Abstract

An interaction between a light field with complex field spatial distribution and a micro-particle leads to forces that drag the particle in space and may confine it in a stable position or a trajectory. The particle behavior is determined by its size with respect to the characteristic length of the spatially periodic or symmetric light field distribution. We study theoretically and experimentally the behavior of a microparticle near the center of an optical vortex beam in a plane perpendicular to the beam propagation. We show that such particle may be stably trapped either in a dark spot on the vortex beam axis, or in one of two points placed off the optical axis. It may also circulate along a trajectory having its radius smaller or equal to the radius of the first bright vortex ring.

© 2012 OSA

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2011

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

V. R. Daria, M. A. Go, and H.-A. Bachor, “Simultaneous transfer of linear and orbital angular momentum to multiple low-index particles,” J. Opt.13, 044004, (2011).
[CrossRef]

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett.98, 081114 (2011).
[CrossRef]

G. Gouesbet, J. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams:localized approximations and localized beam models, a review,” J. Quant. Spectr. & Rad. Transfer112, 1–27 (2011).
[CrossRef]

2010

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun.283, 1889–1893 (2010).
[CrossRef]

I. Ricardez-Vargas and K. Volke-Sepúlveda, “Experimental generation and dynamical reconfiguration of different circular optical lattices for applications in atom trapping,” J. Opt. Soc. Am. B27, 948–955 (2010).
[CrossRef]

R. J. Beck, J. P. Parry, W. N. MacPherson, A. Waddie, N. J. Weston, J. D. Shephard, and D. P. Hand, “Application of cooled spatial light modulator for high power nanosecond laser micromachining,” Opt. Express18, 17059–17065 (2010).
[CrossRef] [PubMed]

J. Ng, Z. Lin, and C. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett.104, 103601 (2010).
[CrossRef] [PubMed]

2009

S. H. Simpson and S. Hanna, “Rotation of absorbing spheres in Laguerre-Gaussian beams,” J. Opt. Soc. Am.26, 173–183 (2009).
[CrossRef]

A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New. J. Phys.11, 043004 (2009).
[CrossRef]

K. Volke-Sepúlveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B42, 085303 (2009).
[CrossRef]

J. M. Taylor and G. D. Love, “Multipole expansion of Bessel and Gaussian beams for Mie scattering calculations,” J. Opt. Soc. Am. A26, 278–282 (2009).
[CrossRef]

T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express17, 15558–15570 (2009).
[CrossRef] [PubMed]

2008

M. Dienerowitz, M. Mazilu, P. J. Reece, T. F. Krauss, and K. Dholakia, “Optical vortex trap for resonant confinement of metal nanoparticles,” Opt. Express16, 4991–4999 (2008).
[CrossRef] [PubMed]

O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express16, 12688–12700 (2008).
[CrossRef] [PubMed]

T. Čižmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, and K. Dholakia, “Generation of multiple Bessel beams for a biophotonic workstation,” Opt. Express16, 14024–14035 (2008).
[CrossRef] [PubMed]

K. Volke-Sepúlveda, A. O. Sántillan, and R. R. Boullosa, “Transfer of angular momentum to matter from acoustical vortices in free space,” Phys. Rev. Lett.100, 024302 (2008).
[CrossRef] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annual Review of Biochemistry77, 205–228 (2008).
[CrossRef] [PubMed]

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett.92, 161111 (2008).
[CrossRef]

P. Jákl, T. Čižmár, M. Šerý, and P. Zemánek, “Static optical sorting in a laser interference field,” Appl. Phys. Lett.92, 161110 (2008).
[CrossRef]

2007

K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Čižmár, “Cellular and colloidal separation using optical forces,” Methods Cell Biology82, 467–495 (2007).
[CrossRef]

D. V. Petrov, “Raman spectroscopy of optically trapped particles,” J. Opt. A: Pure Appl. Opt.9, S139–S156 (2007).
[CrossRef]

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct.36, 171–190 (2007).
[CrossRef] [PubMed]

A. Ohta and Y. Kawata, “Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam,” Opt. Commun.274, 269–273 (2007).
[CrossRef]

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepúlveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express15, 13972–13987 (2007).
[CrossRef] [PubMed]

2006

D. Grier and Y. Roichman, “Holographic optical trapping,” Appl. Opt.45, 880–887 (2006).
[CrossRef] [PubMed]

C. Schmitz, K. Uhring, J. Spatz, and J. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express14, 6604–6612 (2006).
[CrossRef] [PubMed]

