Geometrical optics calculation of forces and torques produced by a ringed beam on a prolate spheroid

doi:10.1364/JOSAB.27.001651

Geometrical optics calculation of forces and torques produced by a ringed beam on a prolate spheroid

Alberto Hinojosa-Alvarado and Julio C. Gutiérrez-Vega »View Author Affiliations

JOSA B, Vol. 27, Issue 8, pp. 1651-1658 (2010)
http://dx.doi.org/10.1364/JOSAB.27.001651

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Abstract

The axial and transverse optical forces and torques exerted by circularly ringed beams on an arbitrarily oriented and homogeneous spheroid are calculated and studied within the framework of the geometrical optics regime. The results are applied to study the behavior of the forces in a counter-propagating optical trap. We calculate the trapping efficiencies and torques for several values of physical parameters, including the beam waist separation distance, the equivalent spheroid radius, the spheroid eccentricity, and the refractive index ratio between the particle and the surrounding medium.

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(290.0290) Scattering : Scattering
(290.5850) Scattering : Scattering, particles

ToC Category:
Scattering

History
Original Manuscript: May 28, 2010
Revised Manuscript: June 23, 2010
Manuscript Accepted: June 28, 2010
Published: July 26, 2010

Virtual Issues
Vol. 5, Iss. 12 Virtual Journal for Biomedical Optics

Citation
Alberto Hinojosa-Alvarado and Julio C. Gutiérrez-Vega, "Geometrical optics calculation of forces and torques produced by a ringed beam on a prolate spheroid," J. Opt. Soc. Am. B 27, 1651-1658 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josab-27-8-1651

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References

S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975). [PubMed]
S. Asano, “Light scattering properties of spheroidal particles,” Appl. Opt. 18, 712–722 (1979). [CrossRef] [PubMed]
J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995). [CrossRef] [PubMed]
J. P. Barton, “Internal, near-surface, and scattered electromagnetic fields for a layered spheroid with arbitrary illumination,” Appl. Opt. 40, 3598–3607 (2001). [CrossRef]
Y. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz–Mie theory for a spheroidal particle with off-axis Gaussian beam illumination,” Appl. Opt. 42, 6621–6629 (2003). [CrossRef] [PubMed]
F. Xu, K. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007). [CrossRef]
F. Xu, K. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007). [CrossRef]
F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. E 78, 013843 (2008).
Y. Han, and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001). [CrossRef]
S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24, 430–443 (2007). [CrossRef]
R. W. Going, B. L. Conover, and M. J. Escuti, “Electrostatic force and torque escription of generalized spheroidal particles in optical landscapes,” Proc. SPIE 7038, 703826 (2008). [CrossRef]
T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001). [CrossRef]
E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991). [CrossRef] [PubMed]
F. Xu, K. F. Ren, X. Cai, and J. Shen, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence,” Appl. Opt. 45, 5000–5009 (2006). [CrossRef] [PubMed]
H. Sosa-Martínez, and J. C. Gutiérrez-Vega, “Optical forces on a Mie spheroidal particle arbitrarily oriented in a counterpropagating trap,” J. Opt. Soc. Am. B 26, 2109–2116 (2009). [CrossRef]
K. Volke-Sepúlveda, S. Chávez-Cerda, V. Garcés-Chávez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B 21, 1749–1757 (2004). [CrossRef]
E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt. 36, 6423–6433 (1997). [CrossRef]
M. Mansuripur, “Geometric-optical rays, Poynting’s vector and field momenta,” Opt. Photonics News 10(3), 53–56 (1999). [CrossRef]
L. Allen, and M. J. Padgett, “The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000). [CrossRef]
V. Garcés-Chávez, K. Volke-Sepulveda, S. Chavez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002). [CrossRef]
K. P. Volke-Sepulveda, V. Garcés-Chávez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S789 (2002). [CrossRef]
C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express 14, 4182–4187 (2006). [CrossRef] [PubMed]
D. Rudd, C. López-Mariscal, M. Summers, A. Shahvisi, J. C. Gutiérrez-Vega and D. McGloin, “Fiber based optical trapping of aerosols,” Opt. Express 16, 14550–14560 (2008). [CrossRef] [PubMed]
M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006); M. Guillon, O. Moine, and B. Stout, erratum, Phys. Rev. 99, 079901 (2007). [CrossRef] [PubMed]
A. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M. Prentiss, “Demonstration of a-fiber-optical light-force trap,” Opt. Lett. 18, 1867–1869 (1993). [CrossRef] [PubMed]
J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001). [CrossRef] [PubMed]
G. Roosen and C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. A 59, 6–8 (1976). [CrossRef]

