Abstract

The T matrix method is used to compute equilibrium positions and orientations for spheroidal particles trapped in Gaussian light beams. It is observed that there is a qualitative difference between the behavior of prolate and oblate ellipsoids in linearly polarized Gaussian beams; the former generally orient with the symmetry axis parallel to the beam except at very small particle sizes, while the latter orient with the symmetry axis perpendicular to the beam. In the presence of a circularly polarized beam, it is demonstrated that oblate ellipsoids will experience a torque about the beam axis. However, for a limited range of particle sizes, where the particle dimensions are comparable with the beam waist, the particles are predicted to rotate in a sense counter to the sense of rotation of the circular polarization. This unusual prediction is discussed in some detail.

© 2007 Optical Society of America

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  2. J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
    [CrossRef]
  3. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
    [CrossRef] [PubMed]
  4. S. H. Simpson and S. Hanna, "Numerical calculation of interparticle forces arising in association with holographic assembly," J. Opt. Soc. Am. A 23, 1419-1431 (2006).
    [CrossRef]
  5. 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).
    [CrossRef]
  6. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  7. K. Ren, G. Grehan, and G. Gouesbet, "Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects," Opt. Commun. 108, 343-354 (1994).
    [CrossRef]
  8. J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
    [CrossRef]
  9. C. J. F. Böttcher, Theory of Electric Polarization, Vol. 1 of Dielectrics in Static Fields, 2nd ed. (Elsevier, 1973).
  10. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).
  11. A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68, 033802 (2003).
    [CrossRef]
  12. K. D. Bonin, B. Kourmanov, and T. G. Walker, "Light torque nanocontrol, nanomotors and nanorockers," Opt. Express 10, 984-989 (2002).
    [PubMed]
  13. P. Galajda and P. Ormos, "Orientation of flat particles in optical tweezers by linearly polarized light," Opt. Express 11, 446-451 (2003).
    [CrossRef] [PubMed]
  14. A. La Porta and M. D. Wang, "Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles," Phys. Rev. Lett. 92, 190801 (2004).
    [CrossRef] [PubMed]
  15. 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, 4327-4332 (2000).
    [CrossRef]
  16. R. C. Gauthier, "Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects," J. Opt. Soc. Am. B 14, 3323-3333 (1997).
    [CrossRef]
  17. R. C. Gauthier, "Optical levitation and trapping of a micro-optic inclined end-surface cylindrical spinner," Appl. Opt. 40, 1961-1973 (2001).
    [CrossRef]
  18. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).
  19. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).
  20. O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005).
    [CrossRef]
  21. G. Gouesbet, J. A. Lock, and G. Grehan, "Partial wave representations of laser beams for use in light scattering calculations," Appl. Opt. 34, 2133-2143 (1995).
    [CrossRef] [PubMed]
  22. G. Gouesbet, "Partial-wave expansions and properties of axisymmetric light beams," Appl. Opt. 35, 1543-1555 (1996).
    [CrossRef] [PubMed]
  23. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
    [CrossRef]
  24. F. Melia, Electrodynamics (The University of Chicago Press, 2001).
  25. P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
    [CrossRef]
  26. S. Chang and S. S. Lee, "Optical torque exerted on a homogeneous sphere levitated in the circularly polarizedfundamental-mode of a laser beam," J. Opt. Soc. Am. B 2, 1853-1860 (1985).
    [CrossRef]
  27. G. Gouesbet, B. Maheu, and G. Grehan, "Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation," J. Opt. Soc. Am. A 5, 1427-1443 (1988).
    [CrossRef]
  28. P. Barber, "Resonance electromagnetic absorption by nonspherical dielectric objects," IEEE Trans. Microwave Theory Tech. 25, 373-381 (1977).
    [CrossRef]
  29. A. Mugnai and W. Wiscombe, "Scattering of radiation by moderately nonspherical particles," J. Atmos. Sci. 37, 1291-1307 (1980).
    [CrossRef]
  30. V. Varadan, A. Lakhtakia, and V. Varadan, "Scattering by 3-dimensional anisotropic scatterers," IEEE Trans. Antennas Propag. 37, 800-802 (1989).
    [CrossRef]
  31. T. G. M. van der Ven, Colloidal Hydrodynamics (Academic, 1989).
  32. A. M. Stewart, "Angular momentum of the electromagnetic field: the plane wave paradox resolved," Eur. J. Phys. 26, 635-641 (2005).
    [CrossRef]
  33. R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
    [CrossRef]
  34. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
    [CrossRef] [PubMed]
  35. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
    [CrossRef]
  36. D. Benito, S. H. Simpson, and S. Hanna are preparing a paper to be called "FDTD calculations of forces and torques on ellipsoidal particles."
  37. S. M. Barnett, "Optical angular-momentum flux," J. Opt. B: Quantum Semiclassical Opt. 4, S7-S16 (2002).
    [CrossRef]

