Abstract

We present a full quantitative mapping of the non-linear optical trapping force associated to an extended interference pattern of fringes as a function of the position. To map this force, we studied the dynamics of microscopic spherical beads of different sizes (8, 10 and 14.5 microns in diameter) moving through the light pattern. For this range of particle sizes, the system is overdamped due to the viscous drag and the effect of thermal noise is negligible. The novel experimental approach consists in tilting the sample cell a small angle with respect to the horizontal, thus we have a deterministic particle in an inclined plane. The combined action of the optical force and gravity gives rise to a washboard potential. We compared our experimental results with a ray optics model and found a good quantitative agreement. For each size of the microsphere we studied different spatial periods of the interference fringes.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. H. He, M. J. E. Friese, N. R. 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]
  6. 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]
  7. K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclassical Opt. 4, S82-S89 (2002).
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  8. M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
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  9. P. Galajda and P. Ormos, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249-251 (2001).
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  10. M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
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    [CrossRef] [PubMed]
  12. K. Dholakia and W. M. Lee, "Optical Trapping Takes Shape: The Use of Structured Light Fields," Adv. At. Mol. Opt. Phys. 56, 261-337 (2008).
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  14. A. Casaburi and G. Pesce and P. Zemánek and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
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    [CrossRef]
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    [CrossRef]
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  27. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, "Towards absolute calibration of optical tweezers," Phys. Rev. E 75, 021914 (2007).
    [CrossRef]
  28. 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]
  29. G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, "Transverse particle dynamics in a Bessel beam," Opt. Express 15, 13972-13987 (2007).
    [CrossRef] [PubMed]
  30. L. Paterson, E. Papagiakoumou, G. Milne, V. Garces-Chavez, S. A. Tatarkova, W. Sibbett, F. Gunn-Moore, P. Bryant, A. Riches, and K. Dholakia, "Light-induced cell separation in a tailored optical landscape," Appl. Phys. Lett. 87, 123901 (2005).
    [CrossRef]
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    [CrossRef]
  32. V. Blickle, T. Speck, U. Seifert, and C. Bechinger, "Characterizing potentials by a generalized Boltzmann factor," Phys. Rev. E 75, 060101 (2007).
    [CrossRef]
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    [CrossRef]
  34. S. A. Tatarkova, W. Sibbett, and K. Dholakia, "Brownian particle in an optical potential of the washboard type," Phys. Rev. Lett. 91, 038101 (2003).
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    [CrossRef] [PubMed]
  37. L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979).
    [CrossRef]
  38. J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179, 298-310 (1996).
    [CrossRef]
  39. A. Savitzky and M. J. E. Golay, "Smoothing and Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627-1639 (1964).
    [CrossRef]

2008 (6)

K. M. Herbert, W. J. Greenleaf, and S. M. Block, "Single-Molecule Studies of RNA Polymerase: Motoring Along," Annu. Rev. Biochem. 77, 149-176 (2008).
[CrossRef] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, "Recent Advances in Optical Tweezers," Annu. Rev. Biochem 77, 205-228 (2008).
[CrossRef] [PubMed]

A. Jonás and P. Zemánek, "Light at work: The use of optical forces for particle manipulation, sorting, and analysis," Electrophoresis 29, 4813-4851 (2008).
[CrossRef]

M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, "Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment," Phys. Rev. E 77, 041107 (2008).
[CrossRef]

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]

K. Dholakia and W. M. Lee, "Optical Trapping Takes Shape: The Use of Structured Light Fields," Adv. At. Mol. Opt. Phys. 56, 261-337 (2008).

2007 (3)

V. Blickle, T. Speck, U. Seifert, and C. Bechinger, "Characterizing potentials by a generalized Boltzmann factor," Phys. Rev. E 75, 060101 (2007).
[CrossRef]

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

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, "Transverse particle dynamics in a Bessel beam," Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

2006 (2)

I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, "Modulated optical sieve for sorting of polydisperse microparticles," Appl. Phys. Lett. 88, 121116 (2006).
[CrossRef]

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

2005 (2)

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

A. Casaburi and G. Pesce and P. Zemánek and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

2004 (1)