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[1] S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975). [PubMed]

[2] S. Asano, “Light scattering properties of spheroidal particles,” Appl. Opt. 18, 712–722 (1979). [CrossRef] [PubMed]

[3] J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995). [CrossRef] [PubMed]

[4] J. P. Barton, “Internal, near-surface, and scattered electromagnetic fields for a layered spheroid with arbitrary illumination,” Appl. Opt. 40, 3598–3607 (2001). [CrossRef]

[5] Y. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz–Mie theory for a spheroidal particle with off-axis Gaussian beam illumination,” Appl. Opt. 42, 6621–6629 (2003). [CrossRef] [PubMed]

[6] F. Xu, K. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007). [CrossRef]

[7] F. Xu, K. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007). [CrossRef]

[8] F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. E 78, 013843 (2008).

[9] Y. Han, and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001). [CrossRef]

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

[11] R. W. Going, B. L. Conover, and M. J. Escuti, “Electrostatic force and torque escription of generalized spheroidal particles in optical landscapes,” Proc. SPIE 7038, 703826 (2008). [CrossRef]

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

[13] E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991). [CrossRef] [PubMed]

[14] F. Xu, K. F. Ren, X. Cai, and J. Shen, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence,” Appl. Opt. 45, 5000–5009 (2006). [CrossRef] [PubMed]

[15] H. Sosa-Martínez, and J. C. Gutiérrez-Vega, “Optical forces on a Mie spheroidal particle arbitrarily oriented in a counterpropagating trap,” J. Opt. Soc. Am. B 26, 2109–2116 (2009). [CrossRef]

[16] K. Volke-Sepúlveda, S. Chávez-Cerda, V. Garcés-Chávez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B 21, 1749–1757 (2004). [CrossRef]

[17] E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt. 36, 6423–6433 (1997). [CrossRef]

[18] M. Mansuripur, “Geometric-optical rays, Poynting’s vector and field momenta,” Opt. Photonics News 10(3), 53–56 (1999). [CrossRef]

[19] L. Allen, and M. J. Padgett, “The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000). [CrossRef]

[20] V. Garcés-Chávez, K. Volke-Sepulveda, S. Chavez-Cerda, W. Sibbett, and K. Dholakia, “Orbital angular momentum transfer to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002). [CrossRef]

[21] K. P. Volke-Sepulveda, V. Garcés-Chávez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclassical Opt. 4, S82–S789 (2002). [CrossRef]

[22] C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne and K. Dholakia, “Orbital angular momentum transfer in helical Mathieu beams,” Opt. Express 14, 4182–4187 (2006). [CrossRef] [PubMed]

[23] D. Rudd, C. López-Mariscal, M. Summers, A. Shahvisi, J. C. Gutiérrez-Vega and D. McGloin, “Fiber based optical trapping of aerosols,” Opt. Express 16, 14550–14560 (2008). [CrossRef] [PubMed]

[24] M. Guillon, O. Moine, and B. Stout, “Longitudinal optical binding of high optical contrast microdroplets in air,” Phys. Rev. Lett. 96, 143902 (2006); M. Guillon, O. Moine, and B. Stout, erratum, Phys. Rev. 99, 079901 (2007). [CrossRef] [PubMed]

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

[26] J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001). [CrossRef] [PubMed]

[27] G. Roosen and C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. A 59, 6–8 (1976). [CrossRef]

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Geometrical optics calculation of forces and torques produced by a ringed beam on a prolate spheroid