2006 (1)

2005 (2)

O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005).
[CrossRef]

A. M. Stewart, "Angular momentum of the electromagnetic field: the plane wave paradox resolved," Eur. J. Phys. 26, 635-641 (2005).
[CrossRef]

2004 (1)

A. La Porta and M. D. Wang, "Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles," Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

2003 (4)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

P. Galajda and P. Ormos, "Orientation of flat particles in optical tweezers by linearly polarized light," Opt. Express 11, 446-451 (2003).
[CrossRef] [PubMed]

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).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68, 033802 (2003).
[CrossRef]

2002 (3)

K. D. Bonin, B. Kourmanov, and T. G. Walker, "Light torque nanocontrol, nanomotors and nanorockers," Opt. Express 10, 984-989 (2002).
[PubMed]

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

S. M. Barnett, "Optical angular-momentum flux," J. Opt. B: Quantum Semiclassical Opt. 4, S7-S16 (2002).
[CrossRef]

2001 (1)

2000 (1)

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

1997 (1)

1996 (2)

G. Gouesbet, "Partial-wave expansions and properties of axisymmetric light beams," Appl. Opt. 35, 1543-1555 (1996).
[CrossRef] [PubMed]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

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

1989 (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

V. Varadan, A. Lakhtakia, and V. Varadan, "Scattering by 3-dimensional anisotropic scatterers," IEEE Trans. Antennas Propag. 37, 800-802 (1989).
[CrossRef]

1988 (1)

1986 (1)

1985 (1)

1984 (1)

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

1980 (1)

A. Mugnai and W. Wiscombe, "Scattering of radiation by moderately nonspherical particles," J. Atmos. Sci. 37, 1291-1307 (1980).
[CrossRef]

1977 (1)

P. Barber, "Resonance electromagnetic absorption by nonspherical dielectric objects," IEEE Trans. Microwave Theory Tech. 25, 373-381 (1977).
[CrossRef]

1970 (1)

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

1936 (1)

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Anderson, E.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Ashkin, A.

Bai, Z.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Barber, P.

P. Barber, "Resonance electromagnetic absorption by nonspherical dielectric objects," IEEE Trans. Microwave Theory Tech. 25, 373-381 (1977).
[CrossRef]

Barnett, S. M.

S. M. Barnett, "Optical angular-momentum flux," J. Opt. B: Quantum Semiclassical Opt. 4, S7-S16 (2002).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (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).
[CrossRef]

Benito, D.

D. Benito, S. H. Simpson, and S. Hanna are preparing a paper to be called "FDTD calculations of forces and torques on ellipsoidal particles."

Beth, R. A.

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Bischof, C.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Bishop, A. I.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68, 033802 (2003).
[CrossRef]

Bjorkholm, J. E.

Blackford, S.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Bonin, K. D.

Böttcher, C. J. F.

C. J. F. Böttcher, Theory of Electric Polarization, Vol. 1 of Dielectrics in Static Fields, 2nd ed. (Elsevier, 1973).

Chang, S.

Chu, S.

Crichton, J. H.

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

Demmel, J.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Dongarra, J.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Du Croz, J.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Dziedzic, J. M.

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Galajda, P.

Gauthier, R. C.

Gouesbet, G.

Greenbaum, A.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Grehan, G.

Grier, D. G.

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Hammarling, S.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Hanna, S.

S. H. Simpson and S. Hanna, "Numerical calculation of interparticle forces arising in association with holographic assembly," J. Opt. Soc. Am. A 23, 1419-1431 (2006).
[CrossRef]

D. Benito, S. H. Simpson, and S. Hanna are preparing a paper to be called "FDTD calculations of forces and torques on ellipsoidal particles."

Heckenberg, N. R.

