Abstract

Holographic optical tweezers use computer-generated holograms to create arbitrary three-dimensional configurations of single-beam optical traps that are useful for capturing, moving, and transforming mesoscopic objects. Through a combination of beam-splitting, mode-forming, and adaptive wavefront correction, holographic traps can exert precisely specified and characterized forces and torques on objects ranging in size from a few nanometers to hundreds of micrometers. Offering nanometer-scale spatial resolution and real-time reconfigurability, holographic optical traps provide unsurpassed access to the microscopic world and have found applications in fundamental research, manufacturing, and materials processing.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  45. A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
    [CrossRef] [PubMed]
  46. J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
    [CrossRef] [PubMed]
  47. K. Ladavac and D. G. Grier, "Microoptomechanical pump assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  51. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
    [CrossRef]
  52. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
    [CrossRef] [PubMed]
  53. C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, "Helico-conical optical beams: a product of helical and conical phase fronts," Opt. Express 13, 1749-1760 (2005).
    [CrossRef] [PubMed]

2005

2004

A. Jesacher, S. Furhpater, S. Bernet, and M. Ritsch-Marte, "Size selective trapping with optical 'cogwheel' tweezers," Opt. Express 12, 4129-4135 (2004).
[CrossRef] [PubMed]

K. Ladavac and D. G. Grier, "Microoptomechanical pump assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
[CrossRef] [PubMed]

C.-S. Guo, X. Liu, J.-L. He, and H.-T. Wang, "Optimal annulus structures of optical vortices," Opt. Express 12, 4625-4634 (2004).
[CrossRef] [PubMed]

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting by periodic potential energy landscapes: optical fractionation," Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

M. Pelton, K. Ladavac, and D. G. Grier, "Transport and fractionation in periodic potential-energy landscapes," Phys. Rev. E 70, 031108 (2004).
[CrossRef]

A. Gopinathan and D. G. Grier, "Statistically locked-in transport in periodic potential landscapes," Phys. Rev. Lett. 92, 130602 (2004).
[CrossRef] [PubMed]

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, "3D manipulation of particles into crystal structures using holographic optical tweezers," Opt. Express 12, 220-226 (2004).
[CrossRef] [PubMed]

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, "Assembly of 3-dimensional structures using programmable holographic optical tweezers," Opt. Express 12, 5475-5480 (2004).
[CrossRef] [PubMed]

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).
[CrossRef]

2003

K. Mangold, P. Leiderer, and C. Bechinger, "Phase transitions of colloidal monolayers in periodic pinning arrays," Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef] [PubMed]

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holographic optical tweezers," Opt. Express 11, 3562-3567 (2003).
[CrossRef] [PubMed]

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

B. A. Koss and D. G. Grier, "Optical peristalsis," Appl. Phys. Lett. 82, 3985-3987 (2003).
[CrossRef]

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

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

2002

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

P. Reimann, "Brownian motors: noisy transport far from equilibrium," Phys. Rep. 361, 57-265 (2002).
[CrossRef]

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

M. P. Hughes, "Strategies for dielectrophoretic separation in laboratory-on-a-ship systems," Electrophoresis 23, 2569-2582 (2002).
[CrossRef] [PubMed]

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier, "Nanofabrication with holographic optical tweezers," Rev. Sci. Instrum. 73, 1956-1957 (2002).
[CrossRef]

M. Meister and R. J. Winfield, "Novel approaches to direct search algorithms for the design of diffractive optical elements," Opt. Commun. 203, 39-49 (2002).
[CrossRef]

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

P. T. Korda, G. C. Spalding, and D. G. Grier, "Evolution of a colloidal critical state in an optical pinning potential," Phys. Rev. B 66, 024504 (2002).
[CrossRef]

2001

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

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

2000

A. T. O'Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

A. Ashkin, "History of optical trapping and manipulation of small-neutral particles, atoms, and molecules," IEEE J. Sel. Top. Quantum Electron. 6, 841-856 (2000).
[CrossRef]

P. C. Mogensen and J. Glückstad, "Dynamic array generation and pattern formation for optical tweezers," Opt. Commun 175, 75-81 (2000).
[CrossRef]

1999

1998

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, "Holographic formation of optical-vortex filaments," J. Opt. Soc. Am. B 15, 2226-2234 (1998).
[CrossRef]

1997

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

1996

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

K. T. Gahagan and G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996), original description of optical vortex.
[CrossRef] [PubMed]

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]

1995

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, 826-829 (1995).
[CrossRef] [PubMed]

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

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

1991

1986

Allen, L.

