Abstract

For a triaxial ellipsoid in an optical trap with spherical aberration, the optical forces, torque and stress are analyzed using vectorial ray tracing. The torque will automatically regulate ellipsoid’s long axis parallel to optic axis. For a trapped ellipsoid with principal axes in the ratio 1:2:3, the high stress distribution appears in x-z plane. And the optical force at x-axis is weaker than at y-axis due to the shape size. While the ellipsoid departs laterally from trap center, the measurable maximum transverse forces will be weakened due to axial equilibrium and affected by inclined orientation. For an appropriate ring beam, the maximum optical forces are strong in three dimensions, thus, this optical trap is appropriate to trap cells for avoiding damage from laser.

©2012 Optical Society of America

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  1. J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).
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    [Crossref] [PubMed]
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    [Crossref]
  26. P. Liu and B. Lu, “Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region,” Opt. Commun. 272(1), 1–8 (2007).
    [Crossref]
  27. S. H. Xu, Y. M. Li, and L. R. Lou, “Axial optical trapping forces on two particles trapped simultaneously by optical tweezers,” Appl. Opt. 44(13), 2667–2672 (2005).
    [Crossref] [PubMed]
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    [Crossref]
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  32. Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
    [Crossref]

2012 (1)

D. H. Li, J. X. Pu, and X. Q. Wang, “Radiation forces of a dielectric medium plate induced by a Gaussian beam,” Opt. Commun. 285(7), 1680–1683 (2012).
[Crossref]

2011 (2)

2009 (2)

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

E. Aspnes, T. D. Milster, and K. Visscher, “Optical force model based on sequential ray tracing,” Appl. Opt. 48(9), 1642–1650 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (6)

P. Liu and B. Lu, “Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region,” Opt. Commun. 272(1), 1–8 (2007).
[Crossref]

P. B. Bareil, Y. Sheng, Y. Q. Chen, and A. Chiou, “Calculation of spherical red blood cell deformation in a dual-beam optical stretcher,” Opt. Express 15(24), 16029–16034 (2007).
[Crossref] [PubMed]

Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
[Crossref]

F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007).
[Crossref] [PubMed]

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24(2), 430–443 (2007).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

2006 (5)

G. Volpe, G. P. Singh, and D. Petrov, “Dynamics of a growing cell in an optical trap,” Appl. Phys. Lett. 88(23), 231106 (2006).
[Crossref]

J. C. Loudet, A. G. Yodh, and B. Pouligny, “Wetting and contact lines of micrometer-sized ellipsoids,” Phys. Rev. Lett. 97(1), 018304 (2006).
[Crossref] [PubMed]

F. Merenda, G. Boer, J. Rohner, G. Delacrétaz, and R. P. Salathé, “Escape trajectories of single-beam optically trapped micro-particles in a transverse fluid flow,” Opt. Express 14(4), 1685–1699 (2006).
[Crossref] [PubMed]

P. B Bareil, Y. L. Sheng, A. Chiou, P. B Bareil, Y. L. Sheng, and A. Chiou, “Local scattering stress distribution on surface of a spherical cell in optical stretcher,” Opt. Express 14(25), 12503–12509 (2006).
[Crossref] [PubMed]

X. Sheng-Hua, L. Yin-Mei, and L. Li-Ren, “Systematical study of the trapping forces of optical tweezers formed by different types of optical ring beams,” Chin. Phys. 15(6), 1391–1397 (2006).
[Crossref]

2005 (1)

2004 (1)

D. P. Cherney, T. E. Bridges, and J. M. Harris, “Optical trapping of unilamellar phospholipid vesicles: investigation of the effect of optical forces on the lipid membrane shape by confocal-Raman microscopy,” Anal. Chem. 76(17), 4920–4928 (2004).
[Crossref] [PubMed]

2003 (1)

S. Bayoudh, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Orientation of biological cells using plane-polarized Gaussian beam optical tweezers,” J. Mod. Opt. 50, 1581–1590 (2003).

