Abstract

An enhanced photon propagation method is used to calculate the forces and torque present on each sphere of a system of particles located in the vicinity of focused laser-trapping beams. Infinitesimal trajectory displacements are computed through classical mechanics and the new particle position used to define the next trapping system geometry considered. Repeated applications of the process, implemented as a computer program, enables full trajectory plotting and the dynamic behavior of the systems to be explored as a function of time.

© 1998 Optical Society of America

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    [CrossRef]

1997

1996

1995

1994

L. Malmqvist, H. M. Hertz, “Two-color trapped-particle optical microscopy,” Opt. Lett. 19, 853–855 (1994).
[CrossRef] [PubMed]

S. Sato, H. Inaba, “Second-harmonic and sum-frequency generation from optically trapped KTiOPO4 microscopic particles by use of Nd:YAG and Ti:Al2O3 lasers,” Opt. Lett. 19, 927–929 (1994).
[CrossRef] [PubMed]

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]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

E. Higurashi, H. Tanaka, O. Ohguchi, “Optically induced rotation of anisotropic micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: picoNewton forces and nanometre steps,” Nature (London) 368, 113–119 (1994).
[CrossRef]

1993

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of Kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by multiple optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

H. Tashiro, M. Uchida, M. Sato-Maeda, “Three-dimensional cell manipulator by means of optical trapping for the specification of cell-to-cell adhesion,” Opt. Eng. 32, 2812–2817 (1993).
[CrossRef]

A. Constable, J. Kim, F. Zarinetchi, M. Prentis, “Demonstration of a fiber-optical light force trap,” Opt. Lett. 18, 1867–1869 (1993).
[CrossRef] [PubMed]

1992

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]

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1992–1930 (1992).
[CrossRef]

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II: Mie scatterers,” Optik 90, 57–60 (1992).

S. C. Kuo, M. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

1991

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajira, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigation on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

1990

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

1989

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

1977

R. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. (Paris) 8, 181–187 (1977).
[CrossRef]

1970

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

Almaas, E.

Angelova, M. I.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Arimondo, E.

S. Grego, E. Arimondo, C. Frediani, “Optical tweezers based on near infrared diode laser,” J. Biomed. Opt. 2, 332–339 (1997).
[CrossRef] [PubMed]

Asch, R. H.

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

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]

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

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

Bakker Schut, T. C.

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigation on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Berg, F. D.

K. Schütze, A. Clement-Sengewald, F. D. Berg, G. Brehm, R. Schütze, “Laser microbeam and optical tweezers: micromanipulation of gametes and embryos,” (Institut für den Wissenschaftlichen Film, Göttingen, 1995).

Berns, M. W.

Y. Liu, G. J. Sonek, M. W. Berns, K. Konig, B. J. Tromberg, “Two-photon fluorescence excitation in continuous-wave infrared optical tweezers,” Opt. Lett. 20, 2246–2248 (1995).
[CrossRef] [PubMed]

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]

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajira, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

Block, S. M.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of Kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Bonder, E. M.

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

Brakenhoff, G. J.

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by multiple optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II: Mie scatterers,” Optik 90, 57–60 (1992).

Brehm, G.

K. Schütze, A. Clement-Sengewald, F. D. Berg, G. Brehm, R. Schütze, “Laser microbeam and optical tweezers: micromanipulation of gametes and embryos,” (Institut für den Wissenschaftlichen Film, Göttingen, 1995).

Brevik, I.

E. Almaas, I. Brevik, “Radiation forces on a micrometer-sized sphere in an evanescent field,” J. Opt. Soc. Am. B 12, 2429–2438 (1995).
[CrossRef]

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1992–1930 (1992).
[CrossRef]

Cai, W.

Cheng, S.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajira, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

Chu, S.

T. T. Perkins, D. E. Smith, R. G. Larson, S. Chu, “Stretching of a single tethered polymer in a uniform flow,” Science 268, 83–87 (1995).
[CrossRef] [PubMed]

Clement-Sengewald, A.

K. Schütze, A. Clement-Sengewald, F. D. Berg, G. Brehm, R. Schütze, “Laser microbeam and optical tweezers: micromanipulation of gametes and embryos,” (Institut für den Wissenschaftlichen Film, Göttingen, 1995).

Collins, S. D.

Colon, J. M.

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

Constable, A.

de Grooth, B. G.

R. M. P. Doornbos, M. Schaeffer, A. G. Hoekstra, P. M. A. Sloot, B. G. de Grooth, J. Greve, “Elastic light-scattering measurements of single biological cells in an optical trap,” Appl. Opt. 35, 729–734 (1996).
[CrossRef] [PubMed]

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigation on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Delaunay, B.

R. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. (Paris) 8, 181–187 (1977).
[CrossRef]

Doornbos, R. M. P.

