Abstract

We demonstrate the simultaneous trapping of multiple high-refractive index (n>2) particles in a dynamic array of counterpropagating optical tweezers in which the destabilizing scattering forces are canceled. These particles cannot be trapped in single-beam optical tweezers. The combined use of two opposing high-numerical aperture objectives and micrometer-sized high-index titania particles yields an at least threefold increase in both axial and radial trap stiffness compared to silica particles under the same conditions. The stiffness in the radial direction is obtained from measured power spectra; calculations are given for both the radial and the axial force components, taking spherical aberrations into account. A pair of acousto-optic deflectors allows for fast, computer-controlled manipulation of the individual trapping positions in a plane, while the method used to create the patterns ensures the possibility of arbitrarily chosen configurations. The manipulation of high-index particles finds its application in, e.g., creating defects in colloidal photonic crystals and in exerting high forces with low laser power in, for example, biophysical experiments.

© 2008 Optical Society of America

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  1. 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]
  2. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  3. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795-799(1996).
    [CrossRef] [PubMed]
  4. P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time three-dimensional optical micromanipulation of multiple particles and living cells,” Opt. Lett. 29, 2270-2272 (2004).
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    [CrossRef]
  6. W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73, 2308-2316 (2002).
    [CrossRef]
  7. A. van der Horst, A. I. Campbell, L. K. van Vugt, D. A. M. Vanmaekelbergh, M. Dogterom, and A. van Blaaderen, “Manipulating metal-oxide nanowires using counter-propagating optical line tweezers,” Opt. Express 15, 11629-11639 (2007).
    [CrossRef] [PubMed]
  8. J. P. Hoogenboom, D. J. L. Vossen, C. Faivre-Moskalenko, M. Dogterom, and A. van Blaaderen, “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828-4830 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. P. A. Maia Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
    [CrossRef]
  11. A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
    [CrossRef]
  12. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
    [CrossRef]
  13. D. L. J. Vossen, A. van der Horst, M. Dogterom, and A. van Blaaderen, “Optical tweezers and confocal microscopy for simultaneous three-dimensional manipulation and imaging in concentrated colloidal dispersions,” Rev. Sci. Instrum. 75, 2960-2970 (2004).
    [CrossRef]
  14. K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
    [CrossRef]
  15. J. Baumgartl and C. Bechinger., “On the limits of digital microscopy,” Europhys. Lett. 71, 487-493 (2005).
    [CrossRef]
  16. M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074-1085(1998).
    [CrossRef] [PubMed]
  17. H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, and H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829-3836 (1991).
    [CrossRef]
  18. A. C. Dogariu and R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770-2778 (2000).
    [CrossRef]
  19. A. Rohrbach and E. H. K. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494-2507(2002).
    [CrossRef] [PubMed]
  20. The code to calculate the axial forces is freely available on www.wave-scattering.com and as supplementary material to this paper.
  21. A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351-1355 (1977).
    [CrossRef]
  22. A. A. R. Neves, A. Fontes, L. de Y. Pozzo, A. A. de Thomaz, E. Chillce, E. Rodriguez, L. C. Barbosa, and C. L. Cesar, “Electromagnetic forces for an arbitrary optical trapping of a spherical dielectric,” Opt. Express 14, 13101-13106(2006).
    [CrossRef] [PubMed]
  23. P. J. Rodrigo, I. R. Perch-Nielsen, and J. Glückstad, “Three-dimensional forces in GPC-based counterpropagating-beam traps,” Opt. Express 14, 5812-5822 (2006).
    [CrossRef] [PubMed]
  24. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263-4269 (2006).
    [CrossRef] [PubMed]
  25. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358-379 (1959).
    [CrossRef]

2007 (2)

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
[CrossRef]

A. van der Horst, A. I. Campbell, L. K. van Vugt, D. A. M. Vanmaekelbergh, M. Dogterom, and A. van Blaaderen, “Manipulating metal-oxide nanowires using counter-propagating optical line tweezers,” Opt. Express 15, 11629-11639 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

J. Baumgartl and C. Bechinger., “On the limits of digital microscopy,” Europhys. Lett. 71, 487-493 (2005).
[CrossRef]

2004 (2)

