Abstract

Conditions for generating a dark focus surrounded by light in all three dimensions are presented. A simple technique for generating such a dark region is demonstrated experimentally. The method is compared with previous attempts at creating a three-dimensional dark focus.

© 2004 Optical Society of America

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References

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  1. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
    [CrossRef]
  2. D. W. Zhang and X.-C. Yuan, Opt. Lett. 28, 740 (2003).
    [CrossRef] [PubMed]
  3. R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, 1750 (1999).
    [CrossRef]
  4. J. Arlt and M. J. Padgett, Opt. Lett. 25, 191 (2000).
    [CrossRef]
  5. D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
    [CrossRef]
  6. J. Courtial, Opt. Commun. 151, 1 (1998).
    [CrossRef]
  7. A. Kaplan, N. Friedman, M. Andersen, and N. Davidson, Phys. Rev. Lett. 87, 274101 (2001).
    [CrossRef]

2003 (2)

D. W. Zhang and X.-C. Yuan, Opt. Lett. 28, 740 (2003).
[CrossRef] [PubMed]

D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
[CrossRef]

2001 (1)

A. Kaplan, N. Friedman, M. Andersen, and N. Davidson, Phys. Rev. Lett. 87, 274101 (2001).
[CrossRef]

2000 (1)

1999 (2)

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
[CrossRef]

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, 1750 (1999).
[CrossRef]

1998 (1)

J. Courtial, Opt. Commun. 151, 1 (1998).
[CrossRef]

Andersen, M.

A. Kaplan, N. Friedman, M. Andersen, and N. Davidson, Phys. Rev. Lett. 87, 274101 (2001).
[CrossRef]

Arlt, J.

Courtial, J.

J. Courtial, Opt. Commun. 151, 1 (1998).
[CrossRef]

Davidson, N.

A. Kaplan, N. Friedman, M. Andersen, and N. Davidson, Phys. Rev. Lett. 87, 274101 (2001).
[CrossRef]

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, 1750 (1999).
[CrossRef]

Dholakia, K.

D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
[CrossRef]

Friedman, N.

A. Kaplan, N. Friedman, M. Andersen, and N. Davidson, Phys. Rev. Lett. 87, 274101 (2001).
[CrossRef]

Haist, T.

Kaplan, A.

A. Kaplan, N. Friedman, M. Andersen, and N. Davidson, Phys. Rev. Lett. 87, 274101 (2001).
[CrossRef]

Khaykovich, L.

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, 1750 (1999).
[CrossRef]

McGloin, D.

D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
[CrossRef]

Melville, H.

D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
[CrossRef]

Ozeri, R.

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, 1750 (1999).
[CrossRef]

Padgett, M. J.

Reicherter, M.

Sibbett, W.

D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
[CrossRef]

Spalding, C. C.

D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
[CrossRef]

Tiziani, H. J.

Wagemann, E. U.

Yuan, X.-C.

Zhang, D. W.

Opt. Commun. (2)

D. McGloin, C. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, Opt. Commun. 225, 215 (2003).
[CrossRef]

J. Courtial, Opt. Commun. 151, 1 (1998).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, 1750 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

A. Kaplan, N. Friedman, M. Andersen, and N. Davidson, Phys. Rev. Lett. 87, 274101 (2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Comparison of three techniques for generating dark focus: a, use of an amplitude hologram (data taken from Ref. 4); b, use of a phase element placed in the beam’s optical path (data taken from Ref. 3); c, use of two interfering beams with different curvatures. The far-field distribution for each method was calculated assuming a Gaussian-shape generating beam with σ=2 mm.

Fig. 2
Fig. 2

Schematic of the optical setup for generating dark focus: M, mirror; BS, beam splitter.

Fig. 3
Fig. 3

(a) Simulation of the optical field distribution around the focal region. Field cross section along the (b) z axis, (c) x axis, (d) the diagonal.

Fig. 4
Fig. 4

Experimental results showing the transverse intensity cross section of the light for different locations along the z axis. The left column shows the light distribution for the dark focus (Δϕ=1.5π), and the right column shows the light distribution of a dark ring (Δϕ=1.4π).

Equations (5)

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SEids=0,
U0,zpapAp expiψpGz+iϕp,
EReexp-r22σ2expikr22δ1+exp-r22σ2expikr22δ2+iΔϕ=2 exp-r22σ2coskr22δ+Δϕ2,
0aexp-r22σ2coskr2Δf4f2+Δϕ2rdr=0,
1δ=1f-1f+Δf/2Δf2f2,    Δf2f1.

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