Abstract

Spatially periodic optical fields can be used to sort dielectric microscopic particles as a function of size, shape or refractive index. In this paper we elucidate through both theory and experiment the behavior of silica microspheres moving under the influence of the periodic optical field provided by a Bessel beam. We compare two different computational models, one based on Mie scattering, the other on geometrical ray optics and find good qualitative agreement, with both models predicting the existence of distinct size-dependent phases of particle behavior. We verify these predictions by providing experimental observations of the individual behavioral phases.

© 2007 Optical Society of America

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    [CrossRef]
  5. M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
    [CrossRef] [PubMed]
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  26. 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 (1989).
    [CrossRef]
  27. 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. A 66, 063402 (2002).
    [CrossRef]
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    [CrossRef]
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  30. N. Chattrapiban, E. A. Rogers, D. Cofield, W. T. Hill, and R. Roy, "Generation of nondiffracting bessel beams by use of a spatial light modulator," Opt. Lett. 28, 2183 (2003).
    [CrossRef] [PubMed]

2006 (5)

K. Dholakia and P. Reece, "Optical micromanipulation takes hold," Nano Today 1, 18 (2006).
[CrossRef]

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

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

S. Lee and D. G. Grier, "One-dimensional optical thermal ratchets," J. Phys.: Condens. Matter 17, S3685-S3695 (2006).
[CrossRef]

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

2005 (3)

T. Cizmar, V. Garcés-Chávez, K. Dholakia, P. Zemanek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

D. McGloin and K. Dholakia, "Bessel Beams: Diffraction in a new light," Contemp. Phys. 46, 15 (2005).
[CrossRef]

2004 (4)

K. Volke-Sepulveda, S. Chávez-Cerda, V. Garcés-Chávez and K. Dholakia, "Three-dimensional optical forces and transfer of orbital angular momentum from multi-ringed light beams to spherical microparticles," J. Opt. Soc. Am. B 21, 1749 (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]

M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
[CrossRef] [PubMed]

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

2003 (6)

C. Bustamante, Z. Bryan, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423 (2003).
[CrossRef] [PubMed]

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

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

S. A. Tatarkova, W. Sibbett and K. Dholakia, "Brownian particle in an optical potential of the washboard type," Phys. Rev. Lett. 91, 038101 (2003).
[CrossRef] [PubMed]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215 (2003).
[CrossRef]

N. Chattrapiban, E. A. Rogers, D. Cofield, W. T. Hill, and R. Roy, "Generation of nondiffracting bessel beams by use of a spatial light modulator," Opt. Lett. 28, 2183 (2003).
[CrossRef] [PubMed]

2002 (3)

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. A 66, 063402 (2002).
[CrossRef]

P. Zemanek, A. Jonas, and M. Liska, "Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave," J. Opt. Soc. Am. A 19, 1025 (2002).
[CrossRef]

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

2001 (1)

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, "Optical dipole traps and atomic waveguides based on Bessel light beams," Phys. Rev. A 63, 063602 (2001).
[CrossRef]

2000 (1)

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1085 (2000).
[CrossRef]

1999 (1)

L. McCann, M. I. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785 (1999).
[CrossRef]

1992 (2)

K. Visscher and G. J. Brakenhoff, "A theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers," Optik 89, 174 (1992).

R. Gussgard, T. Lindmo, and I. Brevik, "Calculation of the trapping force in a strongly focused laser beam," J. Opt. Soc. Am. B 9, 1922 (1992).
[CrossRef]

1989 (1)

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 (1989).
[CrossRef]

1987 (1)

1986 (1)

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 (1989).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, "Optical dipole traps and atomic waveguides based on Bessel light beams," Phys. Rev. A 63, 063602 (2001).
[CrossRef]

Ashkin, A.

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 (1989).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

Bouchal, Z.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Brakenhoff, G. J.

K. Visscher and G. J. Brakenhoff, "A theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers," Optik 89, 174 (1992).

Brevik, I.