S. Parkin, G. Knöner, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the total optical angular momentum transfer in optical tweezers,” Opt. Express14, 6963–6970 (2006).
[CrossRef] [PubMed]

T. Čižmár, M. Šiler, and P. Zemánek, “An optical nanotrap array movable over a milimetre range,” Appl. Phys. B84, 197–203 (2006).
[CrossRef]

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New. J. Phys.8, 43 (2006).
[CrossRef]

S.-H. Lee and D. G. Grier, “Giant colloidal diffusivity on corrugated optical vortices,” Phys. Rev. Lett.96, 190601 (2006).
[CrossRef] [PubMed]

T. Čižmár, M. Šiler, M. Šerý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B74, 035105 (2006).
[CrossRef]

I. Ricárdez-Vargas, P. Rodríguez-Montero, R. Ramos-García, and K. Volke-Sepúlveda, “Modulated optical sieve for sorting of polydisperse microparticles,” Appl. Phys. Lett.88, 121116 (2006).
[CrossRef]

2005

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, “Microfluidic sorting of mammalian cells by optical force switching,” Nature Biotechnol.23, 83–87 (2005).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J.88, 3689–3698 (2005).
[CrossRef] [PubMed]

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

D. S. Bradshaw and D. L. Andrews, “Interactions between spherical nanoparticles optically trapped in Laguerre-Gaussian modes,” Opt. Lett.30, 3039–3041 (2005).
[CrossRef] [PubMed]

2004

2003

D. G. Grier, “A revolution in optical manipulation,” Nature424, 810–816 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett.91, 093602 (2003).
[CrossRef] [PubMed]

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

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature426, 421–424 (2003).
[CrossRef] [PubMed]

2002

M. Babiker, C. Bennett, D. Adrews, and L. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett89, 143601 (2002).
[CrossRef] [PubMed]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A66, 063402 (2002).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt.4, S82–S89 (2002).
[CrossRef]

A. O’Neil, I. MacVicar, L. Allen, and M. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
[CrossRef]

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

P. Zemánek, A. Jonáš, and M. Liška, “Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave,” J. Opt. Soc. Am. A19, 1025–1034 (2002).
[CrossRef]

2001

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A63, 063602 (2001).
[CrossRef]

2000

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177, 297–301 (2000).
[CrossRef]

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre-Gaussian beams by axicon,” Opt. Commun.184, 105–112 (2000).
[CrossRef]

1998

M. Friese, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature394, 348–350 (1998).
[CrossRef]

1997

1996

M. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A54, 1593–1596 (1996).
[CrossRef] [PubMed]

1995

W. Power, L. Allen, M. Babiker, and V. Lembessis, “Atomic motion in light beams possessing orbital angular momentum,” Phys. Rev. A52, 479–488 (1995).
[CrossRef] [PubMed]

H. He, M. Friese, N. 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]

1994

M. Babiker, W. Power, and L. Allen, “Light-induced torque on moving atoms,” Phys. Rev. Lett.73, 1239–1242 (1994).
[CrossRef] [PubMed]

1992

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

1989

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66, 4594–4602 (1989).
[CrossRef]

1988

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.19, 59–67 (1988).
[CrossRef]

1986

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]

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. Shen, “Collective rotation of molecules driven by the angular-momentum of light in a nematic film,” Phys. Rev. Lett.57, 2423–2426 (1986).
[CrossRef] [PubMed]

1936

R. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev.50, 115–125 (1936).
[CrossRef]

Adrews, D.

M. Babiker, C. Bennett, D. Adrews, and L. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett89, 143601 (2002).
[CrossRef] [PubMed]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66, 4594–4602 (1989).
[CrossRef]

Allen, L.

A. O’Neil, I. MacVicar, L. Allen, and M. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett.88, 053601 (2002).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett.22, 52–54 (1997).
[CrossRef] [PubMed]

W. Power, L. Allen, M. Babiker, and V. Lembessis, “Atomic motion in light beams possessing orbital angular momentum,” Phys. Rev. A52, 479–488 (1995).
[CrossRef] [PubMed]

M. Babiker, W. Power, and L. Allen, “Light-induced torque on moving atoms,” Phys. Rev. Lett.73, 1239–1242 (1994).
[CrossRef] [PubMed]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Ananthakrishnan, R.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J.88, 3689–3698 (2005).
[CrossRef] [PubMed]

Andrews, D. L.

