Abstract

Conical diffraction of linearly polarised light in a biaxial crystal produces a beam with a crescent-shaped intensity profile. Rotation of the plane of polarisation produces the unique effect of spatially moving the crescent-shaped beam around a ring. We use this effect to trap microspheres and white blood cells and to position them at any angular position on the ring. Continuous motion around the circle is also demonstrated. This crescent beam does not require an interferometeric arrangement to form it, nor does it carry optical angular momentum. The ability to spatially locate a beam and an associated trapped object simply by varying the polarisation of light suggests that this optical process should find application in the manipulation and actuation of micro- and nano-scale physical and biological objects.

© 2010 OSA

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2009

2008

S. Husale, W. Grange, M. Karle, S. Bürgi, and M. Hegner, “Interaction of cationic surfactants with DNA: a single-molecule study,” Nucleic Acids Res. 36(5), 1443–1449 (2008).
[CrossRef] [PubMed]

M. Salomo, U. F. Keyser, M. Struhalla, and F. Kremer, “Optical tweezers to study single protein A/immunoglobulin G interactions at varying conditions,” Eur. Biophys. J. 37(6), 927–934 (2008).
[CrossRef] [PubMed]

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[CrossRef] [PubMed]

2006

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A. 462(2070), 1629–1642 (2006).
[CrossRef]

2005

K. Ladavac and D. G. Grier, “Colloidal hydrodynamic coupling in concentric optical vortices,” Europhys. Lett. 70(4), 548–554 (2005).
[CrossRef]

2003

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (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(12), 128301 (2002).
[CrossRef] [PubMed]

A. Terray, J. Oakey, and D. W. M. Marr, “Fabrication of linear colloidal structures for microfluidic applications,” Appl. Phys. Lett. 81(9), 1555–1557 (2002).
[CrossRef]

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(5), 053601 (2002).
[CrossRef] [PubMed]

L. Stars and P. Bartlett, “Colliodal dynamics in polymer solutions,” Faraday Discuss. 123, 323–334 (2002).

2001

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[CrossRef] [PubMed]

2000

D. M. Villeneuve, S. A. Aseyev, P. Dietrich, M. Spanner, M. Y. Ivanov, and P. B. Corkum, “Forced molecular rotation in an optical centrifuge,” Phys. Rev. Lett. 85(3), 542–545 (2000).
[CrossRef] [PubMed]

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10(3), 279–285 (2000).
[CrossRef] [PubMed]

1999

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

1997

1996

S. B. Smith, Y. J. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[CrossRef] [PubMed]

1994

K. Svoboda, P. P. Mitra, and S. M. Block, “Fluctuation analysis of motor protein movement and single enzyme kinetics,” Proc. Natl. Acad. Sci. U.S.A. 91(25), 11782–11786 (1994).
[CrossRef] [PubMed]

1987

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[CrossRef] [PubMed]

1986

1837

W. R. Hamilton, “Third supplement to an essay on the theory of system of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).

1833

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Philos. Mag. 1, 112–120 (1833).

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(5), 053601 (2002).
[CrossRef] [PubMed]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Arnold, C. B.

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[CrossRef] [PubMed]

Aseyev, S. A.

D. M. Villeneuve, S. A. Aseyev, P. Dietrich, M. Spanner, M. Y. Ivanov, and P. B. Corkum, “Forced molecular rotation in an optical centrifuge,” Phys. Rev. Lett. 85(3), 542–545 (2000).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[CrossRef] [PubMed]

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(5), 288–290 (1986).
[CrossRef] [PubMed]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Bartlett, P.

L. Stars and P. Bartlett, “Colliodal dynamics in polymer solutions,” Faraday Discuss. 123, 323–334 (2002).

Berry, M. V.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A. 462(2070), 1629–1642 (2006).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. Svoboda, P. P. Mitra, and S. M. Block, “Fluctuation analysis of motor protein movement and single enzyme kinetics,” Proc. Natl. Acad. Sci. U.S.A. 91(25), 11782–11786 (1994).
[CrossRef] [PubMed]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Bürgi, S.

S. Husale, W. Grange, M. Karle, S. Bürgi, and M. Hegner, “Interaction of cationic surfactants with DNA: a single-molecule study,” Nucleic Acids Res. 36(5), 1443–1449 (2008).
[CrossRef] [PubMed]

Bustamante, C.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10(3), 279–285 (2000).
[CrossRef] [PubMed]

S. B. Smith, Y. J. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[CrossRef] [PubMed]

Chu, S.

Collins, S. D.

Corkum, P. B.

D. M. Villeneuve, S. A. Aseyev, P. Dietrich, M. Spanner, M. Y. Ivanov, and P. B. Corkum, “Forced molecular rotation in an optical centrifuge,” Phys. Rev. Lett. 85(3), 542–545 (2000).
[CrossRef] [PubMed]

Cui, Y. J.