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting mesoscopic objects with periodic potential landscapes: Optical fractionation," Phys. Rev. E 70, 010901 (2004).
[CrossRef]

2003 (3)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

B. A. Koss and D. G. Grier, "Optical Peristalsis," Appl. Phys. Lett. 82, 3985-3987 (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]

2002 (2)

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

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclassical Opt. 4, S82-S89 (2002).
[CrossRef]

2001 (3)

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

P. Galajda and P. Ormos, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249-251 (2001).
[CrossRef]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

2000 (2)

C. Mio, T. Gong, A. Terray, and D. W. Marr, "Design of a scanning laser optical trap for multiparticle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

1999 (2)

L. I. McCann, M. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785-787 (1999).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
[CrossRef]

1997 (2)

1996 (1)

J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

1995 (1)

H. He, M. J. E. Friese, N. R. 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]

1992 (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1991 (1)

V. I. Melnikov, "The Kramers problem: Fifty years of development," Phys. Rep. 209, 1-71 (1991).
[CrossRef]

1990 (1)

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

1986 (1)

1979 (1)

L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979).
[CrossRef]

1970 (1)

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

1964 (1)

A. Savitzky and M. J. E. Golay, "Smoothing and Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627-1639 (1964).
[CrossRef]

Allen, L.

Arlt, J.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclassical Opt. 4, S82-S89 (2002).
[CrossRef]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

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

Bechinger, C.

M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, "Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment," Phys. Rev. E 77, 041107 (2008).
[CrossRef]

V. Blickle, T. Speck, U. Seifert, and C. Bechinger, "Characterizing potentials by a generalized Boltzmann factor," Phys. Rev. E 75, 060101 (2007).
[CrossRef]

Bernet, S.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Berns, M. W.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, "Interferometric optical tweezers," Opt. Commun. 133, 7-10 (1997).
[CrossRef]

Bjorkholm, J. E.

Bleil, S.

M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, "Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment," Phys. Rev. E 77, 041107 (2008).
[CrossRef]

Blickle, V.

V. Blickle, T. Speck, U. Seifert, and C. Bechinger, "Characterizing potentials by a generalized Boltzmann factor," Phys. Rev. E 75, 060101 (2007).
[CrossRef]

Block, S. M.

K. M. Herbert, W. J. Greenleaf, and S. M. Block, "Single-Molecule Studies of RNA Polymerase: Motoring Along," Annu. Rev. Biochem. 77, 149-176 (2008).
[CrossRef] [PubMed]

Bryant, P.

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

Burns, M. M.

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, "Recent Advances in Optical Tweezers," Annu. Rev. Biochem 77, 205-228 (2008).
[CrossRef] [PubMed]

Casaburi, A.

A. Casaburi and G. Pesce and P. Zemánek and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

Chavez-Cerda, S.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclassical Opt. 4, S82-S89 (2002).
[CrossRef]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, "Recent Advances in Optical Tweezers," Annu. Rev. Biochem 77, 205-228 (2008).
[CrossRef] [PubMed]

Chiou, A. E.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, "Interferometric optical tweezers," Opt. Commun. 133, 7-10 (1997).
[CrossRef]

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.

Cizmar, T.

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

Crocker, J. C.

J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Davis, L. W.

L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979).
[CrossRef]

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Dholakia, K.

K. Dholakia and W. M. Lee, "Optical Trapping Takes Shape: The Use of Structured Light Fields," Adv. At. Mol. Opt. Phys. 56, 261-337 (2008).

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, "Transverse particle dynamics in a Bessel beam," Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

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

L. Paterson, E. Papagiakoumou, G. Milne, V. Garces-Chavez, S. A. Tatarkova, W. Sibbett, F. Gunn-Moore, P. Bryant, A. 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]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclassical Opt. 4, S82-S89 (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]

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Dykman, M.

L. I. McCann, M. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785-787 (1999).
[CrossRef]

Dziedzic, J. M.

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]

Eichhorn, R.

M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, "Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment," Phys. Rev. E 77, 041107 (2008).
[CrossRef]

Eriksen, R. L.

Evstigneev, M.

M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, "Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment," Phys. Rev. E 77, 041107 (2008).
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Fournier, J. M.

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

Friese, M. E. J.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Friese, M. J. E.

