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 OSA

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  2. 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).
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    [CrossRef]
  4. 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]
  5. 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]
  6. 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]
  7. L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79(4), 645–648 (1997).
    [CrossRef]
  8. 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).
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  9. 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).
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  10. 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]
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    [CrossRef]
  13. S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A84(5), 053808 (2011).
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  14. Z. J. Li, Z. S. Wu, and Q. C. Shang, “Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam,” Opt. Express19(17), 16044–16057 (2011).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  25. 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]
  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]
  28. 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. Express15(24), 16029–16034 (2007).
    [CrossRef] [PubMed]
  29. 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]
  30. P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes - an integral-representation,” J. Opt. Soc. Am. A12(2), 325–332 (1995).
    [CrossRef]
  31. 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. Express14(4), 1685–1699 (2006).
    [CrossRef] [PubMed]
  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)

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A84(5), 053808 (2011).
[CrossRef]

Z. J. Li, Z. S. Wu, and Q. C. Shang, “Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam,” Opt. Express19(17), 16044–16057 (2011).
[CrossRef] [PubMed]

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)

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]

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. Express15(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. A24(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. Express14(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. Express14(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)

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]

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)

J. S. Kim and S. W. Kim, “Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation,” Appl. Opt.39(24), 4327–4332 (2000).
[CrossRef] [PubMed]

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. B14(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)

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes - an integral-representation,” J. Opt. Soc. Am. A12(2), 325–332 (1995).
[CrossRef]

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.

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]

B Bareil, P.

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. Express14(25), 12503–12509 (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. Express14(25), 12503–12509 (2006).
[CrossRef] [PubMed]

Bareil, P. B.

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. Express15(24), 16029–16034 (2007).
[CrossRef] [PubMed]

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.

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. Express14(4), 1685–1699 (2006).
[CrossRef] [PubMed]

Booker, G. R.

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes - an integral-representation,” J. Opt. Soc. Am. A12(2), 325–332 (1995).
[CrossRef]

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.

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]

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.

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. Express15(24), 16029–16034 (2007).
[CrossRef] [PubMed]

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.

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. Express15(24), 16029–16034 (2007).
[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. Express14(25), 12503–12509 (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. Express14(25), 12503–12509 (2006).
[CrossRef] [PubMed]

Delacrétaz, G.

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. Express14(4), 1685–1699 (2006).
[CrossRef] [PubMed]

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.

R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B14(12), 3323–3333 (1997).
[CrossRef]

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. A84(5), 053808 (2011).
[CrossRef]

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A24(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.

J. S. Kim and S. W. Kim, “Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation,” Appl. Opt.39(24), 4327–4332 (2000).
[CrossRef] [PubMed]

Kim, S. W.

J. S. Kim and S. W. Kim, “Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation,” Appl. Opt.39(24), 4327–4332 (2000).
[CrossRef] [PubMed]

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.

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes - an integral-representation,” J. Opt. Soc. Am. A12(2), 325–332 (1995).
[CrossRef]

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.

Z. J. Li, Z. S. Wu, and Q. C. Shang, “Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam,” Opt. Express19(17), 16044–16057 (2011).
[CrossRef] [PubMed]

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.

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. Express14(4), 1685–1699 (2006).
[CrossRef] [PubMed]

Milster, T. D.

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]

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.

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]

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.

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. Express14(4), 1685–1699 (2006).
[CrossRef] [PubMed]

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.

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. Express14(4), 1685–1699 (2006).
[CrossRef] [PubMed]

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.

Z. J. Li, Z. S. Wu, and Q. C. Shang, “Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam,” Opt. Express19(17), 16044–16057 (2011).
[CrossRef] [PubMed]

Sheng, Y.

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. Express15(24), 16029–16034 (2007).
[CrossRef] [PubMed]

Sheng, Y. L.

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. Express14(25), 12503–12509 (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. Express14(25), 12503–12509 (2006).
[CrossRef] [PubMed]

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. A84(5), 053808 (2011).
[CrossRef]

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A24(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.

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes - an integral-representation,” J. Opt. Soc. Am. A12(2), 325–332 (1995).
[CrossRef]

Varga, P.

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes - an integral-representation,” J. Opt. Soc. Am. A12(2), 325–332 (1995).
[CrossRef]

Visscher, K.

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]

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.

Z. J. Li, Z. S. Wu, and Q. C. Shang, “Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam,” Opt. Express19(17), 16044–16057 (2011).
[CrossRef] [PubMed]

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.

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]

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)

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]

J. S. Kim and S. W. Kim, “Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation,” Appl. Opt.39(24), 4327–4332 (2000).
[CrossRef] [PubMed]

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]

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]

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]

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 (2)

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A24(2), 430–443 (2007).
[CrossRef] [PubMed]

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

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]

J. Opt. Soc. Am. A (2)

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive-indexes - an integral-representation,” J. Opt. Soc. Am. A12(2), 325–332 (1995).
[CrossRef]

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

R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B14(12), 3323–3333 (1997).
[CrossRef]

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)

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. Express14(25), 12503–12509 (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. Express14(4), 1685–1699 (2006).
[CrossRef] [PubMed]

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. Express15(24), 16029–16034 (2007).
[CrossRef] [PubMed]

Z. J. Li, Z. S. Wu, and Q. C. Shang, “Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam,” Opt. Express19(17), 16044–16057 (2011).
[CrossRef] [PubMed]

Phys. Rev. A (1)

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A84(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.

Fig. 2
Fig. 2

Stress distribution of a sphere and an ellipsoid.

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.

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.

Fig. 5
Fig. 5

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

Tables (1)

Tables Icon

Table 1 Torque of an Ellipsoid While β axis =0

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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