S. B. Smith, Y. J. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[CrossRef] [PubMed]

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Dao, M.

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Dietrich, P.

D. M. Villeneuve, S. A. Aseyev, P. Dietrich, M. Spanner, M. Y. Ivanov, and P. B. Corkum, “Forced molecular rotation in an optical centrifuge,” Phys. Rev. Lett. 85(3), 542–545 (2000).
[CrossRef] [PubMed]

Donegan, J. F.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[CrossRef] [PubMed]

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(5), 288–290 (1986).
[CrossRef] [PubMed]

Grange, W.

S. Husale, W. Grange, M. Karle, S. Bürgi, and M. Hegner, “Interaction of cationic surfactants with DNA: a single-molecule study,” Nucleic Acids Res. 36(5), 1443–1449 (2008).
[CrossRef] [PubMed]

Grier, D. G.

K. Ladavac and D. G. Grier, “Colloidal hydrodynamic coupling in concentric optical vortices,” Europhys. Lett. 70(4), 548–554 (2005).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (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(12), 128301 (2002).
[CrossRef] [PubMed]

Gutierrez-Vega, J. C.

Hamilton, W. R.

W. R. Hamilton, “Third supplement to an essay on the theory of system of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).

Hegner, M.

S. Husale, W. Grange, M. Karle, S. Bürgi, and M. Hegner, “Interaction of cationic surfactants with DNA: a single-molecule study,” Nucleic Acids Res. 36(5), 1443–1449 (2008).
[CrossRef] [PubMed]

Husale, S.

S. Husale, W. Grange, M. Karle, S. Bürgi, and M. Hegner, “Interaction of cationic surfactants with DNA: a single-molecule study,” Nucleic Acids Res. 36(5), 1443–1449 (2008).
[CrossRef] [PubMed]

Ivanov, M. Y.

D. M. Villeneuve, S. A. Aseyev, P. Dietrich, M. Spanner, M. Y. Ivanov, and P. B. Corkum, “Forced molecular rotation in an optical centrifuge,” Phys. Rev. Lett. 85(3), 542–545 (2000).
[CrossRef] [PubMed]

Jeffrey, M. R.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A. 462(2070), 1629–1642 (2006).
[CrossRef]

Karle, M.

S. Husale, W. Grange, M. Karle, S. Bürgi, and M. Hegner, “Interaction of cationic surfactants with DNA: a single-molecule study,” Nucleic Acids Res. 36(5), 1443–1449 (2008).
[CrossRef] [PubMed]

Keyser, U. F.

M. Salomo, U. F. Keyser, M. Struhalla, and F. Kremer, “Optical tweezers to study single protein A/immunoglobulin G interactions at varying conditions,” Eur. Biophys. J. 37(6), 927–934 (2008).
[CrossRef] [PubMed]

Knoesen, A.

Korda, P. T.

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(12), 128301 (2002).
[CrossRef] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Kremer, F.

M. Salomo, U. F. Keyser, M. Struhalla, and F. Kremer, “Optical tweezers to study single protein A/immunoglobulin G interactions at varying conditions,” Eur. Biophys. J. 37(6), 927–934 (2008).
[CrossRef] [PubMed]

Ladavac, K.

K. Ladavac and D. G. Grier, “Colloidal hydrodynamic coupling in concentric optical vortices,” Europhys. Lett. 70(4), 548–554 (2005).
[CrossRef]

Lim, C. T.

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

Liphardt, J.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10(3), 279–285 (2000).
[CrossRef] [PubMed]

Lloyd, H.

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Philos. Mag. 1, 112–120 (1833).

Lunney, J. G.

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[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(5), 053601 (2002).
[CrossRef] [PubMed]

Marr, D. W. M.

A. Terray, J. Oakey, and D. W. M. Marr, “Fabrication of linear colloidal structures for microfluidic applications,” Appl. Phys. Lett. 81(9), 1555–1557 (2002).
[CrossRef]

Maruo, S.

McLeod, E.

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[CrossRef] [PubMed]

Mitra, P. P.

K. Svoboda, P. P. Mitra, and S. M. Block, “Fluctuation analysis of motor protein movement and single enzyme kinetics,” Proc. Natl. Acad. Sci. U.S.A. 91(25), 11782–11786 (1994).
[CrossRef] [PubMed]

O’Dwyer, D. P.

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(5), 053601 (2002).
[CrossRef] [PubMed]

Oakey, J.

A. Terray, J. Oakey, and D. W. M. Marr, “Fabrication of linear colloidal structures for microfluidic applications,” Appl. Phys. Lett. 81(9), 1555–1557 (2002).
[CrossRef]

Padgett, M. J.

