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.

© 2002 Optical Society of America

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References

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J. Mod. Opt.

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).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

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.

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.

Phys. Rev. Lett.

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]

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]

Phys. World

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

Science

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]

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)

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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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