Bryan, Z.

C. Bustamante, Z. Bryan, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423 (2003).
[CrossRef] [PubMed]

Bryant, P. E.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Bustamante, C.

C. Bustamante, Z. Bryan, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423 (2003).
[CrossRef] [PubMed]

Chattrapiban, N.

Chaumet, P. C.

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1085 (2000).
[CrossRef]

Chávez-Cerda, S.

K. Volke-Sepulveda, S. Chávez-Cerda, V. Garcés-Chávez and K. Dholakia, "Three-dimensional optical forces and transfer of orbital angular momentum from multi-ringed light beams to spherical microparticles," J. Opt. Soc. Am. B 21, 1749 (2004).
[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. A 66, 063402 (2002).
[CrossRef]

Chu, S.

Cizmar, T.

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

T. Cizmar, V. Garcés-Chávez, K. Dholakia, P. Zemanek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Cofield, D.

Dholakia, K.

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

K. Dholakia and P. Reece, "Optical micromanipulation takes hold," Nano Today 1, 18 (2006).
[CrossRef]

T. Cizmar, V. Garcés-Chávez, K. Dholakia, P. Zemanek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

D. McGloin and K. Dholakia, "Bessel Beams: Diffraction in a new light," Contemp. Phys. 46, 15 (2005).
[CrossRef]

K. Volke-Sepulveda, S. Chávez-Cerda, V. Garcés-Chávez and K. Dholakia, "Three-dimensional optical forces and transfer of orbital angular momentum from multi-ringed light beams to spherical microparticles," J. Opt. Soc. Am. B 21, 1749 (2004).
[CrossRef]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215 (2003).
[CrossRef]

S. A. Tatarkova, W. Sibbett and K. Dholakia, "Brownian particle in an optical potential of the washboard type," Phys. Rev. Lett. 91, 038101 (2003).
[CrossRef] [PubMed]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421 (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. A 66, 063402 (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. A 63, 063602 (2001).
[CrossRef]

Durnin, J.

Dykman, M. I.

L. McCann, M. I. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785 (1999).
[CrossRef]

Dziedzic, J. M.

Enger, M. J.

M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
[CrossRef] [PubMed]

Garcés-Chávez, V.

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

T. Cizmar, V. Garcés-Chávez, K. Dholakia, P. Zemanek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

K. Volke-Sepulveda, S. Chávez-Cerda, V. Garcés-Chávez and K. Dholakia, "Three-dimensional optical forces and transfer of orbital angular momentum from multi-ringed light beams to spherical microparticles," J. Opt. Soc. Am. B 21, 1749 (2004).
[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. A 66, 063402 (2002).
[CrossRef]

Goksör, M.

M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
[CrossRef] [PubMed]

Golding, B.

L. McCann, M. I. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785 (1999).
[CrossRef]

Grier, D. G.

S. Lee and D. G. Grier, "One-dimensional optical thermal ratchets," J. Phys.: Condens. Matter 17, S3685-S3695 (2006).
[CrossRef]

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

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

Gunn-Moore, F. J.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Gussgard, R.

Hagberg, P.

M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
[CrossRef] [PubMed]

Hanstorp, D.

M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
[CrossRef] [PubMed]

Hill, W. T.

Jakl, P.

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

Jezek, J.

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

Jonas, A.

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

P. Zemanek, A. Jonas, and M. Liska, "Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave," J. Opt. Soc. Am. A 19, 1025 (2002).
[CrossRef]

Kollarova, V.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Korda, P. T.

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

Ladavac, K.

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

Lee, S.

S. Lee and D. G. Grier, "One-dimensional optical thermal ratchets," J. Phys.: Condens. Matter 17, S3685-S3695 (2006).
[CrossRef]

Lindmo, T.

Liska, M.

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

P. Zemanek, A. Jonas, and M. Liska, "Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave," J. Opt. Soc. Am. A 19, 1025 (2002).
[CrossRef]

MacDonald, M. P.

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

McCann, L.

