett. (5)

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] [PubMed]

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] [PubMed]

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

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

Proc. R. Soc. A (1)

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

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 (1)

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 657.

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Figures (7)

Fig. 1
Fig. 1

Simulation of the propagation of an input Gaussian beam impinging on a phase mask located at z = 4 f L encoding the phase of an even Mathieu beam of order r = 6 and ellipticity parameter q = 18 . (a), (b) Fourier spectrum just before and after the annular screen. (c)–(e) Transverse intensity distribution of the reconstructed field at different planes. (f) Phase mask. (g) Axial intensity distribution along propagation through the 4 f optical system. The dashed lines indicate the planes where the transverse profiles (c)–(e) were taken. The phase in the mask varies from 0 to π.

Fig. 2
Fig. 2

Same as Fig. 1, for a phase mask encoding a helical Mathieu beam of order r = 6 and ellipticity parameter q = 12 . The phase in the mask varies from 0 to 2 π .

Fig. 3
Fig. 3

Experimental setup. HWP, half-wave plate; SLM, spatial light modulator; P, polarizer; L, lenses; CCD, camera.

Fig. 4
Fig. 4

Experimental images of Mathieu–Gauss beams with r = 6 and q = 12 (left) and their corresponding Fourier spectra (right). From top to bottom: even MG beam, odd MG beam, and helical MG beam.

Fig. 5
Fig. 5

Test of the propagation invariance of the generated optical fields. Left column: even MG beam with r = 3 and q = 12 . Right column: odd MG beam with r = 6 and q = 18 . The plane z = 0 corresponds to the back focal plane of the second lens in the 4 f system.

Fig. 6
Fig. 6

Numerical simulations (left column) and experimental results (right column) of the transverse intensity distribution of two helical Mathieu–Gauss beams and their interference patterns with a plane wave propagating at a small angle relative to each other. (a)–(d) r = 6 and q = 18 , (e)–(h) r = 3 and q = 12 .

Fig. 7
Fig. 7

Knife-edge test for helical Mathieu–Gauss beams with r = 6 and q = 12 . (a) Simulation of the knife edge obstructing the beam at the plane z = 0 . (b) Numerical simulations (left) and experimental results (right) at the plane z = 10 cm from the knife edge. The top and bottom rows correspond to helical beams rotating in opposite directions.

Equations (3)

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

M r e ( u , v ) = sgn { c e r ( v ; q ) J e r ( u ; q ) } ,
M r o ( u , v ) = sgn { s e r ( v ; q ) J o r ( u ; q ) } ,
M r h ( u , v ) = exp { ± i arctan ( A r ( q ) c e r ( v ; k t , q ) J e r ( u ; k t , q ) B r ( q ) s e r ( v ; k t , q ) J o r ( u ; k t , q ) ) } .

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