H. He, M. J. E. Friese, N. R. 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]

Galajda, P.

P. Galajda and P. Ormos, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249-251 (2001).
[CrossRef]

Garces-Chavez, V.

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

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

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclassical Opt. 4, S82-S89 (2002).
[CrossRef]

Gluckstad, J.

Golay, M. J. E.

A. Savitzky and M. J. E. Golay, "Smoothing and Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627-1639 (1964).
[CrossRef]

Gold, J.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Golding, B.

L. I. McCann, M. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785-787 (1999).
[CrossRef]

Golovchenko, J. A.

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, "Optical Matter: Crystallization and Binding in Intense Optical Fields," Science 249, 749-754 (1990).
[CrossRef] [PubMed]

Gong, T.

C. Mio, T. Gong, A. Terray, and D. W. Marr, "Design of a scanning laser optical trap for multiparticle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Greenleaf, W. J.

K. M. Herbert, W. J. Greenleaf, and S. M. Block, "Single-Molecule Studies of RNA Polymerase: Motoring Along," Annu. Rev. Biochem. 77, 149-176 (2008).
[CrossRef] [PubMed]

Grier, D. G.

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting mesoscopic objects with periodic potential landscapes: Optical fractionation," Phys. Rev. E 70, 010901 (2004).
[CrossRef]

B. A. Koss and D. G. Grier, "Optical Peristalsis," Appl. Phys. Lett. 82, 3985-3987 (2003).
[CrossRef]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

J. C. Crocker and D. G. Grier, "Methods of Digital Video Microscopy for Colloidal Studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Gunn-Moore, F.

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

Hagberg, P.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Haist, T.

Hanstorp, D.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

He, H.

H. He, M. J. E. Friese, N. R. 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]

Heckenberg, N. R.

H. He, M. J. E. Friese, N. R. 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]

Hecker, N.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Herbert, K. M.

K. M. Herbert, W. J. Greenleaf, and S. M. Block, "Single-Molecule Studies of RNA Polymerase: Motoring Along," Annu. Rev. Biochem. 77, 149-176 (2008).
[CrossRef] [PubMed]

Hong, J.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, "Interferometric optical tweezers," Opt. Commun. 133, 7-10 (1997).
[CrossRef]

Jeffries, G. D. M.

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]

Jonás, A.

A. Jonás and P. Zemánek, "Light at work: The use of optical forces for particle manipulation, sorting, and analysis," Electrophoresis 29, 4813-4851 (2008).
[CrossRef]

Kasza, K.

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting mesoscopic objects with periodic potential landscapes: Optical fractionation," Phys. Rev. E 70, 010901 (2004).
[CrossRef]

Koss, B. A.

B. A. Koss and D. G. Grier, "Optical Peristalsis," Appl. Phys. Lett. 82, 3985-3987 (2003).
[CrossRef]

Ladavac, K.

K. Ladavac, K. Kasza, and D. G. Grier, "Sorting mesoscopic objects with periodic potential landscapes: Optical fractionation," Phys. Rev. E 70, 010901 (2004).
[CrossRef]

Lee, W. M.

K. Dholakia and W. M. Lee, "Optical Trapping Takes Shape: The Use of Structured Light Fields," Adv. At. Mol. Opt. Phys. 56, 261-337 (2008).

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Marr, D. W.

C. Mio, T. Gong, A. Terray, and D. W. Marr, "Design of a scanning laser optical trap for multiparticle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Mazolli, A.

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

McCann, L. I.

L. I. McCann, M. Dykman, and B. Golding, "Thermally activated transitions in a bistable three-dimensional optical trap," Nature 402, 785-787 (1999).
[CrossRef]

McGloin, D.

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]

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, "Transverse particle dynamics in a Bessel beam," Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

Melnikov, V. I.

V. I. Melnikov, "The Kramers problem: Fifty years of development," Phys. Rep. 209, 1-71 (1991).
[CrossRef]

Mesquita, O. N.

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

Milne, G.

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]

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, "Transverse particle dynamics in a Bessel beam," Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

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

Mio, C.

C. Mio, T. Gong, A. Terray, and D. W. Marr, "Design of a scanning laser optical trap for multiparticle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, "Recent Advances in Optical Tweezers," Annu. Rev. Biochem 77, 205-228 (2008).
[CrossRef] [PubMed]

Mogensen, P. C.

