Abstract

Optical tweezers provide a versatile tool in biological and physical researches. Optical tweezers based on optical fibers are more flexible and ready to be integrated when compared with those based on microscope objectives. In this paper, the three-dimensional (3D) trapping ability of an inclined dual-fiber optical tweezers is demonstrated. The trapping efficiency with respect to displacement is experimentally calibrated along two dimensions. The system is studied numerically using a modified ray-optics model. The spring constants obtained in the experiment are predicted by simulations. It is found both experimentally and numerically that there is a critical value for the fiber inclination angle to retain the 3D trapping ability. The inclined dual-fiber optical tweezers are demonstrated to be more robust to z-axis misalignment than the counter-propagating fiber optical tweezers, which is a special case of the former when the fiber inclination angle is 90°. This inclined dual-fiber optical tweezers can serve as both a manipulator and a force sensor in integrated systems, such as microfluidic systems and lab-on-a-chip systems.

© 2009 Optical Society of America

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  28. R. C. Gauthier, "Optical trapping: a tool to assist optical machining," Opt. Laser Technol. 29, 389 (1997).
    [CrossRef]
  29. Y. Liu and M. Yu, "Three-dimensional fiber optical trap for cell manipulation and force measurement," Proc. SPIE 6528, 65280Z (2007).
    [CrossRef]
  30. A. Priyadarshi, L. H. Fen, S. G. Mhaisalkar, V. Kripesh, and A. K. Asundi, "Fiber misalignment in silicon V-groove based optical modules," Opt. Fiber Technol. 12, 170 (2006).
    [CrossRef]

2008 (2)

2007 (3)

Y. Liu and M. Yu, "Three-dimensional fiber optical trap for cell manipulation and force measurement," Proc. SPIE 6528, 65280Z (2007).
[CrossRef]

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
[CrossRef]

K. S. Abedin, C. Kerbage, A. Fernandez-Nieves and D. A. Weitz, "Optical manipulation and rotation of liquid crystal drops using high-index fiber-optics tweezers," Appl. Phys. Lett. 91, 091119 (2007).
[CrossRef]

2006 (5)

T. Numata, A. Takayanagi, Y. Otani and N. Umeda, "Manipulation of metal nanoparticles using fiber-optic laser tweezers with a microspherical focusing lens," Jpn. J. Appl. Phys. 45, 359 (2006).
[CrossRef]

S. Hormeno and J. R. Arias-Gonzalez, "Exploring mechanochemical processes in the cell with optical tweezers," Biol. Cell 98, 679 (2006).
[CrossRef] [PubMed]

A. Priyadarshi, L. H. Fen, S. G. Mhaisalkar, V. Kripesh, and A. K. Asundi, "Fiber misalignment in silicon V-groove based optical modules," Opt. Fiber Technol. 12, 170 (2006).
[CrossRef]

M. Wei, K. Yang, A. Karmenyan, and A. Chiou, "Three-dimensional optical force field on a Chinese hamster ovary cell in a fiber-optical dual-beam trap," Opt. Express 14, 3056 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-7-3056.
[CrossRef] [PubMed]

Z. Liu, C. Guo, J. Yang and L. Yuan, "Tapered fiber optical tweezers for microscopic particle trapping: fabrication and application," Opt. Express 14,12510 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-25-12510.
[CrossRef] [PubMed]

2005 (1)

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460 (2005).
[CrossRef] [PubMed]

2004 (2)

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

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

2003 (1)

2002 (1)

K. Taguchi, M. Tanaka and M. Ikeda, "Investigation on the radius of a hemispherical microlens of an optical fiber end for three-dimensional trapping," Opt. Quantum Electron. 34, 993 (2002).
[CrossRef]

2001 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, "The optical stretcher: a novel laser tool to micromanipulate cells," Biophys. J. 81, 767 (2001).
[CrossRef] [PubMed]

2000 (3)

K. Taguchi, K. Atsuta, T. Nakata and M. Ideda, "Levitation of a microscopic object using plural optical fibers," Opt. Commun. 176, 43 (2000).
[CrossRef]

K. Taguchi, M. Tanaka and M. Ikeda, "Dual-beam trapping method for an object with large relative refractive index," Jpn. J. Appl. Phys. 39, L1302 (2000).
[CrossRef]