D. L. J. Vossen, A. van der Horst, M. Dogterom, and A. van Blaaderen, “Optical tweezers and confocal microscopy for simultaneous three-dimensional manipulation and imaging in concentrated colloidal dispersions,” Rev. Sci. Instrum. 75, 2960-2970 (2004).
[CrossRef]

P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time three-dimensional optical micromanipulation of multiple particles and living cells,” Opt. Lett. 29, 2270-2272 (2004).
[CrossRef] [PubMed]

2003 (1)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

2002 (3)

J. P. Hoogenboom, D. J. L. Vossen, C. Faivre-Moskalenko, M. Dogterom, and A. van Blaaderen, “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828-4830 (2002).
[CrossRef]

W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494-2507(2002).
[CrossRef] [PubMed]

2000 (2)

A. C. Dogariu and R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770-2778 (2000).
[CrossRef]

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

1998 (1)

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074-1085(1998).
[CrossRef] [PubMed]

1997 (1)

1996 (2)

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

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

1994 (1)

K. Svoboda and S. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
[CrossRef] [PubMed]

1991 (1)

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, and H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829-3836 (1991).
[CrossRef]

1986 (1)

1977 (1)

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351-1355 (1977).
[CrossRef]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358-379 (1959).
[CrossRef]

Allersma, M. W.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074-1085(1998).
[CrossRef] [PubMed]

Ashkin, A.

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]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351-1355 (1977).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Barbosa, L. C.

Baumgartl, J.

J. Baumgartl and C. Bechinger., “On the limits of digital microscopy,” Europhys. Lett. 71, 487-493 (2005).
[CrossRef]

Bechinger., C.

J. Baumgartl and C. Bechinger., “On the limits of digital microscopy,” Europhys. Lett. 71, 487-493 (2005).
[CrossRef]

Berns, M. W.

Bjorkholm, J. E.

Block, S.

K. Svoboda and S. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
[CrossRef] [PubMed]

Block, S. M.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Bustamante, C.

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

Campbell, A. I.

Cesar, C. L.

Chillce, E.

Chiou, A. E.

Chu, S.

Cui, Y.

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

Daria, V. R.

de Thomaz, A. A.

deCastro, M. J.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074-1085(1998).
[CrossRef] [PubMed]

Dogariu, A. C.

A. C. Dogariu and R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770-2778 (2000).
[CrossRef]

Dogterom, M.

A. van der Horst, A. I. Campbell, L. K. van Vugt, D. A. M. Vanmaekelbergh, M. Dogterom, and A. van Blaaderen, “Manipulating metal-oxide nanowires using counter-propagating optical line tweezers,” Opt. Express 15, 11629-11639 (2007).
[CrossRef] [PubMed]

D. L. J. Vossen, A. van der Horst, M. Dogterom, and A. van Blaaderen, “Optical tweezers and confocal microscopy for simultaneous three-dimensional manipulation and imaging in concentrated colloidal dispersions,” Rev. Sci. Instrum. 75, 2960-2970 (2004).
[CrossRef]

J. P. Hoogenboom, D. J. L. Vossen, C. Faivre-Moskalenko, M. Dogterom, and A. van Blaaderen, “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828-4830 (2002).
[CrossRef]

Dziedzic, J. M.

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]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351-1355 (1977).
[CrossRef]

Faivre-Moskalenko, C.

J. P. Hoogenboom, D. J. L. Vossen, C. Faivre-Moskalenko, M. Dogterom, and A. van Blaaderen, “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828-4830 (2002).
[CrossRef]

Fontes, A.

Gittes, F.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074-1085(1998).
[CrossRef] [PubMed]

Glückstad, J.

Grange, W.

W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Güntherodt, H.-J.

W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Hegner, M.

W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Hoogenboom, J. P.

J. P. Hoogenboom, D. J. L. Vossen, C. Faivre-Moskalenko, M. Dogterom, and A. van Blaaderen, “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828-4830 (2002).
[CrossRef]

Husale, S.