L. McCann, M. I. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785 (1999).
[CrossRef]

McGloin, D.

D. McGloin and K. Dholakia, "Bessel Beams: Diffraction in a new light," Contemp. Phys. 46, 15 (2005).
[CrossRef]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215 (2003).
[CrossRef]

Melville, H.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215 (2003).
[CrossRef]

Milne, G.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Neuman, K. C.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

Nieto-Vesperinas, M.

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1085 (2000).
[CrossRef]

Papagiakoumou, E.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Paterson, L.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[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]

Ramos-García, R.

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

Ramser, K.

M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
[CrossRef] [PubMed]

Reece, P.

K. Dholakia and P. Reece, "Optical micromanipulation takes hold," Nano Today 1, 18 (2006).
[CrossRef]

Ricárdez-Vargas, I.

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

Riches, A.C.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Rodríguez-Montero, P.

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

Rogers, E. A.

Roy, R.

Schaub, S. A.

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 (1989).
[CrossRef]

Sery, M.

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

Sibbett, W.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

S. A. Tatarkova, W. Sibbett and K. Dholakia, "Brownian particle in an optical potential of the washboard type," Phys. Rev. Lett. 91, 038101 (2003).
[CrossRef] [PubMed]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215 (2003).
[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. A 66, 063402 (2002).
[CrossRef]

Siler, M.

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Smith, S. B.

C. Bustamante, Z. Bryan, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423 (2003).
[CrossRef] [PubMed]

Soneson, J.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, "Optical dipole traps and atomic waveguides based on Bessel light beams," Phys. Rev. A 63, 063602 (2001).
[CrossRef]

Spalding, C.

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

Spalding, G. C.

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

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215 (2003).
[CrossRef]

Tatarkova, S. A.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

S. A. Tatarkova, W. Sibbett and K. Dholakia, "Brownian particle in an optical potential of the washboard type," Phys. Rev. Lett. 91, 038101 (2003).
[CrossRef] [PubMed]

Visscher, K.

K. Visscher and G. J. Brakenhoff, "A theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers," Optik 89, 174 (1992).

Volke-Sepulveda, K.

Volke-Sepúlveda, K.

I. Ricárdez-Vargas, P. Rodríguez-Montero, R. Ramos-García, and K. Volke-Sepúlveda, "A modulated optical sieve for sorting of polydisperse microparticles," Appl. Phys. Lett. 88, 121116 (2006).
[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. A 66, 063402 (2002).
[CrossRef]

Wright, E. M.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, "Optical dipole traps and atomic waveguides based on Bessel light beams," Phys. Rev. A 63, 063602 (2001).
[CrossRef]

Zemanek, P.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

T. Cizmar, V. Garcés-Chávez, K. Dholakia, P. Zemanek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

P. Zemanek, A. Jonas, and M. Liska, "Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave," J. Opt. Soc. Am. A 19, 1025 (2002).
[CrossRef]

Appl. Phys. Lett. (3)

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

T. Cizmar, V. Garcés-Chávez, K. Dholakia, P. Zemanek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A.C. Riches and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, "Bessel Beams: Diffraction in a new light," Contemp. Phys. 46, 15 (2005).
[CrossRef]

J. Appl. Phys. (1)

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 (1989).
[CrossRef]

J. Mod. Opt. (1)

P. Jakl, M. Sery, J. Jezek, A. Jonas, M. Liska, and P. Zemanek, "Behaviour of an optically trapped probe approaching a dielectric interface," J. Mod. Opt. 50, 1615 (2003).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

J. Phys.: Condens. Matter (1)

S. Lee and D. G. Grier, "One-dimensional optical thermal ratchets," J. Phys.: Condens. Matter 17, S3685-S3695 (2006).
[CrossRef]

Lab Chip (1)

M. J. Enger, M. Goksör, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab Chip 4, 196 - 200 (2004).
[CrossRef] [PubMed]

Nano Today (1)