A. Ashkin, "History of optical trapping and manipulation of small-neutral particle, atoms, and molecules," IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).
[CrossRef]

1997 (4)

D. G. Grier, "Optical tweezers in colloid and interface science," Curr. Opin. Colloid. In. 2, 264 (1997).
[CrossRef]

K. Taguchi, H. Ueno, T. Hiramatsu and M. Ikeda, "Optical trapping of dielectric particle and biological cell using optical fibre," Electron. Lett. 33, 413 (1997).
[CrossRef]

R. C. Gauthier, "Optical trapping: a tool to assist optical machining," Opt. Laser Technol. 29, 389 (1997).
[CrossRef]

E. Sidick, S. D. Collins, and A. Knoesen, "Trapping forces in a multiple-beam fiber-optic trap," Appl. Optics 36, 6423 (1997).
[CrossRef]

1995 (1)

E. R. Lyons and G. J. Sonek, "Confinement and bistability in a tapered hemispheically lensed optical fiber trap," Appl. Phys. Lett. 66, 1584 (1995).
[CrossRef]

1993 (1)

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 (1992).
[CrossRef] [PubMed]

Abbondanzieri, E. A.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460 (2005).
[CrossRef] [PubMed]

Abedin, K. S.

K. S. Abedin, C. Kerbage, A. Fernandez-Nieves and D. A. Weitz, "Optical manipulation and rotation of liquid crystal drops using high-index fiber-optics tweezers," Appl. Phys. Lett. 91, 091119 (2007).
[CrossRef]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, "The optical stretcher: a novel laser tool to micromanipulate cells," Biophys. J. 81, 767 (2001).
[CrossRef] [PubMed]

Arias-Gonzalez, J. R.

S. Hormeno and J. R. Arias-Gonzalez, "Exploring mechanochemical processes in the cell with optical tweezers," Biol. Cell 98, 679 (2006).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, "History of optical trapping and manipulation of small-neutral particle, atoms, and molecules," IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).
[CrossRef]

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

Asundi, A. K.

A. Priyadarshi, L. H. Fen, S. G. Mhaisalkar, V. Kripesh, and A. K. Asundi, "Fiber misalignment in silicon V-groove based optical modules," Opt. Fiber Technol. 12, 170 (2006).
[CrossRef]

Atsuta, K.

K. Taguchi, K. Atsuta, T. Nakata and M. Ideda, "Levitation of a microscopic object using plural optical fibers," Opt. Commun. 176, 43 (2000).
[CrossRef]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Block, S. M.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460 (2005).
[CrossRef] [PubMed]

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

Bragheri, F.

F. Bragheri, P. Minzioni, C. Liberale, E. Di Fabrizio, and I. Cristiani, "Design and optimization of a reflection-based fiber-optic tweezers," Opt. Express 16, 17647 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-22-17647.
[CrossRef] [PubMed]

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
[CrossRef]

Chiou, A.

Collins, S. D.

E. Sidick, S. D. Collins, and A. Knoesen, "Trapping forces in a multiple-beam fiber-optic trap," Appl. Optics 36, 6423 (1997).
[CrossRef]

Constable, A.

Cristiani, I

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
[CrossRef]

Cristiani, I.

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, "The optical stretcher: a novel laser tool to micromanipulate cells," Biophys. J. 81, 767 (2001).
[CrossRef] [PubMed]

De Angelis, F.

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
[CrossRef]

Di Fabrizio, E.

F. Bragheri, P. Minzioni, C. Liberale, E. Di Fabrizio, and I. Cristiani, "Design and optimization of a reflection-based fiber-optic tweezers," Opt. Express 16, 17647 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-22-17647.
[CrossRef] [PubMed]

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
[CrossRef]

Fen, L. H.

A. Priyadarshi, L. H. Fen, S. G. Mhaisalkar, V. Kripesh, and A. K. Asundi, "Fiber misalignment in silicon V-groove based optical modules," Opt. Fiber Technol. 12, 170 (2006).
[CrossRef]

Fernandez-Nieves, A.