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

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]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Alonzo, C. A.

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Ashkin, A.

A. Ashkin, "History of optical trapping and manipulation of small-neutral particles, atoms, and molecules," IEEE J. Sel. Top. Quantum Electron. 6, 841-856 (2000).
[CrossRef]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

Bechinger, C.

K. Mangold, P. Leiderer, and C. Bechinger, "Phase transitions of colloidal monolayers in periodic pinning arrays," Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Bernet, S.

Bjorkholm, J. E.

Chu, S.

Clare, H.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).
[CrossRef]

Cooper, J.

Courtial, J.

Crocker, J. C.

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Curtis, J. E.

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

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

Dearing, M. T.

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

Dholakia, K.

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holographic optical tweezers," Opt. Express 11, 3562-3567 (2003).
[CrossRef] [PubMed]

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

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Doskolovich, L.

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Dufresne, E. R.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier, "Nanofabrication with holographic optical tweezers," Rev. Sci. Instrum. 73, 1956-1957 (2002).
[CrossRef]

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

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Dziedzic, J. M.

Flendrig, L.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).
[CrossRef]

Friese, M. E. J.

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, 826-829 (1995).
[CrossRef] [PubMed]

Furhpater, S.

Gahagan, K. T.

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Glückstad, J.

C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, "Helico-conical optical beams: a product of helical and conical phase fronts," Opt. Express 13, 1749-1760 (2005).
[CrossRef] [PubMed]

P. C. Mogensen and J. Glückstad, "Dynamic array generation and pattern formation for optical tweezers," Opt. Commun 175, 75-81 (2000).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gopinathan, A.

A. Gopinathan and D. G. Grier, "Statistically locked-in transport in periodic potential landscapes," Phys. Rev. Lett. 92, 130602 (2004).
[CrossRef] [PubMed]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Grier, D. G.

S. Sundbeck, I. Gruzberg, and D. G. Grier, "Structure and scaling of helical modes of light," Opt. Lett. 30, 477-479 (2005).
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S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier, "Observation of flux reversal in a symmetric optical thermal ratchet," Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef] [PubMed]

S.-H. Lee and D. G. Grier, "Flux reversal in a two-state symmetric optical thermal ratchet," Phys. Rev. E 71, 060102(R) (2005).
[CrossRef]

Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

K. Ladavac and D. G. Grier, "Colloidal hydrodynamic coupling in concentric optical vortices," Europhys. Lett. 70, 548-554 (2005).
[CrossRef]

K. Ladavac and D. G. Grier, "Microoptomechanical pump assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
[CrossRef] [PubMed]

A. Gopinathan and D. G. Grier, "Statistically locked-in transport in periodic potential landscapes," Phys. Rev. Lett. 92, 130602 (2004).
[CrossRef] [PubMed]

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting by periodic potential energy landscapes: optical fractionation," Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

M. Pelton, K. Ladavac, and D. G. Grier, "Transport and fractionation in periodic potential-energy landscapes," Phys. Rev. E 70, 031108 (2004).
[CrossRef]

B. A. Koss and D. G. Grier, "Optical peristalsis," Appl. Phys. Lett. 82, 3985-3987 (2003).
[CrossRef]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

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

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

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

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier, "Nanofabrication with holographic optical tweezers," Rev. Sci. Instrum. 73, 1956-1957 (2002).
[CrossRef]

P. T. Korda, G. C. Spalding, and D. G. Grier, "Evolution of a colloidal critical state in an optical pinning potential," Phys. Rev. B 66, 024504 (2002).
[CrossRef]

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

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

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Gruzberg, I.

Guo, C.-S.

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
[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, 826-829 (1995).
[CrossRef] [PubMed]

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

He, J.-L.

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
[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, 826-829 (1995).
[CrossRef] [PubMed]

Hughes, M. P.

M. P. Hughes, "Strategies for dielectrophoretic separation in laboratory-on-a-ship systems," Electrophoresis 23, 2569-2582 (2002).
[CrossRef] [PubMed]

Jesacher, A.

