Abstract

We present a novel phase with an entangled double-helix structure. Beams with this phase have the same transverse patterns as those of interference between two doughnut beams. This proposed method allows a complete set of the superpositions of the doughnut modes or the orbital angular momentum states with different topological orders to be obtained. Furthermore, it introduces a simple continuous and controlled rotation of the transverse patterns by use of a spatial light modulator. It can be used to form a three-dimensional structure by three-dimensional trapping in an optical tweezers setup or to study the quantum characteristics of an optical vortex.

© 2003 Optical Society of America

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References

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  1. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
    [CrossRef] [PubMed]
  2. M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
    [CrossRef]
  3. M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
    [CrossRef] [PubMed]
  4. J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  5. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  6. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef] [PubMed]
  7. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef] [PubMed]
  8. J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
    [CrossRef]
  9. D. W. Zhang and X.-C. Yuan, Opt. Lett. 28, 740 (2003).
    [CrossRef] [PubMed]
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 67.

2003

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

2001

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

1995

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

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Dholakia, K.

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

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]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 67.

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

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]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

MacDonald, M. P.

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Patterson, L.

M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (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.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, Opt. Express 10, 844 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Volke-Sepulaveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Volke-Sepulveda, K.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Yuan, X.-C.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Zhang, D. W.

Nature

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Opt. Commun.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

M. P. MacDonald, K. Volke-Sepulveda, L. Patterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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

Science

M. P. MacDonald, L. Paterson, K. Volke-Sepulaveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), p. 67.

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Figures (5)

Fig. 1
Fig. 1

(a) Projective plan of the entangled double-helix phase structure. (b) Its 3D view.

Fig. 2
Fig. 2

3D structure and phase difference of the entangled double-helix phase, with (a) the same two helicity chains and (b) the two opposite ones.

Fig. 3
Fig. 3

Superposition states of the different doughnut modes in the simulation. Rotation of (a) |u32, (b) |u42, (c) |u52, (d) |u1,-1, (e) |u2,-1, (f) |u2,-2.

Fig. 4
Fig. 4

Experimental results of the superposition states of |u1,-1,|u2,-1, and |u20,-20 in order from left to right.

Fig. 5
Fig. 5

Theoretical simulation (above) and experimental results (below) of |u5,-2 (left) and |u-5,2 (right).

Equations (2)

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

|umn=(|um+expiφ|un)/2,
E0x,y,z=0=A exp-πx2+y2/ω02expjΦx,y,

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