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).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68, 033802 (2003).
[CrossRef]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

Kim, J.-S.

Kim, S.-W.

Kong, J. A.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Kourmanov, B.

La Porta, A.

A. La Porta and M. D. Wang, "Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles," Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Lakhtakia, A.

V. Varadan, A. Lakhtakia, and V. Varadan, "Scattering by 3-dimensional anisotropic scatterers," IEEE Trans. Antennas Propag. 37, 800-802 (1989).
[CrossRef]

Lee, S. S.

Lock, J. A.

Maheu, B.

Marston, P. L.

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

McKenney, A.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Melia, F.

F. Melia, Electrodynamics (The University of Chicago Press, 2001).

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Moine, O.

Molloy, J. E.

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Mugnai, A.

A. Mugnai and W. Wiscombe, "Scattering of radiation by moderately nonspherical particles," J. Atmos. Sci. 37, 1291-1307 (1980).
[CrossRef]

Nieminen, T. A.

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).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68, 033802 (2003).
[CrossRef]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

Ormos, P.

Padgett, M. J.

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Ren, K.

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

Rubinsztein-Dunlop, H.

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).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68, 033802 (2003).
[CrossRef]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Simpson, S. H.

S. H. Simpson and S. Hanna, "Numerical calculation of interparticle forces arising in association with holographic assembly," J. Opt. Soc. Am. A 23, 1419-1431 (2006).
[CrossRef]

D. Benito, S. H. Simpson, and S. Hanna are preparing a paper to be called "FDTD calculations of forces and torques on ellipsoidal particles."

Sorensen, D.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

Stewart, A. M.

A. M. Stewart, "Angular momentum of the electromagnetic field: the plane wave paradox resolved," Eur. J. Phys. 26, 635-641 (2005).
[CrossRef]

Stout, B.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Tsang, L.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

van der Ven, T. G. M.

T. G. M. van der Ven, Colloidal Hydrodynamics (Academic, 1989).

Varadan, V.

V. Varadan, A. Lakhtakia, and V. Varadan, "Scattering by 3-dimensional anisotropic scatterers," IEEE Trans. Antennas Propag. 37, 800-802 (1989).
[CrossRef]

V. Varadan, A. Lakhtakia, and V. Varadan, "Scattering by 3-dimensional anisotropic scatterers," IEEE Trans. Antennas Propag. 37, 800-802 (1989).
[CrossRef]

Walker, T. G.

Wang, M. D.

A. La Porta and M. D. Wang, "Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles," Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

Wiscombe, W.

A. Mugnai and W. Wiscombe, "Scattering of radiation by moderately nonspherical particles," J. Atmos. Sci. 37, 1291-1307 (1980).
[CrossRef]

Appl. Opt. (4)

Contemp. Phys. (1)

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Eur. J. Phys. (1)

A. M. Stewart, "Angular momentum of the electromagnetic field: the plane wave paradox resolved," Eur. J. Phys. 26, 635-641 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

V. Varadan, A. Lakhtakia, and V. Varadan, "Scattering by 3-dimensional anisotropic scatterers," IEEE Trans. Antennas Propag. 37, 800-802 (1989).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. Barber, "Resonance electromagnetic absorption by nonspherical dielectric objects," IEEE Trans. Microwave Theory Tech. 25, 373-381 (1977).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

J. Atmos. Sci. (1)

A. Mugnai and W. Wiscombe, "Scattering of radiation by moderately nonspherical particles," J. Atmos. Sci. 37, 1291-1307 (1980).
[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).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

S. M. Barnett, "Optical angular-momentum flux," J. Opt. B: Quantum Semiclassical Opt. 4, S7-S16 (2002).
[CrossRef]

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

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

Nature (2)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Phys. Rev. A (3)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68, 033802 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

A. La Porta and M. D. Wang, "Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles," Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

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

Other (8)

C. J. F. Böttcher, Theory of Electric Polarization, Vol. 1 of Dielectrics in Static Fields, 2nd ed. (Elsevier, 1973).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users" Guide, 3rd ed. (Society for Industrial and Applied Mathematics,1999).
[CrossRef]

F. Melia, Electrodynamics (The University of Chicago Press, 2001).

D. Benito, S. H. Simpson, and S. Hanna are preparing a paper to be called "FDTD calculations of forces and torques on ellipsoidal particles."