2001 (1)

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modeling of optical trapping,” Comput. Phys. Commun. 142(1-3), 468–471 (2001).
[Crossref]

2000 (1)

1998 (1)

K. Shima, R. Omori, and A. Suzuki, “Forces of a single-beam gradient-force optical trap on dielectric spheroidal particles in the geometric-optics regime,” Jpn. J. Appl. Phys. 37(Part 1, No. 11), 6012–6015 (1998).
[Crossref]

1997 (3)

R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B 14(12), 3323–3333 (1997).
[Crossref]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[Crossref]

M. Gu, P. C. Ke, and X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68(10), 3666–3668 (1997).
[Crossref]

1996 (2)

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35(15), 2702–2710 (1996).
[Crossref] [PubMed]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

1995 (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(2), 569–582 (1992).
[Crossref] [PubMed]

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance,” J. Appl. Phys. 65(8), 2900–2906 (1989).
[Crossref]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance,” J. Appl. Phys. 65(8), 2900–2906 (1989).
[Crossref]

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (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(2), 569–582 (1992).
[Crossref] [PubMed]

Aspnes, E.

B Bareil, P.

Bareil, P. B.

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance,” J. Appl. Phys. 65(8), 2900–2906 (1989).
[Crossref]

Bayoudh, S.

S. Bayoudh, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Orientation of biological cells using plane-polarized Gaussian beam optical tweezers,” J. Mod. Opt. 50, 1581–1590 (2003).

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[Crossref]

Bishop, A. I.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modeling of optical trapping,” Comput. Phys. Commun. 142(1-3), 468–471 (2001).
[Crossref]

Boer, G.

Booker, G. R.

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

Bridges, T. E.

D. P. Cherney, T. E. Bridges, and J. M. Harris, “Optical trapping of unilamellar phospholipid vesicles: investigation of the effect of optical forces on the lipid membrane shape by confocal-Raman microscopy,” Anal. Chem. 76(17), 4920–4928 (2004).
[Crossref] [PubMed]

Cai, J.

Cai, X. S.

F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007).
[Crossref] [PubMed]

Chen, Y. Q.

Cheng, Z. D.

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

Cherney, D. P.

D. P. Cherney, T. E. Bridges, and J. M. Harris, “Optical trapping of unilamellar phospholipid vesicles: investigation of the effect of optical forces on the lipid membrane shape by confocal-Raman microscopy,” Anal. Chem. 76(17), 4920–4928 (2004).
[Crossref] [PubMed]

Chiou, A.

Delacrétaz, G.

Gan, X. S.

M. Gu, P. C. Ke, and X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68(10), 3666–3668 (1997).
[Crossref]

Gauthier, R. C.

Gong, Z.

Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
[Crossref]

Gouesbet, G.

F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007).
[Crossref] [PubMed]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35(15), 2702–2710 (1996).
[Crossref] [PubMed]

Gréhan, G.

F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007).
[Crossref] [PubMed]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35(15), 2702–2710 (1996).
[Crossref] [PubMed]

Gu, M.

M. Gu, P. C. Ke, and X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68(10), 3666–3668 (1997).
[Crossref]

Hanna, S.

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A 84(5), 053808 (2011).
[Crossref]

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24(2), 430–443 (2007).
[Crossref] [PubMed]

Harada, Y.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

Harris, J. M.

D. P. Cherney, T. E. Bridges, and J. M. Harris, “Optical trapping of unilamellar phospholipid vesicles: investigation of the effect of optical forces on the lipid membrane shape by confocal-Raman microscopy,” Anal. Chem. 76(17), 4920–4928 (2004).
[Crossref] [PubMed]

He, L. Q.

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

S. Bayoudh, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Orientation of biological cells using plane-polarized Gaussian beam optical tweezers,” J. Mod. Opt. 50, 1581–1590 (2003).

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modeling of optical trapping,” Comput. Phys. Commun. 142(1-3), 468–471 (2001).
[Crossref]

Ke, P. C.

M. Gu, P. C. Ke, and X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68(10), 3666–3668 (1997).
[Crossref]

Kim, J. S.

Kim, S. W.

Knoner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

Laczik, Z.

Li, D. H.

