Abstract

Transverse trapping force on three types of metallic Mie particles (gold, nickel, and silver) is measured for different values of the numerical aperture of an objective used for trapping. The experimental results are compared with those calculated with a modified ray-optics model. It is found that, unlike the situation for a trapped dielectric particle, the maximum transverse trapping efficiency for a trapped metallic particle is increased with the numerical aperture of the trapping objective. After consideration of radiometric force, which is caused by the heating effect, and spherical aberration, which is induced by the refractive-index mismatch, the measured results agree well with the theoretical prediction. The magnitude of the radiometric force is approximately ten times stronger than the maximum transverse trapping force.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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1998

1997

T. Sugiura, T. Okada, Y. Inouye, O. Nakamura, S. Kawata, “Gold-bead scanning near-field optical microscope with laser-force position control,” Opt. Lett. 22, 1663–1665 (1997).
[CrossRef]

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

1996

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

1995

1994

1993

W. H. Wright, G. J. Sonek, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

1992

1991

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” J. Biophys. 61, 569–582 (1991).
[CrossRef]

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett. 60, 807–809 (1991).
[CrossRef]

1989

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illumination by a focused laser beam,” J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

1982

M. Lewittes, S. Arnold, G. Oster, “Radiometric levitation of micron sized spheres,” Appl. Phys. Lett. 40, 455–457 (1982).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illumination by a focused laser beam,” J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

Arnold, S.

M. Lewittes, S. Arnold, G. Oster, “Radiometric levitation of micron sized spheres,” Appl. Phys. Lett. 40, 455–457 (1982).
[CrossRef]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” J. Biophys. 61, 569–582 (1991).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illumination by a focused laser beam,” J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

Berns, M. W.

Besancon, R. M.

R. M. Besancon, The Encyclopedia of Physics, 2nd ed. (Van Nostrand Reinhold, New York, 1974), pp. 376.

Block, S. M.

Booker, G. R.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 13, pp. 612–615.

Brevik, I.

Felgner, H.

Furukawa, H.

Gan, X. S.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Gauthier, R. C.

Gu, M.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

P. C. Ke, M. Gu, “Characterisation of trapping force in the presence of spherical aberration,” J. Mod. Opt. (in press).

Gussgard, R.

Harada, Y.

Inaba, H.

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

Inouye, Y.

T. Sugiura, T. Okada, Y. Inouye, O. Nakamura, S. Kawata, “Gold-bead scanning near-field optical microscope with laser-force position control,” Opt. Lett. 22, 1663–1665 (1997).
[CrossRef]

S. Kawata, Y. Inouye, T. Sugiura, “Near-field scanning optical microscope with a laser trapped probe,” Jpn. J. Appl. Phys. 33, L1725–L1727 (1994).
[CrossRef]

Kawata, S.

T. Sugiura, T. Okada, Y. Inouye, O. Nakamura, S. Kawata, “Gold-bead scanning near-field optical microscope with laser-force position control,” Opt. Lett. 22, 1663–1665 (1997).
[CrossRef]

S. Kawata, Y. Inouye, T. Sugiura, “Near-field scanning optical microscope with a laser trapped probe,” Jpn. J. Appl. Phys. 33, L1725–L1727 (1994).
[CrossRef]

Ke, P. C.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

P. C. Ke, M. Gu, “Characterisation of trapping force in the presence of spherical aberration,” J. Mod. Opt. (in press).

Kitamura, N.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett. 60, 807–809 (1991).
[CrossRef]

Koshioka, M.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett. 60, 807–809 (1991).
[CrossRef]

Laczik, Z.

Lewittes, M.

M. Lewittes, S. Arnold, G. Oster, “Radiometric levitation of micron sized spheres,” Appl. Phys. Lett. 40, 455–457 (1982).
[CrossRef]

Lide, D. R.

D. R. Lide, CRC Handbook of Chemistry and Physics, 77th ed. (CRC Press, Boca Raton, Fla., 1996–1997), Sec. 12, pp. 130–143.

Lindmo, T.

Masuhara, H.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett. 60, 807–809 (1991).
[CrossRef]

Misawa, H.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett. 60, 807–809 (1991).
[CrossRef]

Müller, O.

Nakamura, O.

Okada, T.

Oster, G.

M. Lewittes, S. Arnold, G. Oster, “Radiometric levitation of micron sized spheres,” Appl. Phys. Lett. 40, 455–457 (1982).
[CrossRef]

Raznjevic, K.

K. Raznjevic, Handbook of Thermodynamic Tables and Charts (Hemisphere, Washington, D.C., 1976), pp. 3.

Sasaki, K.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett. 60, 807–809 (1991).
[CrossRef]

Sato, S.

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

S. Sato, Y. Harada, Y. Waseda, “Optical trapping of microscopic metal particles,” Opt. Lett. 19, 1807–1809 (1994).
[CrossRef] [PubMed]

S. Sato, “Calculation of optical trapping forces for micrometer-sized particles with complex refractive index,” in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 197.

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illumination by a focused laser beam,” J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

Schilwa, M.

Sonek, G. J.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Sugiura, T.