Dziedzic, J. M.

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

Finer, J. T.

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: picoNewton forces and nanometre steps,” Nature (London) 368, 113–119 (1994).
[CrossRef]

Frediani, C.

S. Grego, E. Arimondo, C. Frediani, “Optical tweezers based on near infrared diode laser,” J. Biomed. Opt. 2, 332–339 (1997).
[CrossRef] [PubMed]

Gahagan, K. T.

Gauthier, R. C.

Gouesbet, G.

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

Grego, S.

S. Grego, E. Arimondo, C. Frediani, “Optical tweezers based on near infrared diode laser,” J. Biomed. Opt. 2, 332–339 (1997).
[CrossRef] [PubMed]

Gréhan, G.

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

Greve, J.

R. M. P. Doornbos, M. Schaeffer, A. G. Hoekstra, P. M. A. Sloot, B. G. de Grooth, J. Greve, “Elastic light-scattering measurements of single biological cells in an optical trap,” Appl. Opt. 35, 729–734 (1996).
[CrossRef] [PubMed]

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigation on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Gussgard, R.

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1992–1930 (1992).
[CrossRef]

Hertz, H. M.

Hesselink, G.

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigation on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Higurashi, E.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polymide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

E. Higurashi, H. Tanaka, O. Ohguchi, “Optically induced rotation of anisotropic micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Hoekstra, A. G.

Imbert, C.

R. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. (Paris) 8, 181–187 (1977).
[CrossRef]

Inaba, H.

Kim, J.

Knoesen, A.

Koehler, D. R.

Konig, K.

Krol, J. J.

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by multiple optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

Kuo, S. C.

S. C. Kuo, M. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

Larson, R. G.

T. T. Perkins, D. E. Smith, R. G. Larson, S. Chu, “Stretching of a single tethered polymer in a uniform flow,” Science 268, 83–87 (1995).
[CrossRef] [PubMed]

Lewis, R.

R. Lewis, “Special delivery for sperm,” Photon. Spectra44–45, (July1996).

Li, F.

Lindmo, T.

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1992–1930 (1992).
[CrossRef]

Liu, Y.

Malmqvist, L.

Martinot-Lagarde, G.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

McGovern, P. G.

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

Numajira, Y.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajira, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

Ohguchi, O.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polymide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

E. Higurashi, H. Tanaka, O. Ohguchi, “Optically induced rotation of anisotropic micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Ord, T.

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

Perkins, T. T.

T. T. Perkins, D. E. Smith, R. G. Larson, S. Chu, “Stretching of a single tethered polymer in a uniform flow,” Science 268, 83–87 (1995).
[CrossRef] [PubMed]

Pouligny, B.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Prentis, M.

Ren, K. F.

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

Roosen, R.

R. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. (Paris) 8, 181–187 (1977).
[CrossRef]

Sarosi, P.

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

Sato, S.

Sato-Maeda, M.

H. Tashiro, M. Uchida, M. Sato-Maeda, “Three-dimensional cell manipulator by means of optical trapping for the specification of cell-to-cell adhesion,” Opt. Eng. 32, 2812–2817 (1993).
[CrossRef]

Sawada, R.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polymide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

Schaeffer, M.

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of Kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of Kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Schütze, K.

K. Schütze, A. Clement-Sengewald, F. D. Berg, G. Brehm, R. Schütze, “Laser microbeam and optical tweezers: micromanipulation of gametes and embryos,” (Institut für den Wissenschaftlichen Film, Göttingen, 1995).

Schütze, R.

K. Schütze, A. Clement-Sengewald, F. D. Berg, G. Brehm, R. Schütze, “Laser microbeam and optical tweezers: micromanipulation of gametes and embryos,” (Institut für den Wissenschaftlichen Film, Göttingen, 1995).

Sheetz, M.

S. C. Kuo, M. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

Sidick, E.

Simmons, R. M.

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: picoNewton forces and nanometre steps,” Nature (London) 368, 113–119 (1994).
[CrossRef]

Skurnik, J.

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

Sloot, P. M. A.

Smith, D. E.

T. T. Perkins, D. E. Smith, R. G. Larson, S. Chu, “Stretching of a single tethered polymer in a uniform flow,” Science 268, 83–87 (1995).
[CrossRef] [PubMed]

Sonek, G. J.

Spudich, J. A.

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: picoNewton forces and nanometre steps,” Nature (London) 368, 113–119 (1994).
[CrossRef]

Steubing, R. W.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajira, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

Sun, S.

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of Kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Swartzlander, G. A.

Tadir, Y.

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

Tamamura, T.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polymide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

Tanaka, H.

E. Higurashi, H. Tanaka, O. Ohguchi, “Optically induced rotation of anisotropic micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Tashiro, H.