K. S. Abedin, C. Kerbage, A. Fernandez-Nieves and D. A. Weitz, "Optical manipulation and rotation of liquid crystal drops using high-index fiber-optics tweezers," Appl. Phys. Lett. 91, 091119 (2007).
[CrossRef]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Gauthier, R. C.

R. C. Gauthier, "Optical trapping: a tool to assist optical machining," Opt. Laser Technol. 29, 389 (1997).
[CrossRef]

Greenleaf, W. J.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460 (2005).
[CrossRef] [PubMed]

Grier, D. G.

D. G. Grier, "Optical tweezers in colloid and interface science," Curr. Opin. Colloid. In. 2, 264 (1997).
[CrossRef]

Guan, C.

L. Yuan, Z. Liu, J. Yang, and C. Guan, "Twin-core fiber optical tweezers," Opt. Express 16, 4551 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-7-4559.
[CrossRef]

Guck, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, "The optical stretcher: a novel laser tool to micromanipulate cells," Biophys. J. 81, 767 (2001).
[CrossRef] [PubMed]

Guo, C.

Hiramatsu, T.

K. Taguchi, H. Ueno, T. Hiramatsu and M. Ikeda, "Optical trapping of dielectric particle and biological cell using optical fibre," Electron. Lett. 33, 413 (1997).
[CrossRef]

Hnatovsky, C.

Hormeno, S.

S. Hormeno and J. R. Arias-Gonzalez, "Exploring mechanochemical processes in the cell with optical tweezers," Biol. Cell 98, 679 (2006).
[CrossRef] [PubMed]

Ideda, M.

K. Taguchi, K. Atsuta, T. Nakata and M. Ideda, "Levitation of a microscopic object using plural optical fibers," Opt. Commun. 176, 43 (2000).
[CrossRef]

Ikeda, M.

K. Taguchi, M. Tanaka and M. Ikeda, "Investigation on the radius of a hemispherical microlens of an optical fiber end for three-dimensional trapping," Opt. Quantum Electron. 34, 993 (2002).
[CrossRef]

K. Taguchi, M. Tanaka and M. Ikeda, "Dual-beam trapping method for an object with large relative refractive index," Jpn. J. Appl. Phys. 39, L1302 (2000).
[CrossRef]

K. Taguchi, H. Ueno, T. Hiramatsu and M. Ikeda, "Optical trapping of dielectric particle and biological cell using optical fibre," Electron. Lett. 33, 413 (1997).
[CrossRef]

Karmenyan, A.

Kas, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, "The optical stretcher: a novel laser tool to micromanipulate cells," Biophys. J. 81, 767 (2001).
[CrossRef] [PubMed]

Kerbage, C.

K. S. Abedin, C. Kerbage, A. Fernandez-Nieves and D. A. Weitz, "Optical manipulation and rotation of liquid crystal drops using high-index fiber-optics tweezers," Appl. Phys. Lett. 91, 091119 (2007).
[CrossRef]

Kim, J.

Knoesen, A.

E. Sidick, S. D. Collins, and A. Knoesen, "Trapping forces in a multiple-beam fiber-optic trap," Appl. Optics 36, 6423 (1997).
[CrossRef]

Kripesh, V.

A. Priyadarshi, L. H. Fen, S. G. Mhaisalkar, V. Kripesh, and A. K. Asundi, "Fiber misalignment in silicon V-groove based optical modules," Opt. Fiber Technol. 12, 170 (2006).
[CrossRef]

Landick, R.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460 (2005).
[CrossRef] [PubMed]

Liberale, C.

F. Bragheri, P. Minzioni, C. Liberale, E. Di Fabrizio, and I. Cristiani, "Design and optimization of a reflection-based fiber-optic tweezers," Opt. Express 16, 17647 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-22-17647.
[CrossRef] [PubMed]

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
[CrossRef]

Liu, Y.

Y. Liu and M. Yu, "Three-dimensional fiber optical trap for cell manipulation and force measurement," Proc. SPIE 6528, 65280Z (2007).
[CrossRef]

Liu, Z.

Lyons, E. R.

E. R. Lyons and G. J. Sonek, "Confinement and bistability in a tapered hemispheically lensed optical fiber trap," Appl. Phys. Lett. 66, 1584 (1995).
[CrossRef]

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, "The optical stretcher: a novel laser tool to micromanipulate cells," Biophys. J. 81, 767 (2001).
[CrossRef] [PubMed]

Mervis, J.