Jordan, P.

Kasza, K.

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting by periodic potential energy landscapes: optical fractionation," Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

Kitamura, N.

Korda, P. T.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier, "Nanofabrication with holographic optical tweezers," Rev. Sci. Instrum. 73, 1956-1957 (2002).
[CrossRef]

P. T. Korda, G. C. Spalding, and D. G. Grier, "Evolution of a colloidal critical state in an optical pinning potential," Phys. Rev. B 66, 024504 (2002).
[CrossRef]

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

Koshio, M.

Koss, B. A.

B. A. Koss and D. G. Grier, "Optical peristalsis," Appl. Phys. Lett. 82, 3985-3987 (2003).
[CrossRef]

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

Kotlyar, V.

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Laczik, Z. J.

Ladavac, K.

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier, "Observation of flux reversal in a symmetric optical thermal ratchet," Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

K. Ladavac and D. G. Grier, "Colloidal hydrodynamic coupling in concentric optical vortices," Europhys. Lett. 70, 548-554 (2005).
[CrossRef]

K. Ladavac and D. G. Grier, "Microoptomechanical pump assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
[CrossRef] [PubMed]

M. Pelton, K. Ladavac, and D. G. Grier, "Transport and fractionation in periodic potential-energy landscapes," Phys. Rev. E 70, 031108 (2004).
[CrossRef]

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting by periodic potential energy landscapes: optical fractionation," Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

Leach, J.

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, "3D manipulation of particles into crystal structures using holographic optical tweezers," Opt. Express 12, 220-226 (2004).
[CrossRef] [PubMed]

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).
[CrossRef]

Lee, S.

Lee, S.-H.

S.-H. Lee and D. G. Grier, "Flux reversal in a two-state symmetric optical thermal ratchet," Phys. Rev. E 71, 060102(R) (2005).
[CrossRef]

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier, "Observation of flux reversal in a symmetric optical thermal ratchet," Phys. Rev. Lett. 94, 110601 (2005).
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Leiderer, P.

K. Mangold, P. Leiderer, and C. Bechinger, "Phase transitions of colloidal monolayers in periodic pinning arrays," Phys. Rev. Lett. 90, 158302 (2003).
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Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Liu, X.

MacDonald, M. P.

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

MacVicar, I.

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
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Mangold, K.

K. Mangold, P. Leiderer, and C. Bechinger, "Phase transitions of colloidal monolayers in periodic pinning arrays," Phys. Rev. Lett. 90, 158302 (2003).
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Masuhara, H.

McGloin, D.

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holographic optical tweezers," Opt. Express 11, 3562-3567 (2003).
[CrossRef] [PubMed]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Meister, M.

M. Meister and R. J. Winfield, "Novel approaches to direct search algorithms for the design of diffractive optical elements," Opt. Commun. 203, 39-49 (2002).
[CrossRef]

Melville, H.

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holographic optical tweezers," Opt. Express 11, 3562-3567 (2003).
[CrossRef] [PubMed]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Milne, G. F.

Misawa, H.

Mogensen, P. C.

P. C. Mogensen and J. Glückstad, "Dynamic array generation and pattern formation for optical tweezers," Opt. Commun 175, 75-81 (2000).
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Neto, P. A. Maia

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
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Nussenzveig, H. M.

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
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O'Neil, A. T.

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

A. T. O'Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

Padgett, M.

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, "Assembly of 3-dimensional structures using programmable holographic optical tweezers," Opt. Express 12, 5475-5480 (2004).
[CrossRef] [PubMed]

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).
[CrossRef]

Padgett, M. J.

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, "3D manipulation of particles into crystal structures using holographic optical tweezers," Opt. Express 12, 220-226 (2004).
[CrossRef] [PubMed]

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

A. T. O'Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

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]

Pelton, M.

M. Pelton, K. Ladavac, and D. G. Grier, "Transport and fractionation in periodic potential-energy landscapes," Phys. Rev. E 70, 031108 (2004).
[CrossRef]

Polin, M.

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier, "Observation of flux reversal in a symmetric optical thermal ratchet," Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
[CrossRef]

Reimann, P.

P. Reimann, "Brownian motors: noisy transport far from equilibrium," Phys. Rep. 361, 57-265 (2002).
[CrossRef]

Ritsch-Marte, M.

