Abstract

We carry out a detailed numerical simulation study to investigate the dependency of optical force on beam polarization. Using the well-known finite-difference time domain method and Maxwell’s stress tensor, we consider general dielectric (e.g., glass) or metallic (e.g., gold) spherical shells immersed in a Gaussian optical beam. Our results show that TE and TM polarized Gaussian beams exert different amounts of optical force depending on the shell dimensions and material properties. We specifically show that purely dielectric shells do not experience different optical forces due to polarization differences but TM polarized beams exert higher optical force on metallic shells than equivalent TM polarized beams.

© 2009 Optical Society of America

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  2. A. Ashkin, J. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
    [CrossRef] [PubMed]
  3. J. Guck, R. Ananthakrishnan, C. C. Cunningham, and J. Kas, “Stretching biological cells with light,” J. Phys. Condens. Matter 14, 4843-4856 (2002).
    [CrossRef]
  4. D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
    [CrossRef]
  5. B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
    [CrossRef]
  6. S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14, 13095-13100 (2006).
    [CrossRef] [PubMed]
  7. M. Premaratne, E. Premaratne, and A. Lowery, “The photon transport equation for turbid biological media with spatially varying isotropic refractive index,” Opt. Express 13, 389-399 (2005).
    [CrossRef] [PubMed]
  8. H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89, 246802 (2002).
    [CrossRef] [PubMed]
  9. A. Zakharian, M. Mansuripur, and J. Moloney, “Radiation pressure and the distribution of electromagnetic force in dielectric media,” Opt. Express 13, 2321-2336 (2005).
    [CrossRef] [PubMed]
  10. J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications (Wiley-IEEE Press, 1998).
  11. D. A. White, “Numerical modeling of optical gradient traps using the vector finite element method,” J. Comput. Phys. 159, 13-37 (2000).
    [CrossRef]
  12. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
  13. 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]
  14. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
    [CrossRef]
  15. A. Kank, G. Kumbhar, and S. Kulkarni, “Coupled magneto-mechanical field computations,” in Proceedings of Power Electronics, Drives and Energy Systems, PEDES '06 International Conference (IEEE, 2006), pp. 1-4.
    [CrossRef]
  16. J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
    [CrossRef]
  17. A. Taflove, K. Umashankar, and T. Jurgens, “Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths,” IEEE Trans. Antennas Propag. 33, 662-666 (1985).
    [CrossRef]
  18. B. Maes, P. Bienstman, and R. Baets, “Bloch modes and self-localized waveguides in nonlinear photonic crystals,” J. Opt. Soc. Am. B 22, 613-619 (2005).
    [CrossRef]
  19. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  20. A. Agrawal and A. Sharma, “Perfectly matched layer in numerical wave propagation: factors that affect its performance,” Appl. Opt. 43, 4225-4231 (2004).
    [CrossRef] [PubMed]
  21. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  22. M. Premaratne and S. K. Halgamuge, “Rigorous analysis of numerical phase and group velocity bounds in Yee's FDTD grid,” IEEE Microw. Wirel. Compon. Lett. 17, 556-558 (2007).
    [CrossRef]
  23. J. D. Jackson, Classical Electrodynamics (Wiley, 1998).
  24. J. V. Stewart, Intermediate Electromagnetic Theory (World Scientific, 2001).
  25. P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
    [CrossRef] [PubMed]
  26. H. X. Zheng and D. Y. Yu, “Simulation of ultrashort laser pulse propagation in silica Fiber by FDTD,” Int. J. Infrared Millim. Waves 25, 799-807 (2004).
    [CrossRef]
  27. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
    [CrossRef] [PubMed]

2007

M. Premaratne and S. K. Halgamuge, “Rigorous analysis of numerical phase and group velocity bounds in Yee's FDTD grid,” IEEE Microw. Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

2006

2005

2004

H. X. Zheng and D. Y. Yu, “Simulation of ultrashort laser pulse propagation in silica Fiber by FDTD,” Int. J. Infrared Millim. Waves 25, 799-807 (2004).
[CrossRef]

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

A. Agrawal and A. Sharma, “Perfectly matched layer in numerical wave propagation: factors that affect its performance,” Appl. Opt. 43, 4225-4231 (2004).
[CrossRef] [PubMed]

2002

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, C. C. Cunningham, and J. Kas, “Stretching biological cells with light,” J. Phys. Condens. Matter 14, 4843-4856 (2002).
[CrossRef]

2000

D. A. White, “Numerical modeling of optical gradient traps using the vector finite element method,” J. Comput. Phys. 159, 13-37 (2000).
[CrossRef]

1996

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

1994

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

1992

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1987

A. Ashkin, J. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

1985

A. Taflove, K. Umashankar, and T. Jurgens, “Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths,” IEEE Trans. Antennas Propag. 33, 662-666 (1985).
[CrossRef]

1970

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

1966

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Agrawal, A.

