Abstract

We use a Laguerre–Gaussian laser mode within an optical tweezers arrangement to demonstrate the transfer of the orbital angular momentum of a laser mode to a trapped particle. The particle is optically confined in three dimensions and can be made to rotate; thus the apparatus is an optical spanner. We show that the spin angular momentum of ± per photon associated with circularly polarized light can add to, or subtract from, the orbital angular momentum to give a total angular momentum. The observed cancellation of the spin and orbital angular momentum shows that, as predicted, a Laguerre–Gaussian mode with an azimuthal mode index l=1 has a well-defined orbital angular momentum corresponding to per photon.

© 1997 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Sec. 17.5, pp. 685–695.
  2. J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
    [CrossRef]
  3. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  4. D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
    [CrossRef]
  5. S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
    [CrossRef]
  6. M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
    [CrossRef]
  7. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
    [CrossRef]
  8. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef]
  9. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
    [CrossRef]
  10. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
    [CrossRef]
  11. M. Babiker, W. L. Power, and L. Allen, Phys. Rev. Lett. 73, 1239 (1994); S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).
    [CrossRef] [PubMed]
  12. N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
    [CrossRef]
  13. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef] [PubMed]
  14. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).
    [CrossRef] [PubMed]
  15. K. T. Gahagan and G. A. Swartzlander, Opt. Lett. 21, 827 (1996).
    [CrossRef] [PubMed]
  16. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
    [CrossRef]
  17. S. Oka, in Rheology, F. R. Eirich, ed. (Academic, New York, 1960), Vol. 3.

1996 (3)

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).
[CrossRef] [PubMed]

K. T. Gahagan and G. A. Swartzlander, Opt. Lett. 21, 827 (1996).
[CrossRef] [PubMed]

1995 (1)

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

1994 (4)

M. Babiker, W. L. Power, and L. Allen, Phys. Rev. Lett. 73, 1239 (1994); S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).
[CrossRef] [PubMed]

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

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

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

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

1992 (3)

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

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

1986 (1)

1980 (1)

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

1979 (1)

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

Agrawal, G. P.

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

Allen, L.

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

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

M. Babiker, W. L. Power, and L. Allen, Phys. Rev. Lett. 73, 1239 (1994); S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).
[CrossRef] [PubMed]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

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

Ashkin, A.

Babiker, M.

M. Babiker, W. L. Power, and L. Allen, Phys. Rev. Lett. 73, 1239 (1994); S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).
[CrossRef] [PubMed]

Barnett, S. M.

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

Beijersbergen, M. W.

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

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

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

Bjorkholm, J. E.

Chu, S.

Coerwinkel, R. P. C.

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

Dziedzic, J. M.

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).
[CrossRef] [PubMed]

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).
[CrossRef] [PubMed]

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

Gahagan, K. T.

Harris, M.

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[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.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).
[CrossRef] [PubMed]

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

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

Hill, C. A.

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

Kristensen, M.

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

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

Oka, S.

S. Oka, in Rheology, F. R. Eirich, ed. (Academic, New York, 1960), Vol. 3.

Padgett, M. J.

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

Pattanayak, D. N.

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

Power, W. L.

M. Babiker, W. L. Power, and L. Allen, Phys. Rev. Lett. 73, 1239 (1994); S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).
[CrossRef] [PubMed]

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

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Sec. 17.5, pp. 685–695.

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

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]

Swartzlander, G. A.

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Vaughan, J. M.

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

White, A. G.

Willetts, D. V.

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

Woerdman, J. P.

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

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

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

J. Mod. Opt. (1)

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

Opt. Commun. (5)

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

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

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

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Phys. Rev. A (3)

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

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

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

M. Babiker, W. L. Power, and L. Allen, Phys. Rev. Lett. 73, 1239 (1994); S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).
[CrossRef] [PubMed]

Other (2)

S. Oka, in Rheology, F. R. Eirich, ed. (Academic, New York, 1960), Vol. 3.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Sec. 17.5, pp. 685–695.

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Figures (2)

Fig. 1
Fig. 1

Experimental configuration of the optical spanner.

Fig. 2
Fig. 2

Successive frames of the video image showing the stop–start behavior of a 2-µm-diameter Teflon particle held with the optical spanner.

Equations (3)

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

l+σz+σz2kzr2p+l+1+1-1
l+σz
ωlim=τ/8πηr3.

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