Rodrigo, P. J.

Roichman, Y.

Rozas, D.

Rubinsztein-Dunlop, 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, 826-829 (1995).
[CrossRef] [PubMed]

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

Sacks, Z. S.

Sasaki, K.

Sheets, S. A.

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

Sibbett, W.

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holographic optical tweezers," Opt. Express 11, 3562-3567 (2003).
[CrossRef] [PubMed]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Simpson, N. B.

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]

Sinclair, G.

Soifer, V.

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Spalding, G. C.

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

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holographic optical tweezers," Opt. Express 11, 3562-3567 (2003).
[CrossRef] [PubMed]

P. T. Korda, G. C. Spalding, and D. G. Grier, "Evolution of a colloidal critical state in an optical pinning potential," Phys. Rev. B 66, 024504 (2002).
[CrossRef]

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier, "Nanofabrication with holographic optical tweezers," Rev. Sci. Instrum. 73, 1956-1957 (2002).
[CrossRef]

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

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
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Sundbeck, S.

Swartzlander, G. A.

Taylor, M. B.

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

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
[CrossRef]

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Wagemann, E. U.

Wang, H.-T.

Winfield, R. J.

M. Meister and R. J. Winfield, "Novel approaches to direct search algorithms for the design of diffractive optical elements," Opt. Commun. 203, 39-49 (2002).
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Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Appl. Phys. Lett.

B. A. Koss and D. G. Grier, "Optical peristalsis," Appl. Phys. Lett. 82, 3985-3987 (2003).
[CrossRef]

Electrophoresis

M. P. Hughes, "Strategies for dielectrophoretic separation in laboratory-on-a-ship systems," Electrophoresis 23, 2569-2582 (2002).
[CrossRef] [PubMed]

Europhys. Lett.

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

K. Ladavac and D. G. Grier, "Colloidal hydrodynamic coupling in concentric optical vortices," Europhys. Lett. 70, 548-554 (2005).
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IEEE J. Sel. Top. Quantum Electron.

A. Ashkin, "History of optical trapping and manipulation of small-neutral particles, atoms, and molecules," IEEE J. Sel. Top. Quantum Electron. 6, 841-856 (2000).
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J. Colloid Interface Sci.

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

J. Mod. Opt.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).
[CrossRef]

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]

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

J. Opt. Soc. Am. B

Nature

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

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

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

Opt. Commun

P. C. Mogensen and J. Glückstad, "Dynamic array generation and pattern formation for optical tweezers," Opt. Commun 175, 75-81 (2000).
[CrossRef]

Opt. Commun.

M. Meister and R. J. Winfield, "Novel approaches to direct search algorithms for the design of diffractive optical elements," Opt. Commun. 203, 39-49 (2002).
[CrossRef]

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

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

A. T. O'Neil and M. J. Padgett, "Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner," Opt. Commun. 185, 139-143 (2000).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Opt. Express

A. Jesacher, S. Furhpater, S. Bernet, and M. Ritsch-Marte, "Size selective trapping with optical 'cogwheel' tweezers," Opt. Express 12, 4129-4135 (2004).
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K. Ladavac and D. G. Grier, "Microoptomechanical pump assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
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C.-S. Guo, X. Liu, J.-L. He, and H.-T. Wang, "Optimal annulus structures of optical vortices," Opt. Express 12, 4625-4634 (2004).
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C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, "Helico-conical optical beams: a product of helical and conical phase fronts," Opt. Express 13, 1749-1760 (2005).
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
[CrossRef] [PubMed]

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holographic optical tweezers," Opt. Express 11, 3562-3567 (2003).
[CrossRef] [PubMed]

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, "Assembly of 3-dimensional structures using programmable holographic optical tweezers," Opt. Express 12, 5475-5480 (2004).
[CrossRef] [PubMed]

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, "3D manipulation of particles into crystal structures using holographic optical tweezers," Opt. Express 12, 220-226 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rep.

