Abstract

Higher-order Bessel beams have been demonstrated to have the ability to trap and rotate low- and high-index particles simultaneously [Phys. Rev. A 66, 063402 (2002)]. The rotation and trapping is caused by the presence of orbital angular momentum arising from its azimuthal phase variation (that changes at integer multiples of 2π) and the concentric rings of the Bessel mode. We demonstrate for the first time to our knowledge a branch from the family of higher-order Bessel beams that has fractional azimuthal variation at its beam axis. This new family of laser beams has the ability to perform dynamic optical manipulation with dynamic control of a spatial light modulator. Furthermore, we take the opportunity to explore the propagation characteristics of higher-order Bessel beams for which the azimuthal phase changes at noninteger multiples of 2π.

© 2003 Optical Society of America

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  1. V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2002 (6)

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Z. Bouchal, Opt. Commun. 210, 155 (2002).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Artl, and K. Dholakia, J. Opt. B: Quantum Semiclassical Opt. 4, S82 (2002).
[CrossRef]

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

A. T. O'Neil, I. Macviar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

2000 (1)

J. Artl and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

1996 (1)

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

1994 (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

1993 (2)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

J. A. Davis, J. Guertin, and D. M. Cottrell, Appl. Opt. 32, 6368 (1993).
[CrossRef] [PubMed]

1988 (1)

Allen, L.

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

A. T. O'Neil, I. Macviar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Arlt, J.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

Artl, J.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Artl, and K. Dholakia, J. Opt. B: Quantum Semiclassical Opt. 4, S82 (2002).
[CrossRef]

J. Artl and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Barnett, S. M.

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Bouchal, Z.

Z. Bouchal, Opt. Commun. 210, 155 (2002).
[CrossRef]

Carcole, E.

Chávez-Cerda, S.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Artl, and K. Dholakia, J. Opt. B: Quantum Semiclassical Opt. 4, S82 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Dholakia, K.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Artl, and K. Dholakia, J. Opt. B: Quantum Semiclassical Opt. 4, S82 (2002).
[CrossRef]

J. Artl and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Franke-Arnold, S.

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

Friberg, A. T.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Artl, and K. Dholakia, J. Opt. B: Quantum Semiclassical Opt. 4, S82 (2002).
[CrossRef]

Guertin, J.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Lancaster, G. P. T.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

Livesey, J.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

Macviar, I.

A. T. O'Neil, I. Macviar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

McGloin, D.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

O'Neil, A. T.

A. T. O'Neil, I. Macviar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

Padgett, M. J.

A. T. O'Neil, I. Macviar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

Rhodes, D. P.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Sibbett, W.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Soskin, M. S.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Turunen, J.

Vasara, A.

Vasnetsov, V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Volke-Sepulveda, K.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Artl, and K. Dholakia, J. Opt. B: Quantum Semiclassical Opt. 4, S82 (2002).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Appl. Opt. (3)

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

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Artl, and K. Dholakia, J. Opt. B: Quantum Semiclassical Opt. 4, S82 (2002).
[CrossRef]

Opt. Commun. (6)

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, Opt. Commun. 214, 247 (2002).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Z. Bouchal, Opt. Commun. 210, 155 (2002).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

J. Artl and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Phys. Rev. A (1)

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Phys. Rev. A (1)

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

A. T. O'Neil, I. Macviar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

a, b, Computer-generated hologram for the Bessel beam of l=4 and l=4.5, respectively. c, d, Simulation results of the Bessel beam generated from the hologram of l=4 and 4.5, respectively, in the central spot. e, f, Phase of the Bessel beam’s central spot generated from the hologram of l=4 and l=4.5, respectively.

Fig. 2
Fig. 2

Setup for observing the fractional Bessel beam generated from the SLM. A, He–Ne laser operating at 632.8 nm; B, nonpolarized beam splitter; C, Boulder Nonlinear spatial light modulator; D, Sony IRIS color CCD; E, variable polarizing plate.

Fig. 3
Fig. 3

Series of the intensity pattern in the higher-order fractional l=4.5 Bessel beam observed from the setup shown in Fig. 2. a, b, and c, Simulation results of the intensity pattern at a distance of 1.0, 1.2, and 1.5 m, respectively. d–f, Actual experimental results at the same intervals.

Fig. 4
Fig. 4

Series of the intensity pattern in the higher-order fractional Bessel beam from l of a, 4.5; b, 4.6; c, 4.7; d, 4.8; e, 4.9; and f, 5, observed at a distance of 1.5 m.

Equations (3)

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

Tr=expilθexp-i2πuxexp-i2πr/r0.
Ar,z=expikz+ikr22zkiz×0D/2ρTρJ0kρrzexpikρ22zdρ,
Γz=P2πvl,

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