Abstract

We investigate the use of liquid crystal (LC) adaptive optics elements to provide full 3 dimensional particle control in an optical tweezer. These devices are suitable for single controllable traps, and so are less versatile than many of the competing technologies which can be used to control multiple particles. However, they have the advantages of simplicity and light efficiency. Furthermore, compared to binary holographic optical traps they have increased positional accuracy. The transmissive LC devices could be retro-fitted to an existing microscope system. An adaptive modal LC lens is used to vary the z-focal position over a range of up to 100 µm and an adaptive LC beam-steering device is used to deflect the beam (and trapped particle) in the x-y plane within an available radius of 10 µm. Furthermore, by modifying the polarisation of the incident light, these LC components also offer the opportunity for the creation of dual optical traps of controllable depth and separation.

© 2006 Optical Society of America

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2006 (1)

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006).
[CrossRef]

2005 (5)

P. J. Rodrigo, V. R. Daria, and J. Gluckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86,074103 (2005).
[CrossRef]

M. Kawamura, M. Ye, and S. Sato, "Optical trapping and manipulation system using liquid-crystal lens with focussing and deflection properties," Jpn. J. Appl. Phys. 44, 6098-6100 (2005).
[CrossRef]

P. J. Rodrigo, V. R. Daria, and J. Gluckstad, "Dynamically reconfigurable optical lattices," Opt. Express 13, 1384-1394 (2005).
[CrossRef] [PubMed]

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

C. H. J. Schmitz, J. P. Spatz, and J. E. Curtis, "High-precision steering of multiple holographic optical traps," Opt. Express 13, 8678-8685 (2005).
[CrossRef] [PubMed]

2004 (5)

2003 (1)

M. J. Lang, P. M. Fordyce, and S. M. Block, "Combined optical trapping and single-molecule fluororescence," J. Biol. 2, 6 (2003).
[CrossRef]

2002 (3)

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

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

R. L. Eriksen, P. C. Mogensen, and J. Gluckstad, "Multiple-beam optical tweezers generated by the generalized phase-contrast method," Opt. Lett. 27, 267-269 (2002).
[CrossRef]

2001 (2)

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]

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

2000 (5)

M. A. A. Neil and R. Juskaitis, "Adaptive aberration correction in a two-photon microscope," J. Microsc. 200, 105-108 (2000).
[CrossRef] [PubMed]

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. Gluckstad and P. C. Mogensen, "Reconfigurable ternary-phase array illuminator based on the generalised phase contrast technique," Opt. Commun. 173, 169-175 (2000).
[CrossRef]

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

T. Nose, Y. Yamada, and S. Sato, "Improvement of optical properties and beam steering functions in a liquid crystal microlens with an extra controlling electrode by a planar surface," Jpn. J. Appl. Phys.,  39, 6383-6387 (2000).
[CrossRef]

1999 (3)

1998 (2)

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

A. F. Naumov, M. Y. Loktev, I. R. Guralnik, and G. V. Vdovin, "Liquid-crystal adaptive lenses with modal control," Opt. Lett. 23, 992-994 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (1)

J. M. R. Fournier, M. M. Burns, and J. A. Golovchenko, "Writing diffractive structures by optical trapping," in Practical Holography IX, S. A. Benton, Proc. SPIE 2406, 101-111 (1995).

1994 (1)

1993 (1)

1984 (1)

A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating light beams," Phys. Rev. Lett. 54, 1245-1248 (1984).
[CrossRef]

1975 (1)

A. F. Fray and D. Jones, "Large-angle beam deflector using liquid crystals," Electron. Lett. 11, 358-359 (1975).
[CrossRef]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating light beams," Phys. Rev. Lett. 54, 1245-1248 (1984).
[CrossRef]

Bhattacharya, S.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

Block, S. M.

M. J. Lang, P. M. Fordyce, and S. M. Block, "Combined optical trapping and single-molecule fluororescence," J. Biol. 2, 6 (2003).
[CrossRef]

Burns, M. M.

