Abstract

In earlier work, we introduced new ways of generating a series of interference patterns formed from Laguerre–Gaussian (LG) beams, which are being used as advanced optical tweezers in creating and manipulating three-dimensional structures. In this work, we have succeeded in demonstrating, for the first time to our knowledge, double LG and LG beams with a Gaussian-beam interference using a Michelson interferometer. We have been able to observe LG interference of unequal azimuthal charge by using just two holograms. This is a new type of optical tweezers because the tweezers have the ability to transfer orbital angular momentum, spin angular momentum, and optical gradient force simultaneously to microparticles. This provides a great opportunity for investigating the force interaction within a single laser beam.

© 2003 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348 (1998).
    [Crossref]
  4. A. T. O’Neil, I. Macviar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
    [PubMed]
  5. J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113 (1994).
    [Crossref] [PubMed]
  6. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002).
    [Crossref]
  7. K. T. Gahagan and G. A. Swartzlander, Jr., “Simultaneous trapping of low-index and high-index microparticles observed with an optical trap,” J. Opt. Soc. Am. B 16, 533 (1999).
    [Crossref]
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    [Crossref] [PubMed]
  9. M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
    [Crossref] [PubMed]
  10. L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).
  11. K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World. 31 (2002).
  12. M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Revolving interference patterns for rotation optically trapped particles,” Opt. Commun. 201, 21 (2002)
    [Crossref]
  13. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422 (1993).
    [Crossref]
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    [Crossref]

2002 (4)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002).
[Crossref]

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World. 31 (2002).

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

2001 (1)

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

2000 (1)

1999 (1)

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348 (1998).
[Crossref]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

1994 (1)

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113 (1994).
[Crossref] [PubMed]

1993 (1)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422 (1993).
[Crossref]

1986 (1)

Allen, L.

A. T. O’Neil, I. Macviar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
[PubMed]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

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

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

Ashkin, A.

Basistiy, I. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422 (1993).
[Crossref]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422 (1993).
[Crossref]

Bjorkholm, J. E.

Bryan, P. E.

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

Chu, S.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002).
[Crossref]

Dholakia, K.

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World. 31 (2002).

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

Dohlakia, K.

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

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

Dultz, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

Dziedzic, J. M.

Finer, J. T.

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113 (1994).
[Crossref] [PubMed]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348 (1998).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Gahagan, K. T.

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002).
[Crossref]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348 (1998).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002).
[Crossref]

MacDonald, M.

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World. 31 (2002).

MacDonald, M. P.

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

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

Macviar, I.

A. T. O’Neil, I. Macviar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
[PubMed]

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348 (1998).
[Crossref]

O’Neil, A. T.

A. T. O’Neil, I. Macviar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
[PubMed]

Padgett, M. J.

A. T. O’Neil, I. Macviar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
[PubMed]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

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

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

Piestun, R.

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348 (1998).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Schmitzer, H.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

Shamir, J.

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

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

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

Simmons, R. M.

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113 (1994).
[Crossref] [PubMed]

Soskin, M. S.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422 (1993).
[Crossref]

Spalding, G.

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World. 31 (2002).

Spudich, J. A.

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113 (1994).
[Crossref] [PubMed]

Swartzlander, Jr., G. A.

Vasnetsov, V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422 (1993).
[Crossref]

Volksepulveda, K.

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

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

Yschechner, Y.

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nature (2)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348 (1998).
[Crossref]

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113 (1994).
[Crossref] [PubMed]

Opt. Commun. (3)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002).
[Crossref]

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

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422 (1993).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826 (1995).
[Crossref] [PubMed]

Phys. World. (1)

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World. 31 (2002).

Science (2)

M. P. MacDonald, L. Paterson, K. Volksepulveda, J. Arlt, W. Sibbett, and K. Dohlakia, “Creation and manipulation of three dimensional optically trapped structure,” Science 296, 1101 (2002).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, P. E. Bryan, J. Arlt, W. Sibbett, and K. Dohlakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912 (2001).
[Crossref] [PubMed]

Other (2)

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles (preprint),” J. Mod. Opt. (to be published).

A. T. O’Neil, I. Macviar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
[PubMed]

Supplementary Material (1)

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Figures (8)

Fig. 1.
Fig. 1.

Simulation results for single LG beam interference with a Gaussian are shown in A-C. Results of the double opposite helical LG beam are shown in D-F.

Fig. 2.
Fig. 2.

Michelson interferometer coupled with a hologram. A is a He–Ne laser operating at 632.8 nm. B is a computer-generated hologram (CGH) imprinted onto 35-mm slides. C is a nonpolarized beam splitter. D and E are two reflecting mirrors. F is a SONY IRIS Color CCD. G is a normal 1-mm-thick glass plate used for changing the path length, which will rotate the intensity pattern.

Fig. 3.
Fig. 3.

Double-hologram setup. A1 is a He–Ne laser operating at 632.8 nm. B1 and D1 are CGHs imprinted onto 35-mm slides. C1 is a normal glass plate of thickness 1 mm. E1 is the SONY IRIS Color CCD used to capture the resulting interference patterns.

Fig. 4.
Fig. 4.

Interference result of +1 and -1 diffraction orders with zeroth order. The -1 diffraction order helical wave front (red arrow) and the +1 diffraction (blue arrow) are shown. The zeroth order is misaligned with the respective diffraction orders (green arrow and yellow arrow).

Fig. 5.
Fig. 5.

Interference of the +1 and −1 diffraction orders. A and B show the interference of two misaligned LG beams, with charges 3 and 4 respectively. C, D, E, and F show collinear interference of two LG beams of opposite helicity with charges 2, 3, 4, and 5, respectively. Note that in A and D, the interference pattern are obtained from the hologram, which was written onto a glass plate with an e-beam.

Fig. 6.
Fig. 6.

Interference using the double-hologram method. A and B show the interference of the misdirected LG beams of charge 1 and 2 with a LG beam of charge 3. C, D, E, and F show the collinear interference of the LG beam with charge 1, 2, 4, and 5, respectively, with LG beam of charge 3.

Fig. 7.
Fig. 7.

Misaligned LG beam of charge 2 with LG beam of charge 3 using double-hologram methods. B and D show the interference pattern in A with the zeroth order. C and E are the collinear interference of the LG beam with charges 2 and 3 with the zeroth order.

Fig. 8.
Fig. 8.

(2.25 MB), Movie of azimuthal variation after interference of LG beams.

Equations (7)

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

E T = E ( L G p 1 l 1 ) + E ( L G p 2 l 2 ) 2 .
E ( L G p l ) [ r 2 w ( z ) ] l L p l [ 2 r 2 w 2 ( z ) ] exp ( r 2 w 2 ( z ) )
× exp ( i k r 2 z 2 ( z 2 + z R 2 ) ) exp ( i l ϕ ) exp i ( 2 p + l + 1 ) tan 1 z z R ,
E ( L G 0 1 ) = E 0 [ r 2 w ( z ) ] l exp i ( θ ) ,
E int = E 01 [ r 2 w ( z ) ] l 1 2 + E 02 [ r 2 w ( z ) ] l 2 2 + 2 E 01 E 02 [ r 2 w ( z ) ] l 1 + l 2 cos ( θ 1 θ 2 ) ,
l R = l 1 + l 2 h ¯ = 3 2 h ¯ = 1 h ¯ ,
N = l 1 l 2 = 3 + 2 = 5 ,

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