K. Dholakia and P. Reece, "Optical micromanipulation takes hold," Nano Today 1, 18 (2006).
[CrossRef]

Nature (3)

C. Bustamante, Z. Bryan, and S. B. Smith, "Ten years of tension: single-molecule DNA mechanics," Nature 421, 423 (2003).
[CrossRef] [PubMed]

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

L. McCann, M. I. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785 (1999).
[CrossRef]

New J. Phys. (1)

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Opt. Commun. (1)

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215 (2003).
[CrossRef]

Opt. Lett. (3)

Optik (1)

K. Visscher and G. J. Brakenhoff, "A theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers," Optik 89, 174 (1992).

Phys. Rev. A (2)

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, "Optical dipole traps and atomic waveguides based on Bessel light beams," Phys. Rev. A 63, 063602 (2001).
[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. A 66, 063402 (2002).
[CrossRef]

Phys. Rev. B (2)

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

T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, "Optical sorting and detection of submicrometer objects in a motional standing wave," Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (1)

S. A. Tatarkova, W. Sibbett and K. Dholakia, "Brownian particle in an optical potential of the washboard type," Phys. Rev. Lett. 91, 038101 (2003).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

Other (1)

G. Milne, "St Andrews Tracker," http://faculty.washington.edu/gmilne/tracker.htm>.

Supplementary Material (2)

» Media 1: AVI (1647 KB)     
» Media 2: AVI (1447 KB)     

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Figures (12)

Fig. 1.
Fig. 1.

(Color online) (a) Cross-section of a Bessel beam along direction of propagation. (b) Cross-section perpendicular to direction of propagation, taken at point A in (a). The figures were generated using a fast Fourier transform beam propagation algorithm, as used in previous work [23].

Fig. 2.
Fig. 2.

(Color online) Overview of the experimental set-up. A system of beam cubes and half-wave plates modulated the power of a collimated 1070nm laser beam. One beam line illuminated an axicon, creating a Bessel beam, which was then imaged onto the sample stage. A second beam line was used to create a standard optical trap, with a 4f lens system mapping a steering mirror to the back aperture of the imaging microscope objective. A CCD camera was used to record particle behavior in the Bessel beam.

Fig. 3.
Fig. 3.

[1.6MB] (Color online) Optical radial forces (red) and corresponding potential profiles (blue) obtained for a silica sphere of radius 1.15μm (refractive index nb=1.4496) immersed in water (nm=1.333) using the Mie scattering theory. The intensity of the Bessel beam on-axis was equal to the intensity obtained from Eq. (2) for z=zmax /2, P=200mW, λ=1070/nm nm, wc=28.3μm, α=7.5°. The dashed curve shows the corresponding radial intensity profile of the Bessel beam. Circles denote the radial equilibrium positions, while * mark the extreme values of the optical force. The corresponding movie shows the dependency on particle radius. [Media 1]

Fig. 4.
Fig. 4.

(Color online) Optical radial forces (red) and corresponding potential energy profiles (blue) obtained for two sizes of silica spheres. From (a) we can see that when R0=2.15μm the radial force is uniformly negative. The potential profile (b) shows only one equilibrium point, at the beam core. In contrast, increasing the particle size slightly to R0=2.5μm (c) reveals a new regime where particles can be trapped radially in equilibrium points located between the rings (d). The dashed curve shows the corresponding radial intensity profile.

Fig. 5.
Fig. 5.

(Color online) Optical radial forces (red) and corresponding potential profiles (blue) obtained for silica spheres of radius 3.42μm. The core equilibrium position is offset from the centre of the Bessel beam by approximately 1μm. Additionally, shallow potential energy wells can be seen 15μm and 18μm from the core (inset).

Fig. 6.
Fig. 6.

[1.5MB] (Color online) Transversal intensity profile of the Bessel beam with the equilibrium position of two selected spheres. The black ring (radius 2.35μm) denotes the first intensity minimum of the Bessel beam. The stable equilibrium point for the smaller particle (a) is localized off axis, while for the larger particle (b) it is aligned with the core of the Bessel beam. The associated movie shows the movement of the core equilibrium position as particle radius is increased. [Media 2]

Fig. 7.
Fig. 7.

