Abstract

We analyze the properties of a dual-beam trap of orthogonally intersecting beams in the geometrical optics regime. We derive analytical expressions for the trapping location and stability criteria for trapping a microparticle with uncollimated Gaussian beams. An upper limit for the beam waist is found. Optical forces and particle trajectories are calculated numerically for the realistic case of a microparticle in intersecting liquid-core waveguides.

© 2013 Chinese Laser Press

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  2. 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]
  3. S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
    [CrossRef]
  4. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
    [CrossRef]
  5. A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
    [CrossRef]
  6. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
    [CrossRef]
  7. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
    [CrossRef]
  8. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
    [CrossRef]
  9. V. Karásek, T. Čižmár, O. Brzobohatý, and P. Zemánek, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
    [CrossRef]
  10. S. Kawata and T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17, 772–774 (1992).
    [CrossRef]
  11. A. E. Cohen, “Suppressing Brownian motion of individual biomolecules in solution,” Proc. Natl. Acad. Sci. USA 103, 4362–4365 (2006).
    [CrossRef]
  12. F. Amblard, B. Yurke, A. Pargellis, and S. Leibler, “A magnetic manipulator for studying local rheology and micromechanical properties of biological systems,” Rev. Sci. Instrum. 67, 818–827 (1996).
    [CrossRef]
  13. M. J. Lang and S. M. Block, “Laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
    [CrossRef]
  14. A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers (World Scientific, 2006).
  15. S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
    [CrossRef]
  16. S. Cran-McGreehin, T. F. Krauss, and K. Dholakia, “Integrated monolithic optical manipulation,” Lab Chip 6, 1122–1124 (2006).
    [CrossRef]
  17. S. Kühn, B. S. Phillips, E. J. Lunt, A. R. Hawkins, and H. Schmidt, “Ultralow power trapping and fluorescence detection of single particles on an optofluidic chip,” Lab Chip 10, 189–194 (2010).
    [CrossRef]
  18. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
    [CrossRef]
  19. S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10, 2408–2411 (2010).
    [CrossRef]
  20. S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99–104 (2010).
    [CrossRef]
  21. C. Adams, H. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
    [CrossRef]
  22. S. Chaudhuri, S. Roy, and C. S. Unnikrishnan, “Evaporative cooling of atoms to quantum degeneracy in an optical dipole trap,” J. Phys. Conf. Ser. 80, 012036 (2007).
    [CrossRef]
  23. M. Barrett, J. Sauer, and M. Chapman, “All-optical formation of an atomic Bose–Einstein condensate,” Phys. Rev. Lett. 87, 010404 (2001).
    [CrossRef]
  24. 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]
  25. S. B. Kim and S. S. Kim, “Radiation forces on spheres in loosely focused Gaussian beam: ray-optics regime,” J. Opt. Soc. Am. B 23, 897–903 (2006).
    [CrossRef]
  26. P. A. M. Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
    [CrossRef]
  27. D. Yin, J. P. Barber, A. R. Hawkins, and H. Schmidt, “Waveguide loss optimization in hollow-core ARROW waveguides,” Opt. Express 13, 9331–9336 (2005).
    [CrossRef]
  28. P. Measor, S. Kühn, E. J. Lunt, B. S. Phillips, A. R. Hawkins, and H. Schmidt, “Hollow-core waveguide characterization by optically induced particle transport,” Opt. Lett. 33, 672–674 (2008).
    [CrossRef]
  29. D. Yin, E. J. Lunt, A. Barman, A. R. Hawkins, and H. Schmidt, “Microphotonic control of single molecule fluorescence correlation spectroscopy using planar optofluidics,” Opt. Express 15, 7290–7295 (2007).
    [CrossRef]

2011 (1)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

2010 (4)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

S. Kühn, B. S. Phillips, E. J. Lunt, A. R. Hawkins, and H. Schmidt, “Ultralow power trapping and fluorescence detection of single particles on an optofluidic chip,” Lab Chip 10, 189–194 (2010).
[CrossRef]

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10, 2408–2411 (2010).
[CrossRef]

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99–104 (2010).
[CrossRef]

2009 (2)

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
[CrossRef]

S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
[CrossRef]

2008 (2)

V. Karásek, T. Čižmár, O. Brzobohatý, and P. Zemánek, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef]

P. Measor, S. Kühn, E. J. Lunt, B. S. Phillips, A. R. Hawkins, and H. Schmidt, “Hollow-core waveguide characterization by optically induced particle transport,” Opt. Lett. 33, 672–674 (2008).
[CrossRef]