J. M. R. Fournier, M. M. Burns, and J. A. Golovchenko, "Writing diffractive structures by optical trapping," in Practical Holography IX, S. A. Benton, Proc. SPIE 2406, 101-111 (1995).

Carruthers, A. E.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Cooper, J.

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

Curtis, J. E.

Daria, V. R.

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.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Dias, D.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

Dirson, C.

V. Laude and C. Dirson, "Liquid crystal active lens: application to image resolution enhancement," Opt. Commun,  163, 72-78 (1999).
[CrossRef]

Dorschner, T. A.

Dufresne, E. R.

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 optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating light beams," Phys. Rev. Lett. 54, 1245-1248 (1984).
[CrossRef]

Eriksen, R. L.

Fordyce, P. M.

M. J. Lang, P. M. Fordyce, and S. M. Block, "Combined optical trapping and single-molecule fluororescence," J. Biol. 2, 6 (2003).
[CrossRef]

Fournier, J. M. R.

J. M. R. Fournier, M. M. Burns, and J. A. Golovchenko, "Writing diffractive structures by optical trapping," in Practical Holography IX, S. A. Benton, Proc. SPIE 2406, 101-111 (1995).

Fray, A. F.

A. F. Fray and D. Jones, "Large-angle beam deflector using liquid crystals," Electron. Lett. 11, 358-359 (1975).
[CrossRef]

Friedman, L. J.

Glockner, R.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

Gluckstad, J.

P. J. Rodrigo, V. R. Daria, and J. Gluckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86,074103 (2005).
[CrossRef]

P. J. Rodrigo, V. R. Daria, and J. Gluckstad, "Dynamically reconfigurable optical lattices," Opt. Express 13, 1384-1394 (2005).
[CrossRef] [PubMed]

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

R. L. Eriksen, P. C. Mogensen, and J. Gluckstad, "Multiple-beam optical tweezers generated by the generalized phase-contrast method," Opt. Lett. 27, 267-269 (2002).
[CrossRef]

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

J. Gluckstad and P. C. Mogensen, "Reconfigurable ternary-phase array illuminator based on the generalised phase contrast technique," Opt. Commun. 173, 169-175 (2000).
[CrossRef]

Golovchenko, J. A.

J. M. R. Fournier, M. M. Burns, and J. A. Golovchenko, "Writing diffractive structures by optical trapping," in Practical Holography IX, S. A. Benton, Proc. SPIE 2406, 101-111 (1995).

Grier, D. G.

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

J. E. Curtis, B. A. Koss and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (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 optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Guralnik, I. R.

Hain, M.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

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]

Hands, P. J. W.

P. J. W. Hands, G. D. Love, and A. K. Kirby, "Adaptive modally addressed liquid crystal lenses," in Liquid Crystals VIII, I.-C. Khoo, Proc. SPIE 5188, 136-143 (2004).
[CrossRef]

Hobbs, D. S.

Honma, M.

Ito, H.

Ito, S. S.

Jones, D.

A. F. Fray and D. Jones, "Large-angle beam deflector using liquid crystals," Electron. Lett. 11, 358-359 (1975).
[CrossRef]

Jordan, P.

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

Juskaitis, R.

M. A. A. Neil and R. Juskaitis, "Adaptive aberration correction in a two-photon microscope," J. Microsc. 200, 105-108 (2000).
[CrossRef] [PubMed]

Kawamura, M.

M. Kawamura, M. Ye, and S. Sato, "Optical trapping and manipulation system using liquid-crystal lens with focussing and deflection properties," Jpn. J. Appl. Phys. 44, 6098-6100 (2005).
[CrossRef]

Kelly, T.-L.

Kirby, A. K.

A. K. Kirby and G. D. Love, "Fast, large and controllable phase modulation using dual frequency liquid crystals," Opt. Express 12, 1470-1475 (2004).
[CrossRef] [PubMed]

P. J. W. Hands, G. D. Love, and A. K. Kirby, "Adaptive modally addressed liquid crystal lenses," in Liquid Crystals VIII, I.-C. Khoo, Proc. SPIE 5188, 136-143 (2004).
[CrossRef]

Koss, B. A.