T. Sugiura, T. Okada, Y. Inouye, O. Nakamura, S. Kawata, “Gold-bead scanning near-field optical microscope with laser-force position control,” Opt. Lett. 22, 1663–1665 (1997).
[CrossRef]

S. Kawata, Y. Inouye, T. Sugiura, “Near-field scanning optical microscope with a laser trapped probe,” Jpn. J. Appl. Phys. 33, L1725–L1727 (1994).
[CrossRef]

Svoboda, K.

Török, P.

Varga, P.

Wallace, S.

Waseda, Y.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 13, pp. 612–615.

Wood, R. M.

R. M. Wood, Laser Damage in Optical Materials (GEC Research, Hirst Research Centre, UK, 1986), Chap. 1, pp. 24–25.

Wright, W. H.

W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Yamaguchi, I.

Appl. Opt.

Appl. Phys. Lett.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett. 60, 807–809 (1991).
[CrossRef]

M. Lewittes, S. Arnold, G. Oster, “Radiometric levitation of micron sized spheres,” Appl. Phys. Lett. 40, 455–457 (1982).
[CrossRef]

W. H. Wright, G. J. Sonek, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illumination by a focused laser beam,” J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

J. Biophys.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” J. Biophys. 61, 569–582 (1991).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

S. Kawata, Y. Inouye, T. Sugiura, “Near-field scanning optical microscope with a laser trapped probe,” Jpn. J. Appl. Phys. 33, L1725–L1727 (1994).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

Rev. Sci. Instrum.

M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).
[CrossRef]

Other

S. Sato, “Calculation of optical trapping forces for micrometer-sized particles with complex refractive index,” in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 197.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 13, pp. 612–615.

P. C. Ke, M. Gu, “Characterisation of trapping force in the presence of spherical aberration,” J. Mod. Opt. (in press).

D. R. Lide, CRC Handbook of Chemistry and Physics, 77th ed. (CRC Press, Boca Raton, Fla., 1996–1997), Sec. 12, pp. 130–143.

R. M. Wood, Laser Damage in Optical Materials (GEC Research, Hirst Research Centre, UK, 1986), Chap. 1, pp. 24–25.

R. M. Besancon, The Encyclopedia of Physics, 2nd ed. (Van Nostrand Reinhold, New York, 1974), pp. 376.

K. Raznjevic, Handbook of Thermodynamic Tables and Charts (Hemisphere, Washington, D.C., 1976), pp. 3.

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Figures (6)

Fig. 1
Fig. 1

Distributions of the total trapping efficiency Q t in the xz plane for (a) gold, (b) nickel, (c) silver particles. The polarization direction of the laser beam is parallel to the x axis. The light distribution over the aperture of the objective is uniform and linearly polarized (λ = 488 nm). An oil-immersion objective (1.25 NA) is assumed for trapping.

Fig. 2
Fig. 2

Axial trapping efficiency as a function of the axial trapping position z when x = 0 for gold, nickel, and silver particles. The other conditions are the same as those in Fig. 1.

Fig. 3
Fig. 3

Transverse trapping efficiency Q tr as a function of the transverse trapping position x for (a) gold, (b) nickel, (c) silver particles. The other conditions are the same as those in Fig. 1. The solid curves correspond to the situation when a maximum transverse trapping efficiency occurs.

Fig. 4
Fig. 4

Transverse trapping efficiency Q tr as a function of the transverse trapping position y for (a) gold, (b) nickel, (c) silver particles. The trapping position is in the yz plane perpendicular to the polarization direction of the illumination beam, and the other conditions are the same as those in Fig. 1.

Fig. 5
Fig. 5

Schematic diagram of the experimental setup for the trapping of metallic particles.

Fig. 6
Fig. 6

Demonstration of a trapped, 3-µm-diameter nickel particle recorded with a CCD camera. Frames (a) and (b) were recorded at different times.

Tables (6)

Tables Icon

Table 1 Maximum Transverse Trapping Efficiency Qtr as a Function of the Effective Numerical Aperture NA′ of the Trapping Objective for Gold Particles

Tables Icon

Table 2 Maximum Transverse Trapping Efficiency Qtr as a Function of the Effective Numerical Aperture NA′ of the Trapping Objective for Nickel Particles

Tables Icon

Table 3 Maximum Transverse Trapping Efficiency Qtr as a Function of the Effective Numerical Aperture NA′ of the Trapping Objective for Silver Particles

Tables Icon

Table 4 Transverse Force as a Function of the Numerical Aperture NA′ of the Trapping Objective for Gold Particles

Tables Icon

Table 5 Transverse Force as a Function of the Numerical Aperture NA′ of the Trapping Objective for Nickel Particles

Tables Icon

Table 6 Transverse Force as a Function of the Numerical Aperture NA′ of the Trapping Objective for Silver Particles

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

Fs=npc1+R cos 2θ, Fg=npRcsin 2θ,
Q=Fc/np,
Fr=C1mgI/r2,
Fr=C2ρpNA2r.
Ftre=Ftr-Ff.
Ff=Ftaμ,
Fta=Fa+Fg-Fb+Fr.
Fg=4/3πr3ρg,
Fb=4/3πr3ρwg,

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