Neto, P. A. M.

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

Nussenzveig, H. M.

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

Ormos, P.

P. Galajda and P. Ormos, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249-251 (2001).
[CrossRef]

Padgett, M. J.

Papagiakoumou, E.

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

Pesce, G.

A. Casaburi and G. Pesce and P. Zemánek and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

Ramos-Garcia, R.

I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, "Modulated optical sieve for sorting of polydisperse microparticles," Appl. Phys. Lett. 88, 121116 (2006).
[CrossRef]

Reicherter, M.

Reimann, P.

M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, "Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment," Phys. Rev. E 77, 041107 (2008).
[CrossRef]

Ricardez-Vargas, I.

I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, "Modulated optical sieve for sorting of polydisperse microparticles," Appl. Phys. Lett. 88, 121116 (2006).
[CrossRef]

Riches, A.

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

Ritsch-Marte, M.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Rocha, M. S.

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

Rodriguez-Montero, P.

I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, "Modulated optical sieve for sorting of polydisperse microparticles," Appl. Phys. Lett. 88, 121116 (2006).
[CrossRef]

Rubinsztein-Dunlop, H.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

H. He, M. J. E. Friese, N. R. 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]

Sasso, A.

A. Casaburi and G. Pesce and P. Zemánek and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

Savitzky, A.

A. Savitzky and M. J. E. Golay, "Smoothing and Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627-1639 (1964).
[CrossRef]

Seifert, U.

V. Blickle, T. Speck, U. Seifert, and C. Bechinger, "Characterizing potentials by a generalized Boltzmann factor," Phys. Rev. E 75, 060101 (2007).
[CrossRef]

Sery, M.

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

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Sibbett, W.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garces-Chavez, S. A. Tatarkova, W. Sibbett, F. Gunn-Moore, P. Bryant, A. 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]

Siler, M.

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

Simpson, N. B.

Singer, W.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, "Recent Advances in Optical Tweezers," Annu. Rev. Biochem 77, 205-228 (2008).
[CrossRef] [PubMed]

Sonek, G. J.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, "Interferometric optical tweezers," Opt. Commun. 133, 7-10 (1997).
[CrossRef]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Speck, T.

V. Blickle, T. Speck, U. Seifert, and C. Bechinger, "Characterizing potentials by a generalized Boltzmann factor," Phys. Rev. E 75, 060101 (2007).
[CrossRef]

Tatarkova, S. A.

L. Paterson, E. Papagiakoumou, G. Milne, V. Garces-Chavez, S. A. Tatarkova, W. Sibbett, F. Gunn-Moore, P. Bryant, A. 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]

Terray, A.

C. Mio, T. Gong, A. Terray, and D. W. Marr, "Design of a scanning laser optical trap for multiparticle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Tiziani, H. J.

Viana, N. B.

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

Volke-Sepulveda, K.

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, "Transverse particle dynamics in a Bessel beam," Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, "Modulated optical sieve for sorting of polydisperse microparticles," Appl. Phys. Lett. 88, 121116 (2006).
[CrossRef]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclassical Opt. 4, S82-S89 (2002).
[CrossRef]

Wagemann, E. U.

Wang, W.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, "Interferometric optical tweezers," Opt. Commun. 133, 7-10 (1997).
[CrossRef]

Zemanek, P.

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemanek, "Transverse particle dynamics in a Bessel beam," Opt. Express 15, 13972-13987 (2007).
[CrossRef] [PubMed]

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

Zemánek, P.

A. Jonás and P. Zemánek, "Light at work: The use of optical forces for particle manipulation, sorting, and analysis," Electrophoresis 29, 4813-4851 (2008).
[CrossRef]

A. Casaburi and G. Pesce and P. Zemánek and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

Zhao, Y.

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]

Zvyagolskaya, O.

M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, "Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment," Phys. Rev. E 77, 041107 (2008).
[CrossRef]

Adv. At. Mol. Opt. Phys. (1)

K. Dholakia and W. M. Lee, "Optical Trapping Takes Shape: The Use of Structured Light Fields," Adv. At. Mol. Opt. Phys. 56, 261-337 (2008).