D. H. Li, J. X. Pu, and X. Q. Wang, “Radiation forces of a dielectric medium plate induced by a Gaussian beam,” Opt. Commun. 285(7), 1680–1683 (2012).
[Crossref]

Li, Y. M.

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

J. H. Zhou, H. L. Ren, J. Cai, and Y. M. Li, “Ray-tracing methodology: application of spatial analytic geometry in the ray-optic model of optical tweezers,” Appl. Opt. 47(33), 6307–6314 (2008).
[Crossref] [PubMed]

Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
[Crossref]

S. H. Xu, Y. M. Li, and L. R. Lou, “Axial optical trapping forces on two particles trapped simultaneously by optical tweezers,” Appl. Opt. 44(13), 2667–2672 (2005).
[Crossref] [PubMed]

Li, Z. J.

Li-Ren, L.

X. Sheng-Hua, L. Yin-Mei, and L. Li-Ren, “Systematical study of the trapping forces of optical tweezers formed by different types of optical ring beams,” Chin. Phys. 15(6), 1391–1397 (2006).
[Crossref]

Liu, P.

P. Liu and B. Lu, “Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region,” Opt. Commun. 272(1), 1–8 (2007).
[Crossref]

Liu, Z.

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

Lou, L. R.

Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
[Crossref]

S. H. Xu, Y. M. Li, and L. R. Lou, “Axial optical trapping forces on two particles trapped simultaneously by optical tweezers,” Appl. Opt. 44(13), 2667–2672 (2005).
[Crossref] [PubMed]

Loudet, J. C.

J. C. Loudet, A. G. Yodh, and B. Pouligny, “Wetting and contact lines of micrometer-sized ellipsoids,” Phys. Rev. Lett. 97(1), 018304 (2006).
[Crossref] [PubMed]

Lu, B.

P. Liu and B. Lu, “Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region,” Opt. Commun. 272(1), 1–8 (2007).
[Crossref]

Lu, D.

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

Merenda, F.

Milster, T. D.

Nieminen, T. A.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

S. Bayoudh, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Orientation of biological cells using plane-polarized Gaussian beam optical tweezers,” J. Mod. Opt. 50, 1581–1590 (2003).

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modeling of optical trapping,” Comput. Phys. Commun. 142(1-3), 468–471 (2001).
[Crossref]

Novotny, L.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[Crossref]

Omori, R.

K. Shima, R. Omori, and A. Suzuki, “Forces of a single-beam gradient-force optical trap on dielectric spheroidal particles in the geometric-optics regime,” Jpn. J. Appl. Phys. 37(Part 1, No. 11), 6012–6015 (1998).
[Crossref]

Petrov, D.

G. Volpe, G. P. Singh, and D. Petrov, “Dynamics of a growing cell in an optical trap,” Appl. Phys. Lett. 88(23), 231106 (2006).
[Crossref]

Pouligny, B.

J. C. Loudet, A. G. Yodh, and B. Pouligny, “Wetting and contact lines of micrometer-sized ellipsoids,” Phys. Rev. Lett. 97(1), 018304 (2006).
[Crossref] [PubMed]

Pu, J. X.

D. H. Li, J. X. Pu, and X. Q. Wang, “Radiation forces of a dielectric medium plate induced by a Gaussian beam,” Opt. Commun. 285(7), 1680–1683 (2012).
[Crossref]

Ren, H. L.

Ren, K. F.

F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007).
[Crossref] [PubMed]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35(15), 2702–2710 (1996).
[Crossref] [PubMed]

Rohner, J.

Rubinsztein-Dunlop, H.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

S. Bayoudh, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Orientation of biological cells using plane-polarized Gaussian beam optical tweezers,” J. Mod. Opt. 50, 1581–1590 (2003).

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modeling of optical trapping,” Comput. Phys. Commun. 142(1-3), 468–471 (2001).
[Crossref]

Salathé, R. P.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance,” J. Appl. Phys. 65(8), 2900–2906 (1989).
[Crossref]

Shang, Q. C.

Sheng, Y.

Sheng, Y. L.

Sheng-Hua, X.