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, C. C. Cunningham, and J. Kas, “Stretching biological cells with light,” J. Phys. Condens. Matter 14, 4843-4856 (2002).
[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, 569-582 (1992).
[CrossRef] [PubMed]

A. Ashkin, J. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

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

Baets, R.

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Bienstman, P.

Bilby, C.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

Chapin, S. C.

Chatterjee, A.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications (Wiley-IEEE Press, 1998).

Chen, J. Y.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[CrossRef]

Chiu, D. T.

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, C. C. Cunningham, and J. Kas, “Stretching biological cells with light,” J. Phys. Condens. Matter 14, 4843-4856 (2002).
[CrossRef]

Draine, B. T.

Dufresne, E. R.

Dziedzic, J.

A. Ashkin, J. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

Erickson, H. M.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

Etchegoin, P. G.

P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Flatau, P. J.

Germain, V.

Gu, M.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[CrossRef]

Guck, J.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

J. Guck, R. Ananthakrishnan, C. C. Cunningham, and J. Kas, “Stretching biological cells with light,” J. Phys. Condens. Matter 14, 4843-4856 (2002).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Halgamuge, S. K.

M. Premaratne and S. K. Halgamuge, “Rigorous analysis of numerical phase and group velocity bounds in Yee's FDTD grid,” IEEE Microw. Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

Hanna, S.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1998).

Jurgens, T.

A. Taflove, K. Umashankar, and T. Jurgens, “Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths,” IEEE Trans. Antennas Propag. 33, 662-666 (1985).
[CrossRef]

Käll, M.

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef] [PubMed]

Kank, A.

A. Kank, G. Kumbhar, and S. Kulkarni, “Coupled magneto-mechanical field computations,” in Proceedings of Power Electronics, Drives and Energy Systems, PEDES '06 International Conference (IEEE, 2006), pp. 1-4.
[CrossRef]

Kas, J.

J. Guck, R. Ananthakrishnan, C. C. Cunningham, and J. Kas, “Stretching biological cells with light,” J. Phys. Condens. Matter 14, 4843-4856 (2002).
[CrossRef]

Kempel, L. C.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications (Wiley-IEEE Press, 1998).

Kulkarni, S.

A. Kank, G. Kumbhar, and S. Kulkarni, “Coupled magneto-mechanical field computations,” in Proceedings of Power Electronics, Drives and Energy Systems, PEDES '06 International Conference (IEEE, 2006), pp. 1-4.
[CrossRef]

Kumbhar, G.

A. Kank, G. Kumbhar, and S. Kulkarni, “Coupled magneto-mechanical field computations,” in Proceedings of Power Electronics, Drives and Energy Systems, PEDES '06 International Conference (IEEE, 2006), pp. 1-4.
[CrossRef]

Lin, Z. F.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[CrossRef]

Lincoln, B.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

Lowery, A.

Maes, B.

Mansuripur, M.

Meyer, M.

P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Mitchell, D.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

Moloney, J.

Premaratne, E.

Premaratne, M.

M. Premaratne and S. K. Halgamuge, “Rigorous analysis of numerical phase and group velocity bounds in Yee's FDTD grid,” IEEE Microw. Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

M. Premaratne, E. Premaratne, and A. Lowery, “The photon transport equation for turbid biological media with spatially varying isotropic refractive index,” Opt. Express 13, 389-399 (2005).
[CrossRef] [PubMed]

Ru, E. C. L.

P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Schinkinger, S.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

Sharma, A.

Simpson, S. H.

Stewart, J. V.

J. V. Stewart, Intermediate Electromagnetic Theory (World Scientific, 2001).

Taflove, A.

A. Taflove, K. Umashankar, and T. Jurgens, “Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths,” IEEE Trans. Antennas Propag. 33, 662-666 (1985).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Ulvick, S.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

Umashankar, K.

A. Taflove, K. Umashankar, and T. Jurgens, “Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths,” IEEE Trans. Antennas Propag. 33, 662-666 (1985).
[CrossRef]

Volakis, J. L.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications (Wiley-IEEE Press, 1998).

Wang, P. N.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[CrossRef]

White, D. A.

D. A. White, “Numerical modeling of optical gradient traps using the vector finite element method,” J. Comput. Phys. 159, 13-37 (2000).
[CrossRef]

Wottawah, F.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

Xu, H.

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef] [PubMed]

Xu, L.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[CrossRef]

Yamane, T.