W. Grange, S. Husale, H.-J. Güntherodt, and M. Hegner, “Optical tweezers system measuring the change in light momentum flux,” Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Kitamura, N.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, and H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829-3836 (1991).
[CrossRef]

Koshioka, M.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, and H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829-3836 (1991).
[CrossRef]

Maia Neto, P. A.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263-4269 (2006).
[CrossRef] [PubMed]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

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

Masuhara, H.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, and H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829-3836 (1991).
[CrossRef]

Mazolli, A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

Mesquita, O. N.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263-4269 (2006).
[CrossRef] [PubMed]

Misawa, H.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, and H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829-3836 (1991).
[CrossRef]

Mozolli, A.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263-4269 (2006).
[CrossRef] [PubMed]

Neves, A. A. R.

Nussenzveig, H. M.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

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

Perch-Nielsen, I. R.

Pozzo, L. de Y.

Rajagopalan, R.

A. C. Dogariu and R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770-2778 (2000).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358-379 (1959).
[CrossRef]

Rocha, M. S.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263-4269 (2006).
[CrossRef] [PubMed]

Rodrigo, P. J.

Rodriguez, E.

Rohrbach, A.

Sasaki, K.

H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, and H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys. 70, 3829-3836 (1991).
[CrossRef]

Schmidt, C. F.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074-1085(1998).
[CrossRef] [PubMed]

Smith, S. B.

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

Sonek, G. J.

Stelzer, E. H. K.

Stewart, R. J.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074-1085(1998).
[CrossRef] [PubMed]

Svoboda, K.

K. Svoboda and S. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285(1994).
[CrossRef] [PubMed]

van Blaaderen, A.

A. van der Horst, A. I. Campbell, L. K. van Vugt, D. A. M. Vanmaekelbergh, M. Dogterom, and A. van Blaaderen, “Manipulating metal-oxide nanowires using counter-propagating optical line tweezers,” Opt. Express 15, 11629-11639 (2007).
[CrossRef] [PubMed]

D. L. J. Vossen, A. van der Horst, M. Dogterom, and A. van Blaaderen, “Optical tweezers and confocal microscopy for simultaneous three-dimensional manipulation and imaging in concentrated colloidal dispersions,” Rev. Sci. Instrum. 75, 2960-2970 (2004).
[CrossRef]

J. P. Hoogenboom, D. J. L. Vossen, C. Faivre-Moskalenko, M. Dogterom, and A. van Blaaderen, “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828-4830 (2002).
[CrossRef]

van der Horst, A.

A. van der Horst, A. I. Campbell, L. K. van Vugt, D. A. M. Vanmaekelbergh, M. Dogterom, and A. van Blaaderen, “Manipulating metal-oxide nanowires using counter-propagating optical line tweezers,” Opt. Express 15, 11629-11639 (2007).
[CrossRef] [PubMed]

D. L. J. Vossen, A. van der Horst, M. Dogterom, and A. van Blaaderen, “Optical tweezers and confocal microscopy for simultaneous three-dimensional manipulation and imaging in concentrated colloidal dispersions,” Rev. Sci. Instrum. 75, 2960-2970 (2004).
[CrossRef]

van Vugt, L. K.

Vanmaekelbergh, D. A. M.

Viana, N. B.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, P. A. Maia Neto, and H. M. Nussenzveig. “Towards absolute calibration of optical tweezers,” Phys. Rev. E 75, 021914(2007).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mozolli, and P. A. Maia Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263-4269 (2006).
[CrossRef] [PubMed]

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Vossen, D. J. L.

J. P. Hoogenboom, D. J. L. Vossen, C. Faivre-Moskalenko, M. Dogterom, and A. van Blaaderen, “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828-4830 (2002).
[CrossRef]

Vossen, D. L. J.

D. L. J. Vossen, A. van der Horst, M. Dogterom, and A. van Blaaderen, “Optical tweezers and confocal microscopy for simultaneous three-dimensional manipulation and imaging in concentrated colloidal dispersions,” Rev. Sci. Instrum. 75, 2960-2970 (2004).
[CrossRef]

Wang, W.

Wolf, E.

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Other (1)

The code to calculate the axial forces is freely available on www.wave-scattering.com and as supplementary material to this paper.