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

Ladavac, K.

Lang, M. J.

M. J. Lang, P. M. Fordyce, and S. M. Block, "Combined optical trapping and single-molecule fluororescence," J. Biol. 2, 6 (2003).
[CrossRef]

Laude, V.

V. Laude and C. Dirson, "Liquid crystal active lens: application to image resolution enhancement," Opt. Commun,  163, 72-78 (1999).
[CrossRef]

Leach, J.

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

Lee, S.-H.

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]

Loktev, M. Y.

Love, G. D.

Major, J. V.

Masuda, S.

Mogensen, P. C.

R. L. Eriksen, P. C. Mogensen, and J. Gluckstad, "Multiple-beam optical tweezers generated by the generalized phase-contrast method," Opt. Lett. 27, 267-269 (2002).
[CrossRef]

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

J. Gluckstad and P. C. Mogensen, "Reconfigurable ternary-phase array illuminator based on the generalised phase contrast technique," Opt. Commun. 173, 169-175 (2000).
[CrossRef]

Naumov, A. F.

Neil, M. A. A.

M. A. A. Neil and R. Juskaitis, "Adaptive aberration correction in a two-photon microscope," J. Microsc. 200, 105-108 (2000).
[CrossRef] [PubMed]

Nose, T.

Padgett, M. J.

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

Polin, M.

Purvis, A.

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]

Resler, D. P.

Rodrigo, P. J.

Roichman, Y.

Sato, S.

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006).
[CrossRef]

M. Kawamura, M. Ye, and S. Sato, "Optical trapping and manipulation system using liquid-crystal lens with focussing and deflection properties," Jpn. J. Appl. Phys. 44, 6098-6100 (2005).
[CrossRef]

T. Nose, Y. Yamada, and S. Sato, "Improvement of optical properties and beam steering functions in a liquid crystal microlens with an extra controlling electrode by a planar surface," Jpn. J. Appl. Phys.,  39, 6383-6387 (2000).
[CrossRef]

Schmitz, C. H. J.

Sharp, R. C.

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]

Sinclair, G.

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

Spalding, G. C.

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]

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Stankovic, S.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

Takahashi, S.

Tatarkova, S. A.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

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]

Tschudi, T.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

Vdovin, G. V.

Wang, B.

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006).
[CrossRef]

Yamada, Y.

T. Nose, Y. Yamada, and S. Sato, "Improvement of optical properties and beam steering functions in a liquid crystal microlens with an extra controlling electrode by a planar surface," Jpn. J. Appl. Phys.,  39, 6383-6387 (2000).
[CrossRef]

Ye, M.

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006).
[CrossRef]

M. Kawamura, M. Ye, and S. Sato, "Optical trapping and manipulation system using liquid-crystal lens with focussing and deflection properties," Jpn. J. Appl. Phys. 44, 6098-6100 (2005).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

P. J. Rodrigo, V. R. Daria, and J. Gluckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86,074103 (2005).
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A. F. Fray and D. Jones, "Large-angle beam deflector using liquid crystals," Electron. Lett. 11, 358-359 (1975).
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J. Biol. (1)

M. J. Lang, P. M. Fordyce, and S. M. Block, "Combined optical trapping and single-molecule fluororescence," J. Biol. 2, 6 (2003).
[CrossRef]

J. Microsc. (1)

M. A. A. Neil and R. Juskaitis, "Adaptive aberration correction in a two-photon microscope," J. Microsc. 200, 105-108 (2000).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

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

Jpn. J. Appl. Phys. (2)

T. Nose, Y. Yamada, and S. Sato, "Improvement of optical properties and beam steering functions in a liquid crystal microlens with an extra controlling electrode by a planar surface," Jpn. J. Appl. Phys.,  39, 6383-6387 (2000).
[CrossRef]