A. Ashkin, J. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Yu, D. Y.

H. X. Zheng and D. Y. Yu, “Simulation of ultrashort laser pulse propagation in silica Fiber by FDTD,” Int. J. Infrared Millim. Waves 25, 799-807 (2004).
[CrossRef]

Yu, J. T.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[CrossRef]

Zakharian, A.

Zare, R. N.

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

Zheng, H. X.

H. X. Zheng and D. Y. Yu, “Simulation of ultrashort laser pulse propagation in silica Fiber by FDTD,” Int. J. Infrared Millim. Waves 25, 799-807 (2004).
[CrossRef]

Appl. Opt.

Biophys. J.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Cytometry, Part A

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry, Part A 59A, 203-209 (2004).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett.

M. Premaratne and S. K. Halgamuge, “Rigorous analysis of numerical phase and group velocity bounds in Yee's FDTD grid,” IEEE Microw. Wirel. Compon. Lett. 17, 556-558 (2007).
[CrossRef]

IEEE Trans. Antennas Propag.

A. Taflove, K. Umashankar, and T. Jurgens, “Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths,” IEEE Trans. Antennas Propag. 33, 662-666 (1985).
[CrossRef]

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Int. J. Infrared Millim. Waves

H. X. Zheng and D. Y. Yu, “Simulation of ultrashort laser pulse propagation in silica Fiber by FDTD,” Int. J. Infrared Millim. Waves 25, 799-807 (2004).
[CrossRef]

J. Am. Chem. Soc.

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

J. Biomed. Opt.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[CrossRef]

J. Chem. Phys.

P. G. Etchegoin, E. C. L. Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

J. Comput. Phys.

D. A. White, “Numerical modeling of optical gradient traps using the vector finite element method,” J. Comput. Phys. 159, 13-37 (2000).
[CrossRef]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Condens. Matter

J. Guck, R. Ananthakrishnan, C. C. Cunningham, and J. Kas, “Stretching biological cells with light,” J. Phys. Condens. Matter 14, 4843-4856 (2002).
[CrossRef]

Nature

A. Ashkin, J. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. Lett.

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

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef] [PubMed]

Other

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

J. D. Jackson, Classical Electrodynamics (Wiley, 1998).

J. V. Stewart, Intermediate Electromagnetic Theory (World Scientific, 2001).

A. Kank, G. Kumbhar, and S. Kulkarni, “Coupled magneto-mechanical field computations,” in Proceedings of Power Electronics, Drives and Energy Systems, PEDES '06 International Conference (IEEE, 2006), pp. 1-4.
[CrossRef]

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications (Wiley-IEEE Press, 1998).

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Figures (13)

Fig. 1
Fig. 1

Yee Lattice.

Fig. 2
Fig. 2

(a) Shows the force exerted on a 1 μ m gold sphere in the free space that is held in the TM polarized Gaussian beam ( λ = 600 nm , the waist radius ω 0 = 300 nm , and the power is 10 mW .). (b) Shows the ratio of the force difference Δ F F . As shown, the ratio is smaller than 3% when the cell size Δ s is smaller than λ 60 .

Fig. 3
Fig. 3

(a) Real and (b) imaginary parts of the dielectric function of gold are shown. These data values are from Eq. (19) and the parameters are obtained from Table 1.

Fig. 4
Fig. 4

Polarization illustration.

Fig. 5
Fig. 5

Shows the simulation structure; ω 0 = 300 nm is the waist radius of the Gaussian beam. The initial position of the spherical shell is decided by x 0 = 3 μ m and y 0 = 0 ; a 0 and b 0 represent the inner radius and outer radius of the shell, respectively.

Fig. 6
Fig. 6

Optical forces on a glass spherical shell in a TE polarized beam and a TM polarized Gaussian beam when a 0 = 100 nm and b 0 is from 120 to 1000 nm .

Fig. 7
Fig. 7

Optical forces on a glass spherical shell in a TE polarized beam and a TM polarized Gaussian beam when a 0 is 0 and b 0 is from 100 to 1000 nm (solid glass sphere).

Fig. 8
Fig. 8

Optical forces on glass spherical shell in a TE polarized beam and a TM polarized Gaussian beam when a 0 is varying from 100 to 980 nm and b 0 is held constant at 1000 nm .

Fig. 9
Fig. 9

Optical forces on a gold spherical shell in a TE polarized beam and a TM polarized Gaussian beam when a 0 = 100 nm and b 0 is from 120 to 1000 nm .

Fig. 10
Fig. 10

Optical forces on a gold spherical shell in a TE polarized beam and a TM polarized Gaussian beam when a 0 is 0 and b 0 is from 100 to 1000 nm (solid gold sphere).

Fig. 11
Fig. 11

Optical forces on a gold spherical shell in a TE polarized beam and a TM polarized Gaussian beam when a 0 is varying from 100 to 980 nm and b 0 is held constant at 1000 nm .

