Abstract

We demonstrate the experimental generation of a fractional Bessel beam by holographic means. Such fractional modes of Bessel beams possess an intrinsic opening gap across concentric intensity rings on propagation. We also show that the opening gaps within the fractional modes are diffraction free for a working distance while a fractional helical wave front is maintained.

© 2004 Optical Society of America

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References

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  1. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  2. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
    [Crossref] [PubMed]
  3. K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
    [Crossref]
  4. J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [Crossref]
  5. D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
    [Crossref]
  6. M. Florjańczyk, R. Tremblay, “Guiding of atoms in a traveling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448–450 (1989).
    [Crossref]
  7. G. Scott, M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
    [Crossref]
  8. J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [Crossref]
  9. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3961 (1988).
    [Crossref] [PubMed]
  10. A. Vasar, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am A 6, 1748–1754 (1989).
    [Crossref]
  11. J. A. Davis, J. Guertin, D. M. Cottrell, “Diffraction-free beams generated with programmable spatial light modulators,” Appl. Opt. 32, 6368–6370 (1993).
    [Crossref] [PubMed]
  12. S. H. Tao, W. M. Lee, X.-C. Yuan, “Dynamic optical manipulation with a higher-order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
    [Crossref] [PubMed]
  13. M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
    [Crossref]
  14. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  15. “512 × 512 multi-level/analog liquid crystal spatial light modulator” (Boulder Nonlinear System, Lafayette, Colo.), http:www.bnonlinear.com/pages/512slm.html .
  16. J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).
  17. W. M. Lee, X.-C. Yuan, D. Y. Tang, “Optical tweezers with multiple optical forces using double hologram interference,” Opt. Exp. 11, 199–207 (2003), http://www.opticsexpress.org .
    [Crossref]

2003 (3)

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

W. M. Lee, X.-C. Yuan, D. Y. Tang, “Optical tweezers with multiple optical forces using double hologram interference,” Opt. Exp. 11, 199–207 (2003), http://www.opticsexpress.org .
[Crossref]

S. H. Tao, W. M. Lee, X.-C. Yuan, “Dynamic optical manipulation with a higher-order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
[Crossref] [PubMed]

2002 (4)

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
[Crossref]

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

2000 (1)

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

1993 (1)

1992 (1)

G. Scott, M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

1989 (2)

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

M. Florjańczyk, R. Tremblay, “Guiding of atoms in a traveling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448–450 (1989).
[Crossref]

1988 (1)

1987 (1)

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

Arlt, J.

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

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
[Crossref]

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

Chavez-Cerda, S.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
[Crossref]

Cottrell, D. M.

Davis, J. A.

Dholakia, K.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
[Crossref]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref] [PubMed]

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

Dohlakia, K.

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

Durnin, J.

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

Eberly, J. H.

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

Florjanczyk, M.

M. Florjańczyk, R. Tremblay, “Guiding of atoms in a traveling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448–450 (1989).
[Crossref]

Friberg, A. T.

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

J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3961 (1988).
[Crossref] [PubMed]

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Guertin, J.

Lancaster, G. P. T.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

Lee, W. M.

S. H. Tao, W. M. Lee, X.-C. Yuan, “Dynamic optical manipulation with a higher-order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
[Crossref] [PubMed]

W. M. Lee, X.-C. Yuan, D. Y. Tang, “Optical tweezers with multiple optical forces using double hologram interference,” Opt. Exp. 11, 199–207 (2003), http://www.opticsexpress.org .
[Crossref]

Livesey, J.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

McArdle, M.

G. Scott, M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

McGloin, D.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref] [PubMed]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref] [PubMed]

Miceli, J. J.

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

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

Rhodes, D. P.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

Scott, G.

G. Scott, M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Tang, D. Y.

W. M. Lee, X.-C. Yuan, D. Y. Tang, “Optical tweezers with multiple optical forces using double hologram interference,” Opt. Exp. 11, 199–207 (2003), http://www.opticsexpress.org .
[Crossref]

Tao, S. H.

Tremblay, R.

M. Florjańczyk, R. Tremblay, “Guiding of atoms in a traveling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448–450 (1989).
[Crossref]

Turunen, J.

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

J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3961 (1988).
[Crossref] [PubMed]

Vasar, A.

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

Vasara, A.

Volke-Sepulveda, K.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
[Crossref]

Volksepulveda, K.

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

Yuan, X.-C.

S. H. Tao, W. M. Lee, X.-C. Yuan, “Dynamic optical manipulation with a higher-order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
[Crossref] [PubMed]

W. M. Lee, X.-C. Yuan, D. Y. Tang, “Optical tweezers with multiple optical forces using double hologram interference,” Opt. Exp. 11, 199–207 (2003), http://www.opticsexpress.org .
[Crossref]

Appl. Opt. (2)

J Opt. B (1)

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J Opt. B 4, S82–S89 (2002).
[Crossref]

J. Mod. Opt. (1)

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

J. Opt. Soc. Am A (1)

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

Nature (1)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref] [PubMed]

Opt. Commun. (5)

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[Crossref]

M. Florjańczyk, R. Tremblay, “Guiding of atoms in a traveling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448–450 (1989).
[Crossref]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, K. Dohlakia, “Revolving interference patterns for rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[Crossref]

Opt. Eng. (1)

G. Scott, M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

Opt. Exp. (1)

W. M. Lee, X.-C. Yuan, D. Y. Tang, “Optical tweezers with multiple optical forces using double hologram interference,” Opt. Exp. 11, 199–207 (2003), http://www.opticsexpress.org .
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

“512 × 512 multi-level/analog liquid crystal spatial light modulator” (Boulder Nonlinear System, Lafayette, Colo.), http:www.bnonlinear.com/pages/512slm.html .

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Figures (7)

Fig. 1
Fig. 1

FBB at z = 0 mm and n = 4.5: (a) intensity, (b) phase.

Fig. 2
Fig. 2

IBB at z = 0 mm and n = 4: (a) intensity, (b) phase.

Fig. 3
Fig. 3

Diffraction intensity distributions of the FBB and the IBB: (a) FBB of n = 4.5 at z = 300 mm, (b) IBB of n = 4 at z = 300 mm.

Fig. 4
Fig. 4

Hologram produced by the interference of the FBB of n = 4.5. The gray scales represent different phase values. The phase is quantized into 32 levels.

Fig. 5
Fig. 5

Schematic of the experimental setup.

Fig. 6
Fig. 6

Reconstructed FBB intensity patterns at several distances z from the SLM, n = 4.5: (a) z = 0.3 m, (b) z = 0.5 m, (c) z = 0.6 m, (d) z = 1 m.

Fig. 7
Fig. 7

Interference patterns at z = 1 m: (a) simulation of interference, n = 4.5 and n = -4.5, (b) simulation of interference, n = 4 and n = -4, (c) experimental interference, n = 4.5 and n = -4.5, (d) experimental interference, n = 4 and n = -4.

Equations (1)

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E±nρ, ϕ=Jnαρexp±inϕ,

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