M. Kawamura, M. Ye, and S. Sato, "Optical trapping and manipulation system using liquid-crystal lens with focussing and deflection properties," Jpn. J. Appl. Phys. 44, 6098-6100 (2005).
[CrossRef]

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[CrossRef]

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M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, "Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup," Opt. Commun. 188, 291-299 (2001).
[CrossRef]

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006).
[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]

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[CrossRef]

Proc. SPIE (2)

P. J. W. Hands, G. D. Love, and A. K. Kirby, "Adaptive modally addressed liquid crystal lenses," in Liquid Crystals VIII, I.-C. Khoo, Proc. SPIE 5188, 136-143 (2004).
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[CrossRef]

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[CrossRef]

Other (3)

K. Dholakia, G. Spalding, and M. MacDonald, "Optical tweezers: the next generation," Phys. World 15, (2002).

A. K. Kirby, P. J. W. Hands, and G. D. Love, "Optical design of liquid crystal lenses: off-axis modelling," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith and R. B. Johnson, eds., Proc. SPIE 5874, 70-79 (2005).

Meadowlark Optics, www.meadowlark.com.

Supplementary Material (4)

» Media 1: AVI (2580 KB)     
» Media 2: AVI (1131 KB)     
» Media 3: AVI (2272 KB)     
» Media 4: AVI (2546 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Construction of the LC beam-steering device

Fig. 2.
Fig. 2.

Electrode connections to the LC beam-steering device

Fig. 3.
Fig. 3.

Contour plot showing phase variation across the LC beam steering device as a function of applied voltage (V1–V2).

Fig. 4.
Fig. 4.

Deflection of a trapped particle over a 10 µm range using LC beam-steering device.

Fig. 5.
Fig. 5.

(video: 2.5 MB). 2x real-time movie of a 3.5 µm trapped particle being moved in the x-y plane by an LC beam-steering device. Circles represent maximum deflection positions. Diameter of total deflection range approximately 20 µm.

Fig. 6.
Fig. 6.

(video: 1.1 MB). “Optical juggling”: Using the LC beam-steering device together with an LC variable retarder, incident polarisation is made to oscillate between states orthogonal and parallel to the rubbing direction. The relative depths (intensities) of the two resulting neighbouring traps is subsequently made to oscillate. A 5 µm trapped particle is therefore repeatedly transferred (juggled) back and forth from one trap to another. (real time)

Fig. 7.
Fig. 7.

Z-axis control of optical trapping using a modal LC lens. (a) Greater than 100 µm of focus variation are achievable with the device. (b) Sequence of images showing how a trapped particle can be moved along the z-axis, in and out of the plane of camera focus. In (1) the trapped particle is in a different vertical plane to most of the other particles (which are stuck to the cover glass. In (2)–(3) the trapped particle is moved in the z-direction – and so its image is defocused. In (4) the camera was refocused on the new particle position. In (5) the lens is switched off and the particle moves back to its original trapped position as shown in (6) and the camera is re-focussed. (c) (video: 2.2 MB) Video of z-axis movement control (3x real-time).

Fig. 8.
Fig. 8.

Diagram showing how deflection of one of the beams within a counter-propagating beams optical trap gives rise to approximately 30 µm of deflection along the beams’ axes. A small and less significant vertical deflection of approximately 2 µm also occurs.

Fig. 9.
Fig. 9.

Movement of two particles held within a single trap formed from two counter-propagating beams combined with an LC beam-steering device. As the beams are deflected, 2 µm of transverse deflection are observed (a), whilst 27 µm of movement is achieved in a direction parallel to the beams’ axes (b).

Fig. 10.
Fig. 10.

(video: 2.5 MB). Movie of particles being moved over a 27 µm range by an LC beam-steering device controlling a trap formed by two counter-propagating beams. (2x real-time)

Equations (2)

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Δ f = f 2 f 1 f 2 f 1 + f 2 d
θ = Δ n · d w

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