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(5), 053601 (2002).
[CrossRef] [PubMed]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Phelan, C. F.

Rakovich, Y. P.

Saito, Y.

Salomo, M.

M. Salomo, U. F. Keyser, M. Struhalla, and F. Kremer, “Optical tweezers to study single protein A/immunoglobulin G interactions at varying conditions,” Eur. Biophys. J. 37(6), 927–934 (2008).
[CrossRef] [PubMed]

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Sidick, E.

Smith, D.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10(3), 279–285 (2000).
[CrossRef] [PubMed]

Smith, S. B.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, “Single-molecule studies of DNA mechanics,” Curr. Opin. Struct. Biol. 10(3), 279–285 (2000).
[CrossRef] [PubMed]

S. B. Smith, Y. J. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[CrossRef] [PubMed]

Sosa-Martínez, H.

Spanner, M.

D. M. Villeneuve, S. A. Aseyev, P. Dietrich, M. Spanner, M. Y. Ivanov, and P. B. Corkum, “Forced molecular rotation in an optical centrifuge,” Phys. Rev. Lett. 85(3), 542–545 (2000).
[CrossRef] [PubMed]

Stars, L.

L. Stars and P. Bartlett, “Colliodal dynamics in polymer solutions,” Faraday Discuss. 123, 323–334 (2002).

Struhalla, M.

M. Salomo, U. F. Keyser, M. Struhalla, and F. Kremer, “Optical tweezers to study single protein A/immunoglobulin G interactions at varying conditions,” Eur. Biophys. J. 37(6), 927–934 (2008).
[CrossRef] [PubMed]

Suresh, S.

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

Svoboda, K.

K. Svoboda, P. P. Mitra, and S. M. Block, “Fluctuation analysis of motor protein movement and single enzyme kinetics,” Proc. Natl. Acad. Sci. U.S.A. 91(25), 11782–11786 (1994).
[CrossRef] [PubMed]

Takaura, 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(12), 128301 (2002).
[CrossRef] [PubMed]

Terray, A.

A. Terray, J. Oakey, and D. W. M. Marr, “Fabrication of linear colloidal structures for microfluidic applications,” Appl. Phys. Lett. 81(9), 1555–1557 (2002).
[CrossRef]

Villeneuve, D. M.

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Supplementary Material (4)

» Media 1: MOV (374 KB)     
» Media 2: MOV (528 KB)     
» Media 3: MOV (500 KB)     
» Media 4: MOV (1978 KB)     

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Figures (7)

Fig. 1
Fig. 1

Conical diffraction of circularly polarised light in the focal image plane and the polarisation distribution around the ring. The ring diameter is 0.61 mm.

Fig. 2
Fig. 2

Experimental set-up showing the 532 nm 200 mW laser together with a half wave-plate and a 532 nm dichroic mirror to direct the laser onto the sample and exclude it from the CCD.

Fig. 3
Fig. 3

Intensity profiles at the FIP (11.54 cm beyond L1) as the fast-axis of the half wave- plate is rotated through 90°. Media 1 shows the rotation of the profile that occurs when the half wave-plate is rotated.

Fig. 4
Fig. 4

Selection of overlayed frames from the continuous circular motion of 5.3μm polystyrene particles around a 35μm circumference conical trap rotating at 0.8Hz. Media 2 shows the continuous motion of a single polystyrene particle of 5.3 micron diameter moving both clockwise and anti-clockwise with power of 87 mW and rotation rate of 0.2 Hz.

Fig. 5
Fig. 5

(a) Optically driven anti-clockwise rotation of a cluster of four 5.3 μm melamine formaldehyde particles. The position of the crescent beam relative to the particles is indicated. Media 3 shows rotation of the 4 melamine formaledehyde particles on the ring with power of 90 mW and rotation rate of 0.22 Hz (b) Circular motion of an 8 μm in diameter white blood cell. Media 4 shows a single white blood cell moving around the circle with 60 mW power and rotation rate of 0.125 Hz.

Fig. 6
Fig. 6

Dependence of the maximum trapping force and speed versus optical power for the crescent-shaped beam for circular and radial motions.

Fig. 7
Fig. 7

Simulation of the radial and tangential trapping forces, in terms of the variable Q (dashed), for 5.3 μm radius polystyrene particle in water and using the intensity profile (solid) in the focal plane of the microscope objective. (a) Variation of Q as the particle is translated from the centre of the crescent beam through the region of maximum intensity. (b) Variation of Q around the crescent beam at the equilibrium radial position req = 5.18 μm.

Equations (3)

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D t = 2 f 3 R 0 f 2
F o p t = 6 π R p η v e
F o p t = Q n P c

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