Supplementary Material (2)

» Media 1: AVI (1604 KB)     
» Media 2: AVI (12639 KB)     

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Figures (8)

Fig. 1
Fig. 1

Schematics of (a) the optical tweezers setup and (b) the counterpropagating traps scanned with one pair of AODs. A pattern of inverted beam traps (∘) is a mirror image of the pattern of upright beam traps (×) with the mirror plane top-to-bottom in the image. In addition, the magnification between the inverted and the upright beam path might differ. By adding a mirrored and appropriately scaled pattern to the original traps, counterpropagating traps (⊗) can be created for which the position of each trap can be chosen arbitrarily.

Fig. 2
Fig. 2

(Multimedia online; ao.osa.org) Stills from a movie in bright-field microscopy of four counterpropagating traps filled with one 1.4 μm diameter Si O 2 (arrow) and three 1.1 μm diameter Ti O 2 particles. The particles are positioned 12 μm away from either wall, and the pattern is changed in 34 steps in 1.2 s . The short version of the movie (1.8 MB) shows this complete change of the pattern four times, while the longer version of the movie (12.3 MB) shows it 28 times. Scale bar is 2 μm .

Fig. 3
Fig. 3

PSD curves of the normalized signal for a Si O 2 (gray solid curve, diameter 1.4 μm ) and a Ti O 2 (black dotted curves, 1.1 μm ) particle in ethanol for given laser powers inside the counterpropagating trap. For clarity only one curve is shown for Si O 2 . Lorentzian fits (dashed curves) are plotted for the 44 mW curves, with f 0 at 115 Hz ( Si O 2 ) and 499 Hz ( Ti O 2 ). Highest laser powers result in lowest plateau values.

Fig. 4
Fig. 4

Calculations of the force per 1 W laser power for 1.1 μm diameter Ti O 2 ( n = 2.4 ) and Si O 2 ( n = 1.45 ) particles in ethanol ( n = 1.36 ) in Gaussian single and cp traps using 100 × , 1.4 NA , oil immersion objectives. Spherical aberrations are accounted for. (a) Axial force, with z as the offset of the particle from the focal plane of one objective and (b) radial force at the trapping plane for 1.4 μm Si O 2 ( z = 0.628 μm ) as a function of the distance to the optical axis. In addition, the curve for 1.4 μm Si O 2 is shown.

Fig. 5
Fig. 5

Calculations of the force per 1 W laser power for 1.1 μm diameter Ti O 2 ( n = 2.4 ) and Si O 2 ( n = 1.45 ) particles in ethanol ( n = 1.36 ) in Gaussian single and cp traps using 100 × , 1.4 NA , oil immersion objectives. Spherical aberrations are neglected. (a) Axial force, with z as the offset of the particle from the focal plane of one objective and (b) radial force at the trapping plane for 1.4 μm Si O 2 ( z = 0.028 μm ) as a function of the distance to the optical axis. In addition, the curve for 1.4 μm Si O 2 is shown.

Fig. 6
Fig. 6

Calculated trap stiffness κ for varying indices of refraction n of a 1.4 μm diameter particle in ethanol ( n = 1.36 ) with and without spherical aberrations. Single-beam trapping (solid curves) is limited to n < 1.87 ; for higher n the particle will be pushed along the beam axis. Because of symmetry, where single-beam trapping is possible, the radial stiffness κ x y is the same as κ x y for cp trapping.

Fig. 7
Fig. 7

Calculated trap stiffness κ z and κ x y for varying radius r of (a) titania ( n = 2.4 ) and (b) silica ( n = 1.45 ) particles in cp traps in ethanol ( n = 1.36 ). The stiffness is calculated at fixed depth z = 0.628 μm , which is not for every radius the position for which F z = 0 . Spherical aberrations were taken into account.

Fig. 8
Fig. 8

Calculated axial force (assuming no spherical aberrations) for a 1.1 μm diameter Ti O 2 particle ( n = 2.4 ) in ethanol ( n = 1.36 ) for high-NA objectives ( 100 × , 1.4 NA ; solid curves) and low-NA objectives ( 60 × , 0.85 NA ; dashed curves). There is no stable trapping position for the single-beam traps. In the counterpropagating (cp) beams, the axial stiffness κ z at the stable trapping position is 1043 pN / ( μm × W ) ( 1.4 NA ) and 103 pN / ( μm × W ) ( 0.85 NA ).

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