T. G. M. van der Ven, Colloidal Hydrodynamics (Academic, 1989).

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Figures (15)

Fig. 1
Fig. 1

Convergence characteristics for force calculations of single silica particles in Gaussian beams: spherical particles with ρ = 1 μ m (open circles) and 2 μ m (triangles); prolate spheroids with δ = 2 and ρ e = 1 μ m and the long axis parallel to the x axis (diamonds) or the z axis (squares); prolate spheroids with δ = 2 and ρ e = 2 μ m and the long axis parallel to the z axis (solid circles). In each case, the particles are displaced below the focus by 0.6 μ m with the beam incident from above.

Fig. 2
Fig. 2

Gaussian beam geometry. Light is incident from above traveling in the negative z direction and polarized parallel to the x axis. A prolate spheroid with a major axis parallel to z is shown.

Fig. 3
Fig. 3

Perpendicular component of the rotational friction tensor f perp r as a function of equivalent radius for spheroids with a range of aspect ratios.

Fig. 4
Fig. 4

Maps showing the equilibrium trapping position, in dimensionless units k z , for prolate spheroidal silica particles with aspect ratios δ 2 and equivalent radii ρ e 1 μ m with the symmetry axis of the particle aligned parallel to (a) x, (b) y, and (c) z axes.

Fig. 5
Fig. 5

Line plots extracted from Fig. 4 showing the equilibrium trapping position as a function of equivalent radius ρ e for spheres ( δ = 1 ) and prolate spheroids with δ = 2 oriented with symmetry axis parallel to each of the coordinate axes.

Fig. 6
Fig. 6

Translational stiffness, K z β t , for spheres and prolate spheroids of silica with δ = 2 oriented parallel to each of the coordinate axes.

Fig. 7
Fig. 7

Rotational stiffness parameters, K α β r , for prolate silica spheroids with δ = 2 aligned with the symmetry axis parallel to (a) x, (b) y, and (c) z axes. For each alignment, parameters are shown for rotations about each of the other two axes.

Fig. 8
Fig. 8

Rotational velocity gradients, G α β , for prolate silica spheroids with δ = 2 aligned with the symmetry axis parallel to (a) x, (b) y, and (c) z axes. As with Fig. 7, parameters are shown for each alignment for rotations about each of the remaining axes.

Fig. 9
Fig. 9

Critical value of particle size, as given by the equivalent radius, ρ e crit , at which the transition occurs between stable orientation of the prolate spheroid parallel to the polarization vector (small particles) and stable orientation parallel to the beam (large particles).

Fig. 10
Fig. 10

(a) Trapping position, expressed as the dimensionless parameter k z , of oblate silica spheroids oriented with the symmetry axis parallel to the y axis and secondary (major) axes parallel to the polarization vector (x axis) and beam axis as a function of the aspect ratio and equivalent radius. (b) Line plots extracted from (a) for spheres and oblate spheroids with δ = 0.5 .

Fig. 11
Fig. 11

(a) Translational stiffness parameter parallel to the beam axis, K z y t , for spheres and oblate spheroids of silica with δ = 0.5 oriented with the symmetry axis parallel to the y axis and secondary axes parallel to the polarization vector (x axis) and the beam axis as a function of equivalent radius. (b) Rotational stiffness parameters, K α y r , for the same oblate spheroid as in (a) for rotations about the x and z axes. (c) Similar plots of the angular velocity gradients G α y .

Fig. 12
Fig. 12

(a) Torque, T z , induced by a 1 mW beam on an oblate silica spheroid with ρ e = 0.5 μ m , and δ = 0.5 . The particle lies with its symmetry axis in the xy plane and an angle ϕ between the long axis of the spheroid and the polarization vector. The solid curve shows the calculated values; the diamonds indicate a sine curve, suitably scaled, for comparison. The height of the particle in the beam corresponds to the equilibrium position when the particle is held with the symmetry axis parallel to the polarization vector, i.e., ϕ = π 2 . (b) z component of force on the particle as ϕ varies.

Fig. 13
Fig. 13

Rotation of an oblate silica spheroid, ρ e = 0.5 μ m , δ = 0.5 , induced by a rotating polarization vector with frequency Ω. The spheroid is oriented with its symmetry axis in the xy plane.