Mhaisalkar, S. G.

A. Priyadarshi, L. H. Fen, S. G. Mhaisalkar, V. Kripesh, and A. K. Asundi, "Fiber misalignment in silicon V-groove based optical modules," Opt. Fiber Technol. 12, 170 (2006).
[CrossRef]

Minzioni, P.

F. Bragheri, P. Minzioni, C. Liberale, E. Di Fabrizio, and I. Cristiani, "Design and optimization of a reflection-based fiber-optic tweezers," Opt. Express 16, 17647 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-22-17647.
[CrossRef] [PubMed]

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
[CrossRef]

Moon, T. J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, "The optical stretcher: a novel laser tool to micromanipulate cells," Biophys. J. 81, 767 (2001).
[CrossRef] [PubMed]

Nakata, T.

K. Taguchi, K. Atsuta, T. Nakata and M. Ideda, "Levitation of a microscopic object using plural optical fibers," Opt. Commun. 176, 43 (2000).
[CrossRef]

Neuman, K. C.

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

Numata, T.

T. Numata, A. Takayanagi, Y. Otani and N. Umeda, "Manipulation of metal nanoparticles using fiber-optic laser tweezers with a microspherical focusing lens," Jpn. J. Appl. Phys. 45, 359 (2006).
[CrossRef]

Otani, Y.

T. Numata, A. Takayanagi, Y. Otani and N. Umeda, "Manipulation of metal nanoparticles using fiber-optic laser tweezers with a microspherical focusing lens," Jpn. J. Appl. Phys. 45, 359 (2006).
[CrossRef]

Prentiss, M.

Priyadarshi, A.

A. Priyadarshi, L. H. Fen, S. G. Mhaisalkar, V. Kripesh, and A. K. Asundi, "Fiber misalignment in silicon V-groove based optical modules," Opt. Fiber Technol. 12, 170 (2006).
[CrossRef]

Shaevitz, J. W.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460 (2005).
[CrossRef] [PubMed]

Sidick, E.

E. Sidick, S. D. Collins, and A. Knoesen, "Trapping forces in a multiple-beam fiber-optic trap," Appl. Optics 36, 6423 (1997).
[CrossRef]

Sonek, G. J.

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K. Taguchi, M. Tanaka and M. Ikeda, "Investigation on the radius of a hemispherical microlens of an optical fiber end for three-dimensional trapping," Opt. Quantum Electron. 34, 993 (2002).
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K. Taguchi, M. Tanaka and M. Ikeda, "Dual-beam trapping method for an object with large relative refractive index," Jpn. J. Appl. Phys. 39, L1302 (2000).
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K. Taguchi, H. Ueno, T. Hiramatsu and M. Ikeda, "Optical trapping of dielectric particle and biological cell using optical fibre," Electron. Lett. 33, 413 (1997).
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T. Numata, A. Takayanagi, Y. Otani and N. Umeda, "Manipulation of metal nanoparticles using fiber-optic laser tweezers with a microspherical focusing lens," Jpn. J. Appl. Phys. 45, 359 (2006).
[CrossRef]

Tanaka, M.

K. Taguchi, M. Tanaka and M. Ikeda, "Investigation on the radius of a hemispherical microlens of an optical fiber end for three-dimensional trapping," Opt. Quantum Electron. 34, 993 (2002).
[CrossRef]

K. Taguchi, M. Tanaka and M. Ikeda, "Dual-beam trapping method for an object with large relative refractive index," Jpn. J. Appl. Phys. 39, L1302 (2000).
[CrossRef]

Taylor, R. S.

Ueno, H.

K. Taguchi, H. Ueno, T. Hiramatsu and M. Ikeda, "Optical trapping of dielectric particle and biological cell using optical fibre," Electron. Lett. 33, 413 (1997).
[CrossRef]

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T. Numata, A. Takayanagi, Y. Otani and N. Umeda, "Manipulation of metal nanoparticles using fiber-optic laser tweezers with a microspherical focusing lens," Jpn. J. Appl. Phys. 45, 359 (2006).
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Yang, K.

Yu, M.

