Abstract

We present a method to build an optical tip at the end of a single-mode optical fiber. The tip is grown by a self-writing process: photopolymerization by the light coming from the optical fiber. We developed a technique to produce a flat end surface on the tip. The good optical quality of the tip and the output laser beam was demonstrated by the fact that a counterpropagating optical trap could be constructed by using the tips with parameters comparable to regular fiber traps. Because of the small size of the tips, the tweezers require a much smaller space than regular fiber traps.

© 2009 Optical Society of America

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  1. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
    [CrossRef]
  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] [PubMed]
  3. K. Svoboda and S. M. Block, “Biological application of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
    [CrossRef] [PubMed]
  4. A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
    [CrossRef] [PubMed]
  5. P. H. Jones, O. M. Marago, and E. P. J. Stride, “Parametrization of trapping forces on microbubbles in scanning optical tweezers,” J. Opt. A Pure Appl. Opt. 9, S278-S283 (2007).
    [CrossRef]
  6. 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]
  7. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  8. M. M. Burns, J. M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233-1236 (1989).
    [CrossRef] [PubMed]
  9. F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
    [CrossRef]
  10. P. B. Bareil, Y. L. Sheng, and A. Chiou, “Local stress distribution on the surface of a spherical cell in an optical stretcher,” Opt. Express 14, 12503-12509 (2006).
    [CrossRef]
  11. S. J. Frisken, “Light-induced optical waveguide uptapers,” Opt. Lett. 18, 1035-1037 (1993).
    [CrossRef] [PubMed]
  12. M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
    [CrossRef]
  13. A. S. Kewitsch and A. Yariv, “Self-focusing and self trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24-26 (1996).
    [CrossRef] [PubMed]
  14. R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D. Lougnot, “Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization,” Appl. Opt. 40, 5860-5871 (2001).
    [CrossRef]
  15. D. McGloin, A. E. Carruthers, K. Dholakia, and E. M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004).
    [CrossRef]
  16. R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813-1822 (1996).
    [CrossRef] [PubMed]
  17. H. Felgner, O. Muller, and M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34, 977-982 (1995).
    [CrossRef] [PubMed]

2007 (1)

P. H. Jones, O. M. Marago, and E. P. J. Stride, “Parametrization of trapping forces on microbubbles in scanning optical tweezers,” J. Opt. A Pure Appl. Opt. 9, S278-S283 (2007).
[CrossRef]

2006 (1)

2005 (1)

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

2004 (1)

D. McGloin, A. E. Carruthers, K. Dholakia, and E. M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004).
[CrossRef]

2002 (2)

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

2001 (1)

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

1996 (2)

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

A. S. Kewitsch and A. Yariv, “Self-focusing and self trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24-26 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

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

1993 (1)

1989 (1)

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

1987 (1)

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] [PubMed]

1986 (1)

1970 (1)

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

Ashkin, A.

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] [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]

Bachelot, R.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D. Lougnot, “Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization,” Appl. Opt. 40, 5860-5871 (2001).
[CrossRef]

Bareil, P. B.

Betz, T.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Block, S. M.

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

Burns, M. M.

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Carruthers, A. E.

D. McGloin, A. E. Carruthers, K. Dholakia, and E. M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004).
[CrossRef]

Chiou, A.

Chu, S.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813-1822 (1996).
[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]

Deloeil, D.

Dholakia, K.

D. McGloin, A. E. Carruthers, K. Dholakia, and E. M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004).
[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] [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]

Ebert, S.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Ecoffet, C.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D. Lougnot, “Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization,” Appl. Opt. 40, 5860-5871 (2001).
[CrossRef]

Ehrlicher, A.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Felgner, H.

Finer, J. T.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

Fournier, J. M.

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Fressengeas, N.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

Frisken, S. J.

Golovchenko, J. A.

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Guck, J.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

Hocine, M.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

Jones, P. H.