X. Sheng-Hua, L. Yin-Mei, and L. Li-Ren, “Systematical study of the trapping forces of optical tweezers formed by different types of optical ring beams,” Chin. Phys. 15(6), 1391–1397 (2006).
[Crossref]

Shima, K.

K. Shima, R. Omori, and A. Suzuki, “Forces of a single-beam gradient-force optical trap on dielectric spheroidal particles in the geometric-optics regime,” Jpn. J. Appl. Phys. 37(Part 1, No. 11), 6012–6015 (1998).
[Crossref]

Simpson, S. H.

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A 84(5), 053808 (2011).
[Crossref]

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24(2), 430–443 (2007).
[Crossref] [PubMed]

Singh, G. P.

G. Volpe, G. P. Singh, and D. Petrov, “Dynamics of a growing cell in an optical trap,” Appl. Phys. Lett. 88(23), 231106 (2006).
[Crossref]

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. Soc. Am. A  9(8), S196–S203 (2007).
[Crossref]

Suzuki, A.

K. Shima, R. Omori, and A. Suzuki, “Forces of a single-beam gradient-force optical trap on dielectric spheroidal particles in the geometric-optics regime,” Jpn. J. Appl. Phys. 37(Part 1, No. 11), 6012–6015 (1998).
[Crossref]

Török, P.

Varga, P.

Visscher, K.

Volpe, G.

G. Volpe, G. P. Singh, and D. Petrov, “Dynamics of a growing cell in an optical trap,” Appl. Phys. Lett. 88(23), 231106 (2006).
[Crossref]

Wang, X. Q.

D. H. Li, J. X. Pu, and X. Q. Wang, “Radiation forces of a dielectric medium plate induced by a Gaussian beam,” Opt. Commun. 285(7), 1680–1683 (2012).
[Crossref]

Wang, Z.

Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
[Crossref]

Wu, J. G.

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

Wu, Z. S.

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[Crossref]

Xu, F.

F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007).
[Crossref] [PubMed]

Xu, S. H.

Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
[Crossref]

S. H. Xu, Y. M. Li, and L. R. Lou, “Axial optical trapping forces on two particles trapped simultaneously by optical tweezers,” Appl. Opt. 44(13), 2667–2672 (2005).
[Crossref] [PubMed]

Yin-Mei, L.

X. Sheng-Hua, L. Yin-Mei, and L. Li-Ren, “Systematical study of the trapping forces of optical tweezers formed by different types of optical ring beams,” Chin. Phys. 15(6), 1391–1397 (2006).
[Crossref]

Yodh, A. G.

J. C. Loudet, A. G. Yodh, and B. Pouligny, “Wetting and contact lines of micrometer-sized ellipsoids,” Phys. Rev. Lett. 97(1), 018304 (2006).
[Crossref] [PubMed]

Zhou, J. H.

Anal. Chem. (1)

D. P. Cherney, T. E. Bridges, and J. M. Harris, “Optical trapping of unilamellar phospholipid vesicles: investigation of the effect of optical forces on the lipid membrane shape by confocal-Raman microscopy,” Anal. Chem. 76(17), 4920–4928 (2004).
[Crossref] [PubMed]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

G. Volpe, G. P. Singh, and D. Petrov, “Dynamics of a growing cell in an optical trap,” Appl. Phys. Lett. 88(23), 231106 (2006).
[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(2), 569–582 (1992).
[Crossref] [PubMed]

Chin. Phys. (1)

X. Sheng-Hua, L. Yin-Mei, and L. Li-Ren, “Systematical study of the trapping forces of optical tweezers formed by different types of optical ring beams,” Chin. Phys. 15(6), 1391–1397 (2006).
[Crossref]

Comput. Phys. Commun. (1)

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modeling of optical trapping,” Comput. Phys. Commun. 142(1-3), 468–471 (2001).
[Crossref]

Cryo Lett. (1)

J. G. Wu, Y. M. Li, D. Lu, Z. Liu, Z. D. Cheng, and L. Q. He, “Mesurement of the membrane elasticity of red blood cell with osmotic pressure by optical tweezers,” Cryo Lett. 30, 89–95 (2009).