H. Tashiro, M. Uchida, M. Sato-Maeda, “Three-dimensional cell manipulator by means of optical trapping for the specification of cell-to-cell adhesion,” Opt. Eng. 32, 2812–2817 (1993).
[CrossRef]

Tromberg, B. J.

Uchida, M.

H. Tashiro, M. Uchida, M. Sato-Maeda, “Three-dimensional cell manipulator by means of optical trapping for the specification of cell-to-cell adhesion,” Opt. Eng. 32, 2812–2817 (1993).
[CrossRef]

Ukita, H.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polymide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

Vafa, O.

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

Visscher, K.

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by multiple optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II: Mie scatterers,” Optik 90, 57–60 (1992).

Wallace, S.

Wang, Y.

Weiss, G.

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

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]

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajira, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

Zarinetchi, F.

Appl. Opt.

Appl. Phys. Lett.

R. C. Gauthier, “Theoretical model for an improved radiation pressure micromotor,” Appl. Phys. Lett. 69, 2015–2017 (1996).
[CrossRef]

E. Higurashi, H. Tanaka, O. Ohguchi, “Optically induced rotation of anisotropic micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Biophys. J.

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]

Cytometry

T. C. Bakker Schut, G. Hesselink, B. G. de Grooth, J. Greve, “Experimental and theoretical investigation on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by multiple optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajira, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
[CrossRef] [PubMed]

Fertil. Steril.

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Micromanipulation of sperm by a laser generated optical trap,” Fertil. Steril. 52, 870–873 (1989).
[PubMed]

J. M. Colon, P. Sarosi, P. G. McGovern, A. Ashkin, J. M. Dziedzic, J. Skurnik, G. Weiss, E. M. Bonder, “Controlled micromanipulation of human sperm in three dimensions with an infrared laser optical trap: effect on sperm velocity,” Fertil. Steril. 57, 695–698 (1992).
[PubMed]

Y. Tadir, W. H. Wright, O. Vafa, T. Ord, R. H. Asch, M. W. Berns, “Force generated by human sperm correlated to velocity and determined using laser generated optical trap,” Fertil. Steril. 53, 944–947 (1990).
[PubMed]

IEEE J. Quantum Electron.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

J. Appl. Phys.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polymide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

J. Biomed. Opt.

S. Grego, E. Arimondo, C. Frediani, “Optical tweezers based on near infrared diode laser,” J. Biomed. Opt. 2, 332–339 (1997).
[CrossRef] [PubMed]

J. Opt. (Paris)

R. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. (Paris) 8, 181–187 (1977).
[CrossRef]

J. Opt. Soc. Am. B

Nature (London)

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: picoNewton forces and nanometre steps,” Nature (London) 368, 113–119 (1994).
[CrossRef]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of Kinesin stepping by optical trapping interferometry,” Nature (London) 365, 721–727 (1993).
[CrossRef]

Opt. Commun.

K. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
[CrossRef]

Opt. Eng.

H. Tashiro, M. Uchida, M. Sato-Maeda, “Three-dimensional cell manipulator by means of optical trapping for the specification of cell-to-cell adhesion,” Opt. Eng. 32, 2812–2817 (1993).
[CrossRef]

Opt. Laser Technol.

R. C. Gauthier, “Optical trapping a tool to assist optical machining,” Opt. Laser Technol. 29, 389–399 (1997).
[CrossRef]

Opt. Lett.

Optik

K. Visscher, G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap. II: Mie scatterers,” Optik 90, 57–60 (1992).

Photon. Spectra

R. Lewis, “Special delivery for sperm,” Photon. Spectra44–45, (July1996).

Phys. Rev. Lett.

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

Pure Appl. Opt.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Gréhan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams: II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995).
[CrossRef]

Science

T. T. Perkins, D. E. Smith, R. G. Larson, S. Chu, “Stretching of a single tethered polymer in a uniform flow,” Science 268, 83–87 (1995).
[CrossRef] [PubMed]

Trends Cell Biol.

S. C. Kuo, M. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

Other

K. Schütze, A. Clement-Sengewald, F. D. Berg, G. Brehm, R. Schütze, “Laser microbeam and optical tweezers: micromanipulation of gametes and embryos,” (Institut für den Wissenschaftlichen Film, Göttingen, 1995).

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Figures (9)

Fig. 1
Fig. 1

Single sphere located in the minimum-waist region of the trapping laser beam. The incident photons are treated as a large number of pencillike streams of photons, or rays, that are reflected and refracted at the sphere ambient medium interface.

