Abstract

Hexagonal arrays of micron sized silica beads have been trapped in three-dimensions within an optical lattice formed by the interference of multiple plane-waves. The optical lattice design with sharply peaked intensity gradients produces a stronger trapping force than the traditionally sinusoidal intensity distributions of other interferometric systems. The plane waves were generated using a single, phase-only, spatial light modulator (SLM), sited near a Talbot image plane of the traps. Compared to conventional optical tweezers, where the traps are formed in the Fourier-plane of the SLM, this approach may offer an advantage in the creation of large periodic array structures. This method of pattern formation may also be applicable to trapping arrays of atoms.

© 2005 Optical Society of America

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J. Mod Opt.

N. B. Simpson, L. Allen and M. J. Padgett, " Optical tweezers and optical spanners with Laguerre-Gaussian modes," J Mod Opt, 43, 2485-2491 (1996).
[CrossRef]

J. Mod. Opt.

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett and J. Cooper, "Defining the trapping limits of holographic optical tweezers," J. Mod. Opt. 51, 409-414 (2004).
[CrossRef]

H. He, N. R. Heckenberg and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams using high efficiency computer generated holograms," J. Mod. Opt, 42(1), 217-223 (1995).

26. M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt., 43, 10, 2139-2164 (1996).
[CrossRef]

JOSA A

R. Piestun and J. Shamir, "Generalized propagation invariant wave-fields," JOSA A., 15, 3039-3034 (1998).
[CrossRef]

Nature

M. P. MacDonald, G. C. Spalding, K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421- 424 (2003).
[CrossRef] [PubMed]

D. G. Grier, "A revolution in optical manipulation," Nature, 424, 810-816 (2003).
[CrossRef] [PubMed]

New J. Phys.

J. Leach, M. Dennis, J. Courtial, and M. Padgett, "Vortex knots in light," New J. Phys. 7, 55.1-55.11 (2005).
[CrossRef]

Opt. Commun.

J. E. Curtis, B. A. Koss and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

P. Zemanek, A. Jonas, P. Jakl, J. Jezek, M. Sery, and M. Liska, "Theoretical comparison of optical traps created by standing wave and single beam," Opt Commun 220, 401-412 (2003).
[CrossRef]

Opt. Express

Opt. Let.

R. Newell, J. Sebby, and T. G. Walker, "Dense atom clouds in a holographic atom trap," Opt. Let. 28, 14, 1266-1268 (2003).
[CrossRef]

Opt. Lett

P.J. Rodrigo,V.R. Daria, J. Gluckstad, "Real-time three-dimensional optical micromanipulation of multiple particles and living cells," Opt Lett 29, 2270-2272 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Optics Commun.

A. E. Chiou, W. Wang., G.J. Sonek, J. Hong, and M. W. Berns, �??Interferometric optical tweezers,�?? Optics Commun., 133, 7-10 (1997).
[CrossRef]

Philos. Mag.

H. F. Talbot, Philos. Mag., 9, 401-407 (1836).

Phys Rev A

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys Rev A, 54, 1593-1596 (1996).
[CrossRef]

Phys. Rev. Lett.,

P. T. Korda, M. B. Taylor, D. G. Grier, "Kinetically locked-in colloidal transport in an array of optical tweezers," Phys. Rev. Lett., 89, 128301 (2002).
[CrossRef] [PubMed]

Progress In Optics XXVII

K. Patorski, The self-imaging phenomenon and its applications, Progress In Optics XXVII, 1-108 (1989).
[CrossRef]

Rev. Sci. Inst.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Inst. 72, 1810-1816 (2001).
[CrossRef]

Review of Scientific Instruments

K. C. Neuman, S. M. Block, "Optical trapping" Review of Scientific Instruments, 75, 2787-2809 (2004).
[CrossRef]

Science

M. M. Burns, J. M. Fournier, and J.A. Golovchenko, �??Optical matter: crystallization and binding in intense optical fields," Science, 249, 749-754 (1990).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Illustration of four different plane wave configurations that form hexagonal lattice structures. Each configuration is described by its k-space representation (left column), by a transverse cut (center column) and an axial cut (right column) of the intensity distribution each taken through a lattice vector direction. (a) The simplest configuration of three waves in k-space, which results in a sinusoidal transverse intensity pattern and a uniform axial profile. (b) A 6-wave configuration giving sharper peaks with small sidelobes transversely and similarly a uniform axial profile. (c) A 12-wave configuration formed by adding the second k-space harmonic of the fundamental hexagon, which increases the peak intensity of the traps but the does not eliminate the sidelobes. Having a second value of kz results in a sinusoidal modulation in the axial intensity. (d) Our experimental configuration with 18 waves containing three values of kz , giving the sharpest peaks and virtually eliminating the transverse sidelobes. The three values of kz , make the Talbot image revival more complicated and give a larger axial periodicity. All intensity plots have been scaled so that there is equal power in each configuration. The transverse periodicity in (a), (b), (c), and (d) is 8λ; the axial periodicity in (c) is 32λ, while the axial periodicity in (d) is 94λ.

Fig. 2.
Fig. 2.

The interference patterns produced when (a) all three sets of beams are in phase (ΔΦ=0) and the image at the half Talbot distance is the phase contrast image, and (b) when the phase is set to give the half Talbot image. In the later instance, the hexagonal trapping pattern is recovered after propagation through a fraction of the Talbot distance.

Fig. 3.
Fig. 3.

(a) Intensity distribution of the interfering beams in the image plane of the SLM where all the 18 beams are in phase. (b) A similar distribution when the phase of all 18 beams are set to be midway between Talbot images. It is this image (b), with the addition of a linear phase, that forms the multiplicative mask upon which the hologram design is derived.

Figure 4.
Figure 4.

Schematic of the optical tweezers 4f setup. The lens L1, L2, L3 and L4 have focal lengths of 100mm, 160mm 140mm and 80mm respectively.

Fig. 5.
Fig. 5.

Multiple patterns of 2 µm diameter silica spheres trapped in the hexagonal interference pattern. (a) A 9-sphere array, (b) A 12-sphere arrow pattern array, and (c) a 19-sphere hexagonal array.

Fig. 6.
Fig. 6.

A square array structure consisting of 15 2 µm diameter silica spheres trapped in a hexagonal interference pattern. (a) The structure is lifted axially by 8µm. (b) Structure is moved to the left by 46 µm. (c) Structure then moved in the positive y direction by a total of 25µm, (d)–(e). Array was then moved right by a total of 52 µm. (f) Structure then moved in the negative y direction by 27 µm,(g), before being lowered by 8 µm back down to its original position (h).

Equations (4)

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

k 0 = k r 2 + k z 2
k z k 0 k r 2 2 k 0
z Talbot = 2 π Δ k z ( 1 , 3 ) Δ k z ( 1 , 2 )
Φ ( x , y ) holo = π + ( ( Φ ( x , y ) + Φ ( x , Λ ) ) mod 2 π π ) × sin⁡ c 2 ( ( 1 I ( x , y ) ) π )

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