2007 (2)

D. Yin, E. J. Lunt, A. Barman, A. R. Hawkins, and H. Schmidt, “Microphotonic control of single molecule fluorescence correlation spectroscopy using planar optofluidics,” Opt. Express 15, 7290–7295 (2007).
[CrossRef]

S. Chaudhuri, S. Roy, and C. S. Unnikrishnan, “Evaporative cooling of atoms to quantum degeneracy in an optical dipole trap,” J. Phys. Conf. Ser. 80, 012036 (2007).
[CrossRef]

2006 (3)

S. Cran-McGreehin, T. F. Krauss, and K. Dholakia, “Integrated monolithic optical manipulation,” Lab Chip 6, 1122–1124 (2006).
[CrossRef]

A. E. Cohen, “Suppressing Brownian motion of individual biomolecules in solution,” Proc. Natl. Acad. Sci. USA 103, 4362–4365 (2006).
[CrossRef]

S. B. Kim and S. S. Kim, “Radiation forces on spheres in loosely focused Gaussian beam: ray-optics regime,” J. Opt. Soc. Am. B 23, 897–903 (2006).
[CrossRef]

2005 (1)

2004 (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

2003 (1)

M. J. Lang and S. M. Block, “Laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

2001 (1)

M. Barrett, J. Sauer, and M. Chapman, “All-optical formation of an atomic Bose–Einstein condensate,” Phys. Rev. Lett. 87, 010404 (2001).
[CrossRef]

2000 (1)

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

1996 (1)

F. Amblard, B. Yurke, A. Pargellis, and S. Leibler, “A magnetic manipulator for studying local rheology and micromechanical properties of biological systems,” Rev. Sci. Instrum. 67, 818–827 (1996).
[CrossRef]

1995 (1)

C. Adams, H. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef]

1992 (2)

S. Kawata and T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17, 772–774 (1992).
[CrossRef]

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]

1987 (2)

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

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef]

1986 (2)

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef]

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]

1970 (1)

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

Adams, C.

C. Adams, H. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef]

Amblard, F.

F. Amblard, B. Yurke, A. Pargellis, and S. Leibler, “A magnetic manipulator for studying local rheology and micromechanical properties of biological systems,” Rev. Sci. Instrum. 67, 818–827 (1996).
[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]

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef]

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

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef]

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]

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

A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers (World Scientific, 2006).

Barber, J. P.

Barman, A.

Barrett, M.

M. Barrett, J. Sauer, and M. Chapman, “All-optical formation of an atomic Bose–Einstein condensate,” Phys. Rev. Lett. 87, 010404 (2001).
[CrossRef]

Bjorkholm, J.

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

M. J. Lang and S. M. Block, “Laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

Brzobohatý, O.

V. Karásek, T. Čižmár, O. Brzobohatý, and P. Zemánek, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef]

Cable, A.

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef]

Chapman, M.

M. Barrett, J. Sauer, and M. Chapman, “All-optical formation of an atomic Bose–Einstein condensate,” Phys. Rev. Lett. 87, 010404 (2001).
[CrossRef]

Chaudhuri, S.

S. Chaudhuri, S. Roy, and C. S. Unnikrishnan, “Evaporative cooling of atoms to quantum degeneracy in an optical dipole trap,” J. Phys. Conf. Ser. 80, 012036 (2007).
[CrossRef]

Chu, S.

C. Adams, H. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef]

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]

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef]

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

V. Karásek, T. Čižmár, O. Brzobohatý, and P. Zemánek, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef]

Cohen, A. E.

A. E. Cohen, “Suppressing Brownian motion of individual biomolecules in solution,” Proc. Natl. Acad. Sci. USA 103, 4362–4365 (2006).
[CrossRef]

Cran-McGreehin, S.

S. Cran-McGreehin, T. F. Krauss, and K. Dholakia, “Integrated monolithic optical manipulation,” Lab Chip 6, 1122–1124 (2006).
[CrossRef]

Crozier, K.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10, 2408–2411 (2010).
[CrossRef]

Davidson, N.

C. Adams, H. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef]

Deamer, D. W.

S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
[CrossRef]

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

S. Cran-McGreehin, T. F. Krauss, and K. Dholakia, “Integrated monolithic optical manipulation,” Lab Chip 6, 1122–1124 (2006).
[CrossRef]

Dziedzic, J.