Arlt, J.

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt.4, S82–S89 (2002).
[CrossRef]

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A63, 063602 (2001).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177, 297–301 (2000).
[CrossRef]

Ashkin, A.

Ashok, P. C.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett.98, 081114 (2011).
[CrossRef]

Babiker, M.

M. Babiker, C. Bennett, D. Adrews, and L. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett89, 143601 (2002).
[CrossRef] [PubMed]

W. Power, L. Allen, M. Babiker, and V. Lembessis, “Atomic motion in light beams possessing orbital angular momentum,” Phys. Rev. A52, 479–488 (1995).
[CrossRef] [PubMed]

M. Babiker, W. Power, and L. Allen, “Light-induced torque on moving atoms,” Phys. Rev. Lett.73, 1239–1242 (1994).
[CrossRef] [PubMed]

Bachor, H.-A.

V. R. Daria, M. A. Go, and H.-A. Bachor, “Simultaneous transfer of linear and orbital angular momentum to multiple low-index particles,” J. Opt.13, 044004, (2011).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66, 4594–4602 (1989).
[CrossRef]

Beck, R. J.

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Bennett, C.

M. Babiker, C. Bennett, D. Adrews, and L. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett89, 143601 (2002).
[CrossRef] [PubMed]

Beth, R.

R. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev.50, 115–125 (1936).
[CrossRef]

Bilby, C.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J.88, 3689–3698 (2005).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Block, S. M.

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct.36, 171–190 (2007).
[CrossRef] [PubMed]

Bouchal, Z.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New. J. Phys.8, 43 (2006).
[CrossRef]

Boullosa, R. R.

K. Volke-Sepúlveda, A. O. Sántillan, and R. R. Boullosa, “Transfer of angular momentum to matter from acoustical vortices in free space,” Phys. Rev. Lett.100, 024302 (2008).
[CrossRef] [PubMed]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

Bradshaw, D. S.

Brzobohatý, O.

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annual Review of Biochemistry77, 205–228 (2008).
[CrossRef] [PubMed]

Butler, W. F.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, “Microfluidic sorting of mammalian cells by optical force switching,” Nature Biotechnol.23, 83–87 (2005).
[CrossRef]

Chan, C.

J. Ng, Z. Lin, and C. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett.104, 103601 (2010).
[CrossRef] [PubMed]

Chávez-Cerda, S.

K. Volke-Sepúlveda, S. Chávez-Cerda, V. Garcés-Chávez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B21, 1749–1757 (2004).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt.4, S82–S89 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A66, 063402 (2002).
[CrossRef]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annual Review of Biochemistry77, 205–228 (2008).
[CrossRef] [PubMed]

Chiu, D. T.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett.92, 161111 (2008).
[CrossRef]

Chu, S.

Cižmár, T.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett.98, 081114 (2011).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express17, 15558–15570 (2009).
[CrossRef] [PubMed]

O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express16, 12688–12700 (2008).
[CrossRef] [PubMed]

T. Čižmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, and K. Dholakia, “Generation of multiple Bessel beams for a biophotonic workstation,” Opt. Express16, 14024–14035 (2008).
[CrossRef] [PubMed]

P. Jákl, T. Čižmár, M. Šerý, and P. Zemánek, “Static optical sorting in a laser interference field,” Appl. Phys. Lett.92, 161110 (2008).
[CrossRef]

K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Čižmár, “Cellular and colloidal separation using optical forces,” Methods Cell Biology82, 467–495 (2007).
[CrossRef]

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New. J. Phys.8, 43 (2006).
[CrossRef]

T. Čižmár, M. Šiler, M. Šerý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B74, 035105 (2006).
[CrossRef]

T. Čižmár, M. Šiler, and P. Zemánek, “An optical nanotrap array movable over a milimetre range,” Appl. Phys. B84, 197–203 (2006).
[CrossRef]

Curtis, J.

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

Daino, B.

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. Shen, “Collective rotation of molecules driven by the angular-momentum of light in a nematic film,” Phys. Rev. Lett.57, 2423–2426 (1986).
[CrossRef] [PubMed]

Dalgarno, D. I. C.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett.98, 081114 (2011).
[CrossRef]

Daria, V. R.