P. Reimann, "Brownian motors: noisy transport far from equilibrium," Phys. Rep. 361, 57-265 (2002).
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Phys. Rev. A

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. B

P. T. Korda, G. C. Spalding, and D. G. Grier, "Evolution of a colloidal critical state in an optical pinning potential," Phys. Rev. B 66, 024504 (2002).
[CrossRef]

Phys. Rev. E

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting by periodic potential energy landscapes: optical fractionation," Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

M. Pelton, K. Ladavac, and D. G. Grier, "Transport and fractionation in periodic potential-energy landscapes," Phys. Rev. E 70, 031108 (2004).
[CrossRef]

S.-H. Lee and D. G. Grier, "Flux reversal in a two-state symmetric optical thermal ratchet," Phys. Rev. E 71, 060102(R) (2005).
[CrossRef]

Phys. Rev. Lett.

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier, "Observation of flux reversal in a symmetric optical thermal ratchet," Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef] [PubMed]

A. Gopinathan and D. G. Grier, "Statistically locked-in transport in periodic potential landscapes," Phys. Rev. Lett. 92, 130602 (2004).
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K. Mangold, P. Leiderer, and C. Bechinger, "Phase transitions of colloidal monolayers in periodic pinning arrays," Phys. Rev. Lett. 90, 158302 (2003).
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P. T. Korda, M. B. Taylor, and D. G. Grier, "Kinetically locked-in colloidal transport in an array of optical tweezers," Phys. Rev. Lett. 89, 128301 (2002).
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J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
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Figures (7)

Fig. 1
Fig. 1

(Color online) Two beams of light focus to two optical tweezers and also form an interference pattern at the lens's input pupil. The same traps can be created from a single input beam by placing an equivalent hologram in the input pupil.

Fig. 2
Fig. 2

(Color online) Schematic implementation of holographic optical traps. An expanded laser beam is reflected by a liquid-crystal spatial light modulator (SLM), which imprints a CGH onto its wavefronts. The 200 × 200 pixel region of the CGH shown encodes a pattern of 119 optical tweezers in a quasiperiodic arrangement. The phase hologram is relayed to the input pupil of an objective lens that focuses it into holographic optical traps, shown here trapping 1.5 μm diameter colloidal spheres in water. M1–M3, mirrors.

Fig. 3
Fig. 3

(Color online) Two views of a rotating icosahedron of colloidal spheres created with dynamic holographic optical tweezers.

Fig. 4
Fig. 4

(Color online) Measured trajectories of fluid-borne micrometer-diameter colloidal particles encountering a 10 × 10 square array of holographic optical traps with a lattice constant of 3 μm.

Fig. 5
Fig. 5

(Color online) Optical fractionation: (a) Measured trajectories of large colloidal spheres, 1.58 μm in diameter, dispersed in water flowing at 50 μm∕s, are deflected by a line of 12 holographic optical traps, whose positions are indicated by circles. (b) Smaller 1 micrometer diameter spheres dispersed in the same flow that are not deflected.

Fig. 6
Fig. 6

(Color online) Thermal ratchet implemented with holographic optical tweezers. (a) Focused light from a 20 × 5 array with manifolds separated by L = 3.8 μm. (b) Dispersion of 1.58 μm diameter spheres interacting with the array. (c) After repeated displacements of the array by L∕3 and 2L∕3, with each step lasting T = 5 s, all the spheres are translated to the right. (d) Transport velocity v as a function of dwell time shows flux reversal as the cycle rate increases.

Fig. 7
Fig. 7

(a) Phase-mask encoding a 3 × 2 array of counter-rotating optical vortices with ℓ = ±30. (b) Micro-optomechanical pump created by projecting the vortex array into a colloidal dispersion. Fluid flows from right to left as the rings of particles circulate. (c) Phase mask encoding concentric optimized optical vortices. (d) A micro-optomechanical Couette rheometer created by projecting the concentric vortices into a colloidal dispersion.

Equations (8)

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ψ ( ρ ) = u ( ρ ) exp [ i φ ( ρ ) ]
ψ ( r ) = m = 1 M ψ m δ ( r r m ) ,
ψ m = α m exp ( i ϕ m ) ,
ψ m = j = 1 N T m , j u j   exp ( i φ j ) ,
T m , j ( 0 ) = 1 λ f  exp ( i 2 π r m ρ j λ f ) .
T m , j = Π k = 0 K m T m , j ( k ) ,
T m , j z = exp ( i π ρ j       2 z m λ f 2 )
E = | ψ m | 2 + γ ( | ψ m | 2 α m       2 | ψ m | 2 α m       2 α m         4 ) 2 ,

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