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef]

Dziedzic, J. M.

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

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]

Erickson, D.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99–104 (2010).
[CrossRef]

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
[CrossRef]

Hawkins, A. R.

Karásek, V.

V. Karásek, T. Čižmár, O. Brzobohatý, and P. Zemánek, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef]

Kasevich, M.

C. Adams, H. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef]

Kawata, S.

Kim, S. B.

Kim, S. S.

Klug, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
[CrossRef]

Krauss, T. F.

S. Cran-McGreehin, T. F. Krauss, and K. Dholakia, “Integrated monolithic optical manipulation,” Lab Chip 6, 1122–1124 (2006).
[CrossRef]

Kühn, S.

S. Kühn, B. S. Phillips, E. J. Lunt, A. R. Hawkins, and H. Schmidt, “Ultralow power trapping and fluorescence detection of single particles on an optofluidic chip,” Lab Chip 10, 189–194 (2010).
[CrossRef]

S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
[CrossRef]

P. Measor, S. Kühn, E. J. Lunt, B. S. Phillips, A. R. Hawkins, and H. Schmidt, “Hollow-core waveguide characterization by optically induced particle transport,” Opt. Lett. 33, 672–674 (2008).
[CrossRef]

Lang, M. J.

M. J. Lang and S. M. Block, “Laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

Lee, H.

C. Adams, H. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef]

Leibler, S.

F. Amblard, B. Yurke, A. Pargellis, and S. Leibler, “A magnetic manipulator for studying local rheology and micromechanical properties of biological systems,” Rev. Sci. Instrum. 67, 818–827 (1996).
[CrossRef]

Lin, S.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10, 2408–2411 (2010).
[CrossRef]

Lipson, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
[CrossRef]

Lunt, E. J.

S. Kühn, B. S. Phillips, E. J. Lunt, A. R. Hawkins, and H. Schmidt, “Ultralow power trapping and fluorescence detection of single particles on an optofluidic chip,” Lab Chip 10, 189–194 (2010).
[CrossRef]

S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
[CrossRef]

P. Measor, S. Kühn, E. J. Lunt, B. S. Phillips, A. R. Hawkins, and H. Schmidt, “Hollow-core waveguide characterization by optically induced particle transport,” Opt. Lett. 33, 672–674 (2008).
[CrossRef]

D. Yin, E. J. Lunt, A. Barman, A. R. Hawkins, and H. Schmidt, “Microphotonic control of single molecule fluorescence correlation spectroscopy using planar optofluidics,” Opt. Express 15, 7290–7295 (2007).
[CrossRef]

Mandal, S.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99–104 (2010).
[CrossRef]

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

Measor, P.

S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
[CrossRef]

P. Measor, S. Kühn, E. J. Lunt, B. S. Phillips, A. R. Hawkins, and H. Schmidt, “Hollow-core waveguide characterization by optically induced particle transport,” Opt. Lett. 33, 672–674 (2008).
[CrossRef]

Moore, S. D.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
[CrossRef]

Neto, P. A. M.

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

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

Nussenzveig, H. M.

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

Pargellis, A.

F. Amblard, B. Yurke, A. Pargellis, and S. Leibler, “A magnetic manipulator for studying local rheology and micromechanical properties of biological systems,” Rev. Sci. Instrum. 67, 818–827 (1996).
[CrossRef]

Phillips, B. S.

S. Kühn, B. S. Phillips, E. J. Lunt, A. R. Hawkins, and H. Schmidt, “Ultralow power trapping and fluorescence detection of single particles on an optofluidic chip,” Lab Chip 10, 189–194 (2010).
[CrossRef]

S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
[CrossRef]

P. Measor, S. Kühn, E. J. Lunt, B. S. Phillips, A. R. Hawkins, and H. Schmidt, “Hollow-core waveguide characterization by optically induced particle transport,” Opt. Lett. 33, 672–674 (2008).
[CrossRef]

Roy, S.

S. Chaudhuri, S. Roy, and C. S. Unnikrishnan, “Evaporative cooling of atoms to quantum degeneracy in an optical dipole trap,” J. Phys. Conf. Ser. 80, 012036 (2007).
[CrossRef]

Sauer, J.

M. Barrett, J. Sauer, and M. Chapman, “All-optical formation of an atomic Bose–Einstein condensate,” Phys. Rev. Lett. 87, 010404 (2001).
[CrossRef]

Schmidt, B. S.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
[CrossRef]

Schmidt, H.