Fig. 12
Fig. 12

E y field comparison between glass and gold. In (a), the electric fields only penetrate into the gold shell surface to a very thin level when the inner radius is smaller than the skin depth, however, penetrating into the glass shell to very deep inside. In (b), when the inner radius is greater than the skin depth, the electric fields penetrates into both gold and glass to a deep level.

Fig. 13
Fig. 13

Optical force on a gold shell with higher resolution. Inner radius a 0 is varying from 820 to 980 nm and outer radius is 1000 nm as constant.

Tables (2)

Tables Icon

Table 1 Parameter in Eq. (19) for Property of Gold

Tables Icon

Table 2 Parameters in Eq. (20) for Property of Glass

Equations (30)

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

B t = × E ,
D t = × H ,
B = μ H ,
D = ε E ,
E x n ( i + 1 2 , j , k ) = K 1 x ( i + 1 2 , j , k ) E x n 1 ( i + 1 2 , j , k ) + K 2 x ( i + 1 2 , j , k ) { [ H z n 1 2 ( i + 1 2 , j + 1 2 , k ) H z n 1 2 ( i + 1 2 , j 1 2 , k ) ] Δ z [ H y n 1 2 ( i + 1 2 , j , k + 1 2 ) H y n 1 2 ( i + 1 2 , j , k 1 2 ) ] Δ y } ,
H x n + 1 2 ( i , j + 1 2 , k + 1 2 ) = H x n 1 2 ( i , j + 1 2 , k + 1 2 ) K 3 x ( i , j + 1 2 , k + 1 2 ) × { [ E z n ( i , j + 1 , k + 1 2 ) E z n ( i , j , k + 1 2 ) ] Δ z [ E y n ( i , j + 1 2 , k + 1 ) E y n ( i + , + 1 2 j , k ) ] Δ y } ,
K 1 x ( i + 1 2 , j , k ) = 1 σ ( i + 1 2 , j , k ) Δ t 2 ε ( i + 1 2 , j , k ) 1 + σ ( i + 1 2 , j , k ) Δ t 2 ε ( i + 1 2 , j , k ) ,
K 2 x ( i + 1 2 , j , k ) = Δ t ε ( i + 1 2 , j , k ) 1 + σ ( i + 1 2 , j , k ) Δ t 2 ε ( i + 1 2 , j , k ) 1 Δ y Δ z ,
K 3 x ( i , j + 1 2 , k + 1 2 ) = Δ t μ ( i , j + 1 2 , k + 1 2 ) 1 Δ y Δ z ,
F = q ( E + v × B ) = ( ρ B + J × B ) d τ ,
d P d t = ( ρ E + J × B ) d τ ,
ρ = ε Δ E ,
J = 1 μ Δ × B ε E t .
d P d t = { ε [ ( E ) E + ( E ) E 1 2 ( E 2 ) ] + 1 μ [ ( B ) B + ( B ) B 1 2 ( B 2 ) ] } d τ ε μ d d t d τ .
d P d t = T d S 1 c 2 d d t d τ ,
T i j = ε E i E j + 1 μ B i B j 1 2 ( ε E 2 + 1 μ B 2 ) δ i j ,
δ i j = { 1 if i = j 0 if i j } .
F o ( t ) = s T ( t ) n d s ,
T = [ T i i T i j T i k T j i T j j T j k T k i T k j T k k ] ,
ε Au = ε 1 λ p 2 ( 1 λ 2 + i γ p ) + i = 1 , 2 [ A i λ i e i ϕ i ( 1 λ i 1 λ i γ i ) + e i ϕ i ( 1 λ i + 1 λ + 1 γ i ) ] ,
ε r ( ω ) = 1 + i = 1 3 a i ω i 2 ( ω i 2 ω 2 ) ,
E x t = 1 ε ( H z y H y z ) ,
H y t = 1 μ E x z ,
H z t = 1 μ E x y ,
H x t = 1 μ ( E y z E z y ) ,
E y t = 1 ε H x z ,
E z t = 1 ε H x y .
F = n 1 P c { 1 + R TM TE cos 2 θ T TM TE 2 [ cos ( 2 θ 2 γ ) + R TM TE cos 2 θ ] 1 + R TM TE 2 + 2 R TM TE cos 2 γ } ,
R TM = n 2 cos θ n 1 1 ( n 1 n 2 sin θ ) 2 n 2 cos θ + n 1 1 ( n 1 n 2 sin θ ) 2 ,
R TE = n 1 cos θ n 2 1 ( n 1 n 2 sin θ ) 2 n 1 cos θ + n 2 1 ( n 1 n 2 sin θ ) 2 .

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