Fig. 2
Fig. 2

Initial two-sphere system configuration viewed from the side and includes time-evolution trajectories of the central coordinate. Time points from A1 to F1 and A2 to F2 correspond for each sphere. One sphere is pulled into the beam while the other is pushed out of the beam and drops under the influence of gravity. The dropping sphere eventually encounters the photon stream, centers on the beam axis, and rises into contact with the initially centered top sphere. A stable trap configuration persists afterwards. Insert 1, enhanced view of the trajectory of sphere two. Insert 2, final stable system configuration showing spheres and trapping beam.

Fig. 3
Fig. 3

Dynamic behavior of the two-sphere system configuration when it consists of one reflecting and one refracting sphere. The refracting sphere is pulled into alignment with the central propagation axis of the beam while the reflecting sphere is pushed out of the beam and falls under the influence of gravity. When the reflecting drops far enough to encounter the photon stream, it is further pushed away from central alignment by the reflecting photons.

Fig. 4
Fig. 4

(a) Top view of the initial triangular sphere configuration. Spheres are in contact at two points. The beam propagates in the +z direction. (b) Side view of the initial sphere system with time-evolution trajectories of the sphere’s central coordinate. (c) Side view, rotated 90° with respect to (b), which includes trajectories and spheres arranged in the final stable configuration.

Fig. 5
Fig. 5

(a) Top view of the four-sphere rectangular configuration. The beam propagates along the +z axis with the waist centered at (0, 0, 0). (b) Side view of the initial system including time-evolution trajectories of the central coordinate of the spheres. Trajectories end when the stable configuration has been obtained. (c) Side view, rotated by 90°, with respect to (b), of the sphere trajectories with the spheres shown in the final stable trap configuration. (c) 1, dropping zone; beam propagates through the central opening between the spheres; 2, one of the spheres gets pulled into alignment with the beam’s central propagation axis; 3, one of the spheres is centered onto the beam whereas the others are pushed out and immediately centered under the upper sphere. 4, furthest sphere gets pulled into the beam.

Fig. 6
Fig. 6

Trajectory of a sphere displaced from the laser-beam axis and given an initial x-velocity component of -5 μm/s. (a) Top view, (b) side view, (c) 90° rotated side view of the trajectory and initial sphere position (5, 5, 0). With the energy dissipating factor of 2, the sphere rapidly acquires a radial velocity component and settles in central alignment with the laser beam’s propagation axis.

Fig. 7
Fig. 7

Same system as for Fig. 6 but the energy dissipating factor has been reduced to 0.5 mg/s. The sphere now executes a spiraling motion about the central axis of the beam as it gradually centers onto the beam’s central axis. The trajectory trace suggests the name eddy trapping for this type of dynamic behavior.

Fig. 8
Fig. 8

Dual-beam laser trap configuration seen from the (a) end and (b) side of the beams. Gravity is present and acts in the -z direction. The center of the sphere is displaced from the coordinate origin to the position (15, 2, 15). It is free to fall under the influence of gravity and encounters the laser beams. The sphere is trapped and guided to the stable trap position of (0, 0, z). The z stable trap coordinate is not zero because an upward-directed radial force is required to counteract the downward-directed gravity. In (c) an enlargement of the spheres central coordinate trajectory clearly shows the displacement into the coordinate origin stable trapping position.

Fig. 9
Fig. 9

z-axis position of the sphere versus time when subjected to a cycled laser beam directed along the z axis. The sphere settles into an oscillatory motion about a z-axis position. During the falling motion of the sphere, gravity acts against the damping force. In the rising portion of the sphere’s motion, the radiation pressure force acts against gravity and damping forces. The linear approximation of the trace segments during the falling and rising motions enables the determination of the radiation pressure force present on the sphere when the sphere is located in this region.

Equations (12)

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

P 0 = k 0 = 2 π λ l 0 x ˆ + m 0 y ˆ + n 0 z ˆ ,
d P r = hn in λ 0 l 0 - l r x ˆ + m 0 - m r y ˆ + n 0 - n r z ˆ
d P t = hn in λ 0 l 0 - n rel l t x ˆ + m 0 - n rel m t y ˆ + n 0 - n rel n t z ˆ ,
d F = N i R ave d P r + 1 - R ave d P t ,
N i = I x ,   y ,   z λ 0 d A hc .
F per particle = all   points   of intercept per   particle d F .
τ per particle = all   points of   incidence per   particle d τ   = all   points   of incidence   per particle r   ×   d F .
x t = x 0 + v 0 x d t , y t = y 0 + v 0 y d t , z t = z 0 + v 0 z d t ,
v x = v 0 x + F x - b x v 0 x m d t , v y = v 0 y + F y - b y v 0 y m d t , v z = v 0 z + F z - b z v 0 z m d t ,
| F g | = | F d | = 4 3   π r 3 ρ s - ρ a g ,
| F l | = | F g | + | F d | .
| F l | = 2 * | F g | = 8 3   π r 3 ρ s - ρ a g .

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