V. R. Daria, M. A. Go, and H.-A. Bachor, “Simultaneous transfer of linear and orbital angular momentum to multiple low-index particles,” J. Opt.13, 044004, (2011).
[CrossRef]

Dees, B.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, “Microfluidic sorting of mammalian cells by optical force switching,” Nature Biotechnol.23, 83–87 (2005).
[CrossRef]

Dholakia, K.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett.98, 081114 (2011).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express17, 15558–15570 (2009).
[CrossRef] [PubMed]

T. Čižmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, and K. Dholakia, “Generation of multiple Bessel beams for a biophotonic workstation,” Opt. Express16, 14024–14035 (2008).
[CrossRef] [PubMed]

M. Dienerowitz, M. Mazilu, P. J. Reece, T. F. Krauss, and K. Dholakia, “Optical vortex trap for resonant confinement of metal nanoparticles,” Opt. Express16, 4991–4999 (2008).
[CrossRef] [PubMed]

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepúlveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express15, 13972–13987 (2007).
[CrossRef] [PubMed]

K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Čižmár, “Cellular and colloidal separation using optical forces,” Methods Cell Biology82, 467–495 (2007).
[CrossRef]

T. Čižmár, M. Šiler, M. Šerý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B74, 035105 (2006).
[CrossRef]

K. Volke-Sepúlveda, S. Chávez-Cerda, V. Garcés-Chávez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B21, 1749–1757 (2004).
[CrossRef]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature426, 421–424 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett.91, 093602 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A66, 063402 (2002).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt.4, S82–S89 (2002).
[CrossRef]

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A63, 063602 (2001).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun.177, 297–301 (2000).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett.22, 52–54 (1997).
[CrossRef] [PubMed]

Dienerowitz, M.

Dultz, W.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett.91, 093602 (2003).
[CrossRef] [PubMed]

Dziedzic, J. M.

Ebert, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J.88, 3689–3698 (2005).
[CrossRef] [PubMed]

Edgar, J. S.

Y. Zhao, G. Milne, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Quantitative force mapping of an optical vortex trap,” Appl. Phys. Lett.92, 161111 (2008).
[CrossRef]

Enger, J.

M. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A54, 1593–1596 (1996).
[CrossRef] [PubMed]

Erickson, H. M.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J.88, 3689–3698 (2005).
[CrossRef] [PubMed]

Flores-Pérez, A.

A. O. Santillán, K. Volke-Sepúlveda, and A. Flores-Pérez, “Wave fields with a periodic orbital angular momentum gradient along a single axis: a chain of vortices,” New. J. Phys.11, 043004 (2009).
[CrossRef]

Forster, A. H.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, “Microfluidic sorting of mammalian cells by optical force switching,” Nature Biotechnol.23, 83–87 (2005).
[CrossRef]

Friese, M.

M. Friese, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature394, 348–350 (1998).
[CrossRef]

M. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A54, 1593–1596 (1996).
[CrossRef] [PubMed]

H. He, M. Friese, N. 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]

Garcés-Chávez, V.

T. Čižmár, M. Šiler, M. Šerý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B74, 035105 (2006).
[CrossRef]

K. Volke-Sepúlveda, S. Chávez-Cerda, V. Garcés-Chávez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B21, 1749–1757 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett.91, 093602 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, K. Volke-Sepúlveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A66, 063402 (2002).
[CrossRef]

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt.4, S82–S89 (2002).
[CrossRef]

Go, M. A.

V. R. Daria, M. A. Go, and H.-A. Bachor, “Simultaneous transfer of linear and orbital angular momentum to multiple low-index particles,” J. Opt.13, 044004, (2011).
[CrossRef]

Gouesbet, G.

G. Gouesbet, J. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams:localized approximations and localized beam models, a review,” J. Quant. Spectr. & Rad. Transfer112, 1–27 (2011).
[CrossRef]

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.19, 59–67 (1988).
[CrossRef]

G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories (Springer, 2011).
[CrossRef]

Greenleaf, W. J.

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct.36, 171–190 (2007).
[CrossRef] [PubMed]

Gréhan, G.

G. Gouesbet, J. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams:localized approximations and localized beam models, a review,” J. Quant. Spectr. & Rad. Transfer112, 1–27 (2011).
[CrossRef]

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.19, 59–67 (1988).
[CrossRef]

G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories (Springer, 2011).
[CrossRef]

Grier, D.

Grier, D. G.