Anal. Chem. (1)

A. Savitzky and M. J. E. Golay, "Smoothing and Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627-1639 (1964).
[CrossRef]

Annu. Rev. Biochem (1)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, "Recent Advances in Optical Tweezers," Annu. Rev. Biochem 77, 205-228 (2008).
[CrossRef] [PubMed]

Annu. Rev. Biochem. (1)

K. M. Herbert, W. J. Greenleaf, and S. M. Block, "Single-Molecule Studies of RNA Polymerase: Motoring Along," Annu. Rev. Biochem. 77, 149-176 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (6)

I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, "Modulated optical sieve for sorting of polydisperse microparticles," Appl. Phys. Lett. 88, 121116 (2006).
[CrossRef]

B. A. Koss and D. G. Grier, "Optical Peristalsis," Appl. Phys. Lett. 82, 3985-3987 (2003).
[CrossRef]

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements," Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

P. Galajda and P. Ormos, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249-251 (2001).
[CrossRef]

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]

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

Biophys. J. (1)

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the physical system. A spherical particle is moving down a inclined plane in a washboard potential in the overdamped regime. The y axis is normal to the plane of the figure according to a right-hand system. W is the effective weight of the particle, N is the normal force, γẋ is the damping force, V(x) is an optical potential and ψ is the inclination angle.

Fig. 2.
Fig. 2.

Experimental setup. Mirrors and lenses are represented by M and L, respectively; CL denotes a cylindrical lens and DM are dichroic mirrors. PBS are polarizing beam splitter cubes and NPBS is a non-polarizing beam splitter. Half-wave plates (λ/2) are used to control the laser intensity. A microscope objective (×20) is used to generate an optical tweezers and to observe the sample. The tweezers beam is blocked while the particle travels down the interference pattern with a shutter modulus (SM). CCD1 records the path of the particle, while CCD2 monitors the interference fringes.

Fig. 3.
Fig. 3.

(a) Experimental data: Curves of the position as a function of time for eleven repetitions of the experiment for each particle size: 8μm, 10μm and 14.5μm of diameter. In all cases, the spatial period of the interference pattern of fringes was L = 20.2μm and the recording rate was 30 frames/s. (b) Close up of three paths for the 14.5μm diameter particle illustrating the original experimental data (color curves) in comparison with the curves obtained after performing a smoothing process (in black).

Fig. 4.
Fig. 4.

Curves of velocity as a function of position for the same data of Fig. 3: (a) 2R 0 = 10μm and (b) 2R 0 = 14.5μm. Plot in black is the resulting average.

Fig. 5.
Fig. 5.

Experimental force profile (red circles) of a particle ((a) 2R 0 = 10μm and (b) 2R 0 = 14.5μm) running in a fringes pattern with spatial periodicity L = 20.2μm. Solid blue lines are the corresponding theoretical predictions according to Eqs. (2) and (3). Experimental results correspond to the average in black in Fig. 4.

Fig. 6.
Fig. 6.

Comparison of experimental force with the theoretical model for spheres of 10μm of diameter (left column) and 14.5μm of diameter (right column), for spatial periods of: (a) and (b) L = 13.25μm; (c) and (d) L = 17.16μm; (e) and (f) L = 25.21μm

Fig. 7.
Fig. 7.

Comparison between the theoretical predictions (lines) and experimental results (markers) for the maximum optical force as a function of the period of the interference fringes for the particles of 10μm diameter (red) and 14.5μm diameter (blue).

Equations (4)

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γ x ˙ ( t ) = V ( x ( t ) ) + F g ,
F x ( x 0 , y 0 ) = n m ( R 0 ) 2 2 c 0 π / 2 0 2 π ( R sin ( 2 θ ) T 2 sin ( 2 θ 2 θ t ) + R sin ( 2 θ ) 1 + R 2 + 2 R cos ( 2 θ t ) )
× I ( x , y ) sin ( 2 θ ) cos φ d φ d θ .
I ( x , y ) = 4 P π w x w y exp [ 2 ( ( x ξ ) 2 w x 2 + ( y η ) 2 w y 2 ) ] cos 2 ( π L ( x ξ ) ) ,

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