Schonbrun, E.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10, 2408–2411 (2010).
[CrossRef]

Serey, X.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99–104 (2010).
[CrossRef]

Sugiura, T.

Unnikrishnan, C. S.

S. Chaudhuri, S. Roy, and C. S. Unnikrishnan, “Evaporative cooling of atoms to quantum degeneracy in an optical dipole trap,” J. Phys. Conf. Ser. 80, 012036 (2007).
[CrossRef]

Yamane, T.

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

Yang, A. H. J.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
[CrossRef]

Yin, D.

Yurke, B.

F. Amblard, B. Yurke, A. Pargellis, and S. Leibler, “A magnetic manipulator for studying local rheology and micromechanical properties of biological systems,” Rev. Sci. Instrum. 67, 818–827 (1996).
[CrossRef]

Zemánek, P.

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Am. J. Phys. (1)

M. J. Lang and S. M. Block, “Laser-based optical tweezers,” Am. J. Phys. 71, 201–215 (2003).
[CrossRef]

Biophys. J. (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).
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S. Kühn, P. Measor, E. J. Lunt, B. S. Phillips, D. W. Deamer, A. R. Hawkins, and H. Schmidt, “Loss-based optical trap for on-chip particle analysis,” Lab Chip 9, 2212–2216 (2009).
[CrossRef]

S. Cran-McGreehin, T. F. Krauss, and K. Dholakia, “Integrated monolithic optical manipulation,” Lab Chip 6, 1122–1124 (2006).
[CrossRef]

S. Kühn, B. S. Phillips, E. J. Lunt, A. R. Hawkins, and H. Schmidt, “Ultralow power trapping and fluorescence detection of single particles on an optofluidic chip,” Lab Chip 10, 189–194 (2010).
[CrossRef]

Nano Lett. (2)

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10, 2408–2411 (2010).
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S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99–104 (2010).
[CrossRef]

Nat. Photonics (2)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

Nature (2)

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

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 71–75 (2009).
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Science (1)

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Figures (4)

Fig. 1.
Fig. 1.

(a) Single-beam tweezer trap ( F G , gradient force; F S , scattering force), (b) dual-beam trap (Beam 1 is shown in red and Beam 2 is shown in blue to aid in identifying from which beam these forces originated), (c) OBT, and (d)  z -dependent forces at fixed x coordinate highlighted in (c); trapping occurs at z T , where the gradient force from Beam 2 is restoring.

Fig. 2.
Fig. 2.

Analytically calculated forces on microbead in identical collimated beams. (a) Gradient force along z from Beam 2 and scattering force along x from Beam 1 versus transverse coordinate; curves need to intersect between the origin and location of maximum gradient force to form a stable trap [locations of maximum gradient and maximum scattering force used for (b) are shown with green arrows]. (b) Particle size dependence of forces at relevant points (symbols) and fits with second-order polynomial (lines).

Fig. 3.
Fig. 3.

(a) Calculated particle trajectory exhibiting trapping at beam intersection (all dimensions to scale), (b) total force at the beam intersection, trapping point (black), w 0 from Beam 1 (red), and w 0 Beam 2 (blue) shown with dotted lines, and (c) time dependence of particle velocities along x and z showing acceleration due to Beam 2, followed by trapping.

Fig. 4.
Fig. 4.

(a) Calculated potential profile along the direction of Beam 1 ( z ) and (b) trap stability plot. Symbols delineate the validity limit of the relation in Eq. (7) for a given particle size, and the line shows the linear fit.

Equations (9)

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I 1 ( x ) = I 0 · e γ x 2 ; I 2 ( z ) = I 0 · e γ z 2 ,
F S 1 ( x ) = k S · I 1 ( x ) = Q S · A c · I 1 ( x ) ,
F G 1 ( x ) = k G · | ∇⃗ I 1 ( x ) | = 2 γ k G · x · I 1 ( x ) = Q G ( x ) · A c · I 1 ( x ) ,
F S 1 ( x ) = F G 2 ( z ) ,
F G 1 ( x ) = F S 2 ( z ) ,
x T = z T = k S k G 1 2 γ = k S k G w 0 2 4 ,
w 0 2 k G k S .
m z ¨ = F optical ( z ) + F drag ( z ) = F S 1 ( z ) + F G 2 ( z ) + 3 π η d z ˙ ,
m x ¨ = F optical ( x ) + F drag ( x ) = F S 2 ( x ) + F G 1 ( x ) + 3 π η d x ˙ .

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