Typical transversal trajectory of a R0=1.15μm silica sphere in a Bessel beam. When a sphere escapes a ring, its transition to the adjacent ring is relatively direct.

Fig. 8.
Fig. 8.

(Color online) Histograms for the transition times of a R0=1.15μm sphere from the 5th-ring of a Bessel beam for different values of the overall beam power: (a) 50mW, (b) 100mW, (c) 150mW, (d) 200mW. The mean escape time increases as the beam power is increased. Histograms have bin widths of 10secs. Red bars represent hops outwards, green represent hops inwards towards beam core. In each case τin represents the estimated mean first passage time, in seconds, towards the core of the beam.

Fig. 9.
Fig. 9.

(Color online) (a) A typical trajectory for a R0=2.5μm silica particle in a Bessel beam closer to the core. (b) Away from the core, R0=2.5μm particles can be trapped loosely across two rings. Beam power is 200mW in both cases.

Fig. 10.
Fig. 10.

(Color online) A with R0=3.42μm particle has been tracked for over 15 minutes. Its centre of mass, which moves due to Brownian motion, remains approximately 1μm from the beam core (red cross) at all times.

Fig. 11.
Fig. 11.

(Color online) Two comparative plots showing predictions for radial force in a Bessel beam, showing our geometric model (GM) against our Mie model (Mie). (a) R0=0.5μm. (b) R0=4.7μm.

Fig. 12.
Fig. 12.

(Color online) (a) Plot of radial optical force due to a Bessel beam as a function of particle-core separation and particle diameter. (b) Radial intensity profile of Bessel beam for comparison.

Tables (1)

Tables Icon

Table 1. Comparison of Computation Times for Our Two Theoretical Models

Equations (13)

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

E ( r , t ) = E 0 B J 0 ( k r r ) exp { i ( k z z ω t ) } ,
I ( r , z ) = 4 k r P w c z z max J 0 2 ( k r r ) exp { 2 z 2 z max 2 } .
z max = w c tan ( α ) ,
Δ ρ λ 2 sin α ,
E ( r , ϕ , z ) = E B 0 exp ( ik z z ) { [ J 0 ( k r r ) + J 2 ( k r r ) β 2 cos ( 2 ϕ ) ] e x
+ J 2 ( k r r ) β 2 sin ( 2 ϕ ) e y i 2 J 1 ( k r r ) β cos ( ϕ ) e z } ,
B ( r , ϕ , z ) = k ω E B 0 exp ( ik z z ) { J 2 ( k r r ) β 2 sin ( 2 ϕ ) e x
+ [ J 0 ( k r r ) J 2 ( k r r ) β 2 cos ( 2 ϕ ) ] e y i 2 J 1 ( k r r ) β sin ( ϕ ) e z } ,
A lm = 1 l ( l + 1 ) ψ . ( ξ ) 0 2 π 0 2 π sin θ E r i ( r 0 , z 0 ) Y lm * ( θ , φ ) dθdφ ,
B lm = 1 l ( l + 1 ) ψ . ( ξ ) 0 2 π 0 2 π sin θ B r i ( r 0 , z 0 ) Y lm * ( θ , φ ) dθdφ ,
r 0 = r 2 + R 0 2 sin 2 θ + 2 R 0 r cos ( φ φ 0 ) sin θ , z 0 = z + R 0 cos θ
F ρ ( r , z ) = n m R 0 2 2 c 0 π 2 0 2 π I ( r 0 , z 0 ) [ R sin 2 θ T 2 ( sin 2 ( θ θ t ) + R sin 2 θ 1 + R 2 + 2 R cos 2 θ t ) ] sin 2 θ cos φdφdθ .
U = ( r , z = z pezk ) = 0 r E ρ ( r , z = z peak ) dr .

Metrics