Fig. 14
Fig. 14

Trapping position expressed as the dimensionless parameter k z of an oblate silica spheroid oriented with its symmetry axis in the xy plane. The plot compares the effect of a circularly polarized beam with the linear polarization aligned parallel (x axis) and perpendicular (y axis) to the symmetry axis of the particle.

Fig. 15
Fig. 15

Frequency of rotation of oblate silica particles trapped in a 1 mW circularly polarized Gaussian beam. The particles are oriented with their symmetry axes in the xy plane. (a) Map showing the frequency as a function of aspect ratio δ and equivalent radius ρ e . (b) Single plot taken from (a) δ = 0.5 .

Equations (37)

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δ = a b ,
E inc ( r ) = n = 1 m = n n [ a m n Rg M m n ( k r ) + b m n Rg N m n ( k r ) ] ,
E sca ( r ) = n = 1 m = n n [ p m n M m n ( k r ) + q m n N m n ( k r ) ] .
p ̃ = T a ̃ ,
F = S T ͇ M ( r ) d S ,
T ͇ M ( r ) = 1 2 R { ε E ( r ) E * ( r ) + μ H ( r ) H * ( r ) 1 2 [ ε E ( r ) 2 + μ H ( r ) 2 ] I ͇ } .
Γ = S r d S [ T ͇ M ( r ) × r ̂ ] .
a m n = i a m n n m k 2 A 2 [ n ( n + 1 ) ] 1 2 , p m n = i p m n n m k 2 A 2 [ n ( n + 1 ) ] 1 2 ,
b m n = b m n k 2 A 2 [ n ( n + 1 ) ] 1 2 , q m n = q m n k 2 A 2 [ n ( n + 1 ) ] 1 2 ,
Γ x = E 0 2 ϵ m 8 π k 3 n = 1 m = n n R { ( n m ) ( n + m + 1 ) [ q m n q m + 1 , n * + p m n p m + 1 , n * + 1 2 ( q m n b m + 1 , n * + q m + 1 , n b m n * + p m n a m + 1 , n * + p m + 1 , n a m n * ) ] } ,
Γ y = E 0 2 ϵ m 8 π k 3 n = 1 m = n n I { ( n m ) ( n + m + 1 ) [ q m n q m + 1 , n * + p m n p m + 1 , n * + 1 2 ( q m n b m + 1 , n * q m + 1 , n b m n * + p m n a m + 1 , n * p m + 1 , n a m n * ) ] } ,
Γ z = E 0 2 ϵ m 8 π k 3 n = 1 m = n n m [ q m n 2 + p m n 2 + R ( p m n a m n * + q m n b m n * ) ] .
F i F i 1 F i 1 0.001 ,
K z β t = Q F , z z ,
Q F , z = F z c n m P .
K α β r = Q T , α θ α ,
Q T , α = T α c n m P λ ,
F = f ͇ t v ,
T = f ͇ r ω ,
f perp r = 16 π η 3 [ a 2 + b 2 α a a 2 + α b b 2 ] ,
α a = 0 d λ ( a 2 + λ ) 3 2 ( b 2 + λ ) ,
α b = 0 d λ ( a 2 + λ ) ( b 2 + λ ) 3 2 .
G α β = ω α θ α .
f perp r θ ̇ = T z sin [ 2 ( Ω t θ ) ] ,
θ = Ω t ϕ ,
sin ϕ = f perp r Ω T z ,
Ω crit = T z f perp r
j = D × B ,
l = r × D × B ,
j i t + T M , i j x j = 0 ,
l i t M i j x j = 0 .
a 1 n = a 1 n = b 1 n = b 1 n = ( i ) n + 1 [ 4 π ( 2 n + 1 ) ] 1 2 g 5 , n ,
g 5 , n = g 3 , n + exp [ s 2 ( n 1 ) ( n + 2 ) ] ( n 1 ) 2 ( n + 2 ) 2 s 8
× [ 10 5 ( n 1 ) ( n + 2 ) s 2 + 0.5 ( n 1 ) 2 ( n + 2 ) 2 s 4 ] ,
g 3 , n = g 1 , n + exp [ s 2 ( n 1 ) ( n + 2 ) ] ( n 1 ) ( n + 2 ) s 4
× [ 3 ( n 1 ) ( n + 2 ) s 2 ] ,
g 1 , n = exp [ s 2 ( n 1 ) ( n + 2 ) ] .

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