P. H. Jones, O. M. Marago, and E. P. J. Stride, “Parametrization of trapping forces on microbubbles in scanning optical tweezers,” J. Opt. A Pure Appl. Opt. 9, S278-S283 (2007).
[CrossRef]

Kas, J.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Kewitsch, A. S.

Koch, D.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

Kugel, G.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

Lincoln, B.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Lougnot, D.

Marago, O. M.

P. H. Jones, O. M. Marago, and E. P. J. Stride, “Parametrization of trapping forces on microbubbles in scanning optical tweezers,” J. Opt. A Pure Appl. Opt. 9, S278-S283 (2007).
[CrossRef]

McGloin, D.

D. McGloin, A. E. Carruthers, K. Dholakia, and E. M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004).
[CrossRef]

Milner, V.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Muller, K.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Muller, O.

Raizen, M. G.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Royer, P.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D. Lougnot, “Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization,” Appl. Opt. 40, 5860-5871 (2001).
[CrossRef]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

Sauer, F.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Schinkinger, S.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Schliwa, M.

Sheng, Y. L.

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

Simmons, R. M.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

Spudich, J. A.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

Stride, E. P. J.

P. H. Jones, O. M. Marago, and E. P. J. Stride, “Parametrization of trapping forces on microbubbles in scanning optical tweezers,” J. Opt. A Pure Appl. Opt. 9, S278-S283 (2007).
[CrossRef]

Stuhrmann, B.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Svoboda, K.

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

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

Travis, K.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Wottawah, F.

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Wright, E. M.

D. McGloin, A. E. Carruthers, K. Dholakia, and E. M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004).
[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] [PubMed]

Yariv, A.

Acta Biomaterialia (1)

F. Wottawah, S. Schinkinger, B. Lincoln, S. Ebert, K. Muller, F. Sauer, K. Travis, and J. Guck, “Characterizing single suspended cells by optorheology,” Acta Biomaterialia 1, 263-271 (2005).
[CrossRef]

Annu. Rev. Biophys. Biomol. Struct. (1)

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

Appl. Opt. (2)

Biophys. J. (1)

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

J. Opt. A Pure Appl. Opt. (1)

P. H. Jones, O. M. Marago, and E. P. J. Stride, “Parametrization of trapping forces on microbubbles in scanning optical tweezers,” J. Opt. A Pure Appl. Opt. 9, S278-S283 (2007).
[CrossRef]

Nature (1)

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] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Phys. Lett. (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Lett. 78, 4713-4716 (1997).
[CrossRef]

Phys. Rev. E (1)

D. McGloin, A. E. Carruthers, K. Dholakia, and E. M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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

M. M. Burns, J. M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, “Guiding neuronal growth with light,” Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Synth. Met. (1)

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, “End-of-fiber polymer tip: manufacturing and modeling,” Synth. Met. 127, 313-318 (2002).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Scheme of the chamber to grow the tip by photopolymerization. The left and right sides of the brick-shaped chamber are open, and the resin is held in place by surface tension.

Fig. 2
Fig. 2

Image of a typical tip grown at the end of the optical fiber. Notice the flat end of the tip. The white bar represents 20 μm .

Fig. 3
Fig. 3

Schematic of the optical tweezers setup. The beam of the 1043 nm laser was divided in to two by a beam splitter cube (BSC). The two beams than were coupled (FC) into the optical fibers. The output ends were held by manipulators in the test volume positioned on a motorized stage and the sample was observed from below.

Fig. 4
Fig. 4

Image of the tweezers trapping a 1 μm bead. The white bar represents 10 μm .

Fig. 5
Fig. 5

Optical binding observed. The optical forces hold four beads in line between the tips. The white bar represents 10 μm .

Fig. 6
Fig. 6

Distribution of the positions of the bead undergoing Brownian motion in the trap. The figure shows the density of bead positions (black circles) and the fitted Gaussian curve (continuous curve) in the (a) axial and (b) transversal directions. The corresponding spring constants of the optical trap are inserted.

Metrics