S.-H. Lee and D. G. Grier, “Giant colloidal diffusivity on corrugated optical vortices,” Phys. Rev. Lett.96, 190601 (2006).
[CrossRef] [PubMed]

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

D. G. Grier, “A revolution in optical manipulation,” Nature424, 810–816 (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, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207, 169–175 (2002).
[CrossRef]

Guck, J.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J.88, 3689–3698 (2005).
[CrossRef] [PubMed]

Gunn-Moore, F.

Gunn-Moore, F. J.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett.98, 081114 (2011).
[CrossRef]

Guo, C.-S.

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun.283, 1889–1893 (2010).
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Figures (11)

Fig. 1
Fig. 1

(a) The optical force acting upon the polystyrene particle of radius 1 μm in the radial direction. Solid curves show the force along the beam polarization (i.e. x axis) dashed curves show the force in direction perpendicular to the beam polarization (y axis). Red (regime R1), green (regime R2), and blue (regime R3) curves show the forces for vortex beam of corresponding core radii ρ0 = 5μm, ρ0 = 1.25μm and ρ0 = 1μm, respectively. Note that the red curve is multiplied by factor 10. (b) The azimuthal optical force acting upon the same particle placed in the stable radial distance r denoted in Fig. 1(a), i.e. r = ρ1 = 0.7656ρ0 = 3.828μm for beam core radius ρ0 = 5μm (red curve) and r = 468nm for ρ0 = 1.25μm (green curve).

Fig. 2
Fig. 2

Optical forces and trajectories of a particle of radius 1 μm placed in an optical vortex beam of topological charge m = 1 having various BB core radii (a: ρ0 = 5μm, b: ρ0 = 1.25μm, c: ρ0 = 1μm, d: ρ0 = 0.58μm, e: ρ0 = 0.5μm, f: ρ0 = 0.45μm). The background pseudo-color plot shows the electric field intensity |E|2 normalized relative to the maximal intensity in (f). The magenta curves denote the deterministic trajectories of a particle (i.e. without considering the Brownian motion) starting at different locations and following the particle motion towards an equilibrium point or a stable orbit. The blue circle depicts the particle edge, its center is shown by the blue dot. The black and cyan contour represents the zero forces in the radial and azimuthal directions, respectively. If the magenta trajectories follow the black curve (zero radial force), see (a) and (d), this black curve forms a set of equilibrium positions and the particle orbits along the black curve (the particle center is drawn just in one selected position). If black and cyan curves intersect there exist equilibrium positions of the particle off the vortex axis, see (b,d). One of such possible stable positions of the particle center is denoted by the full blue dot. In other cases, see (c,f), the particle is trapped with its center on the vortex beam axis.

Fig. 3
Fig. 3

Phase map summarizing three different regimes of behavior of polystyrene particles as a function of the particle radii a and the BB core radii ρ0 in the optical vortex beam of topological charge m = 1. The particle orbits along the circular trajectories (red areas, R1, it corresponds to cases in Fig. 2(a,d)), settles in one of two off-axis positions (green areas, R2, similar to cases in Fig. 2(b,e)) or in the dark center of the vortex beam (blue areas, R3, it corresponds to cases in Fig. 2(c,f)). The particle is surrounded either by water (a) or air (b).

Fig. 4
Fig. 4

Stable radial distance of the particle r from the beam axis in the regimes R1 and R2 plotted relatively to the radius ρ1 of the optical vortex beam having topological charge m = 1. The particle is immersed either in water (a) or air (b). The black curves show the borders between all regimes (see Fig. 3).

Fig. 5
Fig. 5

The angular velocity ω (see the text) of the orbiting particle along a circular trajectory (R1) in water (a) or air (b). The black curves show the borders between all regimes.

Fig. 6
Fig. 6

Azimuthal position Φ of the particle trapped in one of the stable positions placed off the vortex axis. The angle Φ shows angular position of the first trap with respect to the polarization of the incident beam directed along the x-axis. The second trap is located symmetrically with respect to the vortex axis, the particle is immersed either in water (a) or in air (b).

Fig. 7
Fig. 7

The axial force Fz pushing the particle along the beam propagation axis for ambient water (a) or air (b). The average force along the particle orbit (in regime R1) or the force at the particle’s lateral stable position (off-axial in R2 or on-axial in R3) is shown. The black curves denote the borders between regimes.