Y. Liu and M. Yu, "Three-dimensional fiber optical trap for cell manipulation and force measurement," Proc. SPIE 6528, 65280Z (2007).
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Appl. Optics (1)

E. Sidick, S. D. Collins, and A. Knoesen, "Trapping forces in a multiple-beam fiber-optic trap," Appl. Optics 36, 6423 (1997).
[CrossRef]

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K. S. Abedin, C. Kerbage, A. Fernandez-Nieves and D. A. Weitz, "Optical manipulation and rotation of liquid crystal drops using high-index fiber-optics tweezers," Appl. Phys. Lett. 91, 091119 (2007).
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[CrossRef]

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C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I Cristiani, "Miniaturized all-fiber probe for three-dimensional optical trapping and manipulation," Nat. Photonics 1, 723 (2007).
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Supplementary Material (1)

» Media 1: MOV (2664 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Illustration of forces applied to a trapped particle in (a) SFOTs and (b) DFOTs. Fs represents the axial net force of the scattering force and the axial gradient force and Fg denotes the transverse gradient force.

Fig. 2.
Fig. 2.

(a). Experimental setup of the inclined DFOTs system. (b). Close-up showing the optical trap built from the two beams emitted from tapered fibers.

Fig. 3.
Fig. 3.

Silica bead with a diameter of 4.74 µm being manipulated in three dimensions by the DFOTs. The arrows indicate the next motion direction of the coverglass. (a) Initial positions of free beads with the coverglass moving along +y. (b)–(c) The coverglass moving along +x with Bead 1 trapped. (c)–(e) The coverglass moving along +y, -x, and then -y. Bead 2 was moved out of the view field and another free bead, Bead 3, was brought in. (e)–(f) The trap together with Bead 1 moving out of focus along +z. (f)–(h) The coverglass moving downwards (+x) with Bead 3 moving freely below Bead 1. (Media 1) 2.7 MB.

Fig. 4.
Fig. 4.

Calibration curves of x-axis trapping efficiencies obtained with different laser powers. The experiments were carried out with silica beads of 4.74 µm in diameter. The optical powers shown are the total powers from both fibers.

Fig. 5.
Fig. 5.

Lorentzian fitting (red curve) of experimentally measured power spectrum (black squares). Here, the corner frequency fx is 11.3 Hz, which gives a spring constant kx of 2.82 pN/µm.

Fig. 6.
Fig. 6.

The simulation results of optical force versus bead displacement along z axis with different θ values. G is the gravity and Fb is the buoyancy of the trapped silica bead. The optical force should be larger than G-Fb in order to trap the bead in the z direction. The figure implies that 50° is the critical angle for z-axis trapping, which coincides with the experimentally observed value. The total optical power emitted from both fibers is 8.05 mW. The bead size is 4.74 µm in diameter.

Fig. 7.
Fig. 7.

The simulation results of optical force versus bead displacement along z axis with different bead sizes. G is the gravity and Fb is the buoyancy of the trapped silica bead. For each bead sizes, G-Fb is expressed with a horizontal dashed line with the same color as the optical force curve. The figure implies that large particles are more difficult to be lifted up. The total optical power emitted from both fibers is 8.05 mW. The inclination angle θ is 50°.

Fig. 8.
Fig. 8.

The dependence of optical forces on bead displacements along (a) the x axis and (b) the y axis at different fiber inclination angles. The total optical power emitted from both fibers is 15.3 mW. The bead size is 4.74 µm in diameter. The fiber separation along the y axis is 45 µm.

Fig. 9.
Fig. 9.

Simulation results of the forces applied on a 4.74-µm bead in the yz plane with a misalignment of 1 µm along the z axis for (a) the inclined DFOTs (θ=50°) and (b) the counter propagation DFOTs (θ=90°). The blue dash-dotted lines indicate the optical axes of the two fibers. It is noted that the forces are the net forces of optical forces, gravity, and buoyancy applied on the beads.

Tables (1)

Tables Icon

Table 1. Spring constants of different bead sizes.

Equations (5)

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Fdrag,bead=6πμvr,
Fdrag,cyl=4πμvlc0.5γln(ρvD4μ),
Q=FcnP,
Px=D2πf2+fc2,
kx=12πμrfc.

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