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance,” J. Appl. Phys. 65(8), 2900–2906 (1989).
[Crossref]

J. Mod. Opt. (1)

S. Bayoudh, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Orientation of biological cells using plane-polarized Gaussian beam optical tweezers,” J. Mod. Opt. 50, 1581–1590 (2003).

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

K. Shima, R. Omori, and A. Suzuki, “Forces of a single-beam gradient-force optical trap on dielectric spheroidal particles in the geometric-optics regime,” Jpn. J. Appl. Phys. 37(Part 1, No. 11), 6012–6015 (1998).
[Crossref]

Opt. Commun. (4)

D. H. Li, J. X. Pu, and X. Q. Wang, “Radiation forces of a dielectric medium plate induced by a Gaussian beam,” Opt. Commun. 285(7), 1680–1683 (2012).
[Crossref]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

P. Liu and B. Lu, “Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region,” Opt. Commun. 272(1), 1–8 (2007).
[Crossref]

Z. Gong, Z. Wang, Y. M. Li, L. R. Lou, and S. H. Xu, “Axial deviation of an optically trapped particle in trapping force calibration using the drag force method,” Opt. Commun. 273(1), 37–42 (2007).
[Crossref]

Opt. Express (4)

Phys. Rev. A (1)

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A 84(5), 053808 (2011).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[Crossref]

J. C. Loudet, A. G. Yodh, and B. Pouligny, “Wetting and contact lines of micrometer-sized ellipsoids,” Phys. Rev. Lett. 97(1), 018304 (2006).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

M. Gu, P. C. Ke, and X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68(10), 3666–3668 (1997).
[Crossref]

Other (1)

M. Born and E. Wolf, “Reflectivity and transmissivity,” in Principles of Optics (Cambridge University Press, 1999).

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Figures (5)

Fig. 1
Fig. 1

Tracing a single ray striking an ellipsoid. P(x0, y0, z0) is the center of the ellipsoid. Mi is the i-th incident point of the ray striking ellipsoid. Length a, b and c indicate the semi-principal axes. (a) Scheme of the ray (n1) deflected by an objective with spherical aberration; (b) Spatial orientation of incident ray ni, reflective ray ni + 1 and outward normal n for the i-th incident point Mi; (c) The vectors in (b) after rotating coordinate system with n as z’-axis; (d) An ellipsoid with the arbitrary orientation (βell, γell); (e) Spatial orientation of a surface element of dA, (F)i is the total force on this surface element.

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Fig. 2
Fig. 2

Stress distribution of a sphere and an ellipsoid.

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Fig. 3
Fig. 3

Optical forces of an ellipsoid with polarized beams. Normalized transverse displacement ρ= D i /( ε i r bead ) , the index i is x or y. (a) Transverse forces in transverse directions; (b) Axial pushing force in transverse directions; (c) Axial force at z-axis.

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Fig. 4
Fig. 4

Ring beam profiles ( n=1 ) and optical forces on an ellipsoid in an optical trap formed by ring beams. (a) Beam profiles of intensity on the objective entrancing aperture; (b) Axial force at z-axis; Transverse (c) and axial (d) forces at x-axis; Transverse (e) and axial (f) forces at y-axis.

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Fig. 5
Fig. 5

Optical forces of an inclined ellipsoid. (a) Type-A; (b) Type-B; (c) At z-axis.

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Tables (1)

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Table 1 Torque of an Ellipsoid While β axis =0

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Equations (7)

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

F= P c [ n p Tcosγ− n m cosθ(1+R)]n,
E x (r)=A ( r 2 ω 0 2 ) n exp(− r 2 ω 0 2 ), n=0,1,2,⋅⋅⋅,
ΔP= P 2 2n+1 2n!π ω 0 2 ( r 2 ω 0 2 ) 2n exp(− 2 r 2 ω 0 2 )Δs.
n 1 ( n 1x , n 1y , n 1z )=(−sin α 2 cos β 0 , −sin α 2 sin β 0 ,cos α 2 ),
Δz= z cg +| z cg |tan α 1 /tan α 2 .
x 2 a 2 + y 2 b 2 + z 2 c 2 =1,
x− x i n ix = y− y i n iy = z− z i n iz =t.

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