Fig. 8
Fig. 8

(a) Phase map showing three different regimes R1, R2, and R3 of the particle behavior in the optical vortex beam of the topological charges m = 1, 2, 3, 5, 10 for a particle having radius a = 1μm immersed in water. (b) The stable radial distance r of this particle from the axis of the vortex beam (in R1 and R2) plotted relatively to the radius of the innermost bright vortex fringe ρm, m = 1, 2, 3, 5 and 10. (c) Angular velocity of the particle motion in regime R1.

Fig. 9
Fig. 9

Experimental setup (description in the text).

Fig. 10
Fig. 10

Examples of particle (radius 2 μm) motion when the BB is changed from the zero-order to high-order with m = 1 − 5, ρ0 = 870 nm in all cases. Top row: Theoretical predictions of particle trajectories following the conventions of Fig. 2. Bottom row: Experimental observations. Background plot shows the measured intensity profile of the vortex beam. Yellow spots denote the particle trapped in the zero-order BB core and magenta curves show the motion of the particle when its is illuminated by the high-order BB. The beams are polarized along horizontal axis.

Fig. 11
Fig. 11

Measured stable radial position r of the particle in the vortex beam relative to the radius of the innermost vortex ring ρm of different corresponding ρ0. Blue (positive topological charge m > 0) and green (negative topological charge m < 0) points correspond to the measured data, the error-bars indicate 95 % confidence level of the average. The red curves denote the theoretical prediction for the measured beam parameters. The BBs of various corresponding beam core radius ρ0 and topological charges m = 1 − 5 (rows from the top to the bottom) were generated by the setup shown in Fig. 9. The left and right column corresponds to polystyrene particle of radii 1 μm and 2 μm, respectively.

Tables (1)

Tables Icon

Table 1 Different regimes of particle’s behavior in non-diffracting vortex beam

Equations (7)

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E ( ρ , ϕ , z ) = E 0 ( α 0 ) e i k z cos α 0 ( i ) m e i m ϕ × ( { J m ( k r ρ ) + 1 2 [ J m + 2 ( k r ρ ) e 2 i ϕ + J m 2 ( k r ρ ) e 2 i ϕ ] P } e x + 1 2 i [ J m + 2 ( k r ρ ) e 2 i ϕ J m 2 ( k r ρ ) e 2 i ϕ ] P e y i [ J m + 1 ( k r ρ ) e i ϕ J m 1 ( k r ρ ) e i ϕ ] P | | e z ) ,
where P = 1 cos α 0 1 + cos α 0 , P | | = sin α 0 1 + cos α 0 ,
ρ 0 = 2.4048 k r = 2.4048 k sin ( α 0 ) .
P m , core π k E 0 2 ρ 0 2 2 ω 0 μ 0 σ m 2 σ 0 2 J m 1 ( σ m ) J m + 1 ( σ m ) ,
2 F r ε 0 ε 1 = α k r E 0 2 { 1 2 J m ( J m 1 J m + 1 ) ( 1 P | | 2 ) 1 2 P | | 2 ( J m + 1 J m + 2 J m 1 J m 2 ) + 1 4 P | | 4 [ J m + 2 ( J m + 1 J m + 3 ) + J m 2 ( J m + 3 J m 1 ) ] + 1 4 P | | 2 [ ( 3 J m 2 3 J m + J m + 2 ) ( J m 1 J m + 1 ) + J m ( J m 3 J m + 3 ) ] cos 2 ϕ } + α k r E 0 2 1 4 P | | 2 { ( J m + 1 + J m 1 ) ( J m + 2 + J m 2 J m ) J m ( J m + 3 + J m 3 ) } sin 2 ϕ ,
2 F ϕ ε 0 ε 1 = 2 r α E 0 2 P | | 2 [ 1 2 J m ( J m + 2 + J m 2 ) J m + 1 J m 1 ] sin 2 ϕ + 1 r α E 0 2 { m J m 2 + P | | 2 [ J m + 1 2 ( m + 1 ) + J m 1 2 ( m 1 ) ] + 1 2 P | | 4 [ J m + 1 2 ( m + 1 ) + J m 2 2 ( m 1 ) ] + m P | | 2 [ J m ( J m + 2 + J m 2 ) 2 J m + 1 J m 1 ] cos 2 ϕ } ,
2 F z ε 0 ε 1 = α k cos α 0 E 0 2 { J m 2 + P | | 2 ( J m + 1 2 + J m 1 2 ) + 1 2 P | | 4 ( J m + 2 2 + J m 2 2 ) + P | | 2 [ J m ( J m + 2 + J m 2 ) 2 J m + 1 J m 1 ] cos 2 ϕ } ,

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