Abstract

Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
    [PubMed]
  2. M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” in Proceedings of the National Academy of Science of the United States of America86, (1989), pp. 7914–7918.
  3. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
    [PubMed]
  4. G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).
  5. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” in Proceedings of the National Academy of Science of the United States of America94, (1997), pp. 4853–4860.
  6. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
    [PubMed]
  7. D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
    [PubMed]
  8. L. A. Ambrosio and H. E. Hernández-Figueroa, “Inversion of gradient forces for high refractive index particles in optical trapping,” Opt. Express 18(6), 5802–5808 (2010).
    [PubMed]
  9. V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 4, 509–514 (1968).
  10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
    [PubMed]
  11. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [PubMed]
  12. N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).
  13. N. Engheta and R. Ziolkowski, Metamaterials – Physics and Engineering Explorations (IEEE press, Wiley-Interscience, John Wiley & Sons, 2006).
  14. C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (IEEE press, Wiley-Interscience, John Wiley & Sons, 2006).
  15. L. A. Ambrosio and H. E. Hernández-Figueroa, “Trapping double negative particles in the ray optics regime using optical tweezers with focused beams,” Opt. Express 17(24), 21918–21924 (2009).
    [PubMed]
  16. 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).
    [PubMed]
  17. A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
    [PubMed]
  18. Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Antireflection coating for improved optical trapping,” J. Appl. Phys. 103, 093119 (2008).
  19. G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
  20. G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
  21. B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
  22. G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz-Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
  23. C. F. Bohren, and D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, John Wiley & Sons, 1983).
  24. G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
  25. K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
    [PubMed]
  26. G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
  27. G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
  28. H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).
  29. K. F. Ren, G. Gréhan, 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).
  30. K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11, 1812–1817 (1994).
  31. A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
  32. A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
  33. A. Ashkin and J. M. Dziedzic, “Optical levitation in high vacuum,” Appl. Phys. Lett. 28, 333–335 (1976).
  34. A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).
  35. A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19(5), 660–668 (1980).
    [PubMed]
  36. K. R. Fen, Diffusion des Faisceaux Feuille Laser par une Particule Sphérique et Applications aux Ecoulements Diphasiques (Ph.D thesis, Faculté des Sciences de L’Université de Rouen, 1995).
  37. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [PubMed]

2010 (1)

2009 (1)

2008 (2)

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Antireflection coating for improved optical trapping,” J. Appl. Phys. 103, 093119 (2008).

2007 (1)

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).

2005 (1)

N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).

2004 (2)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[PubMed]

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
[PubMed]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[PubMed]

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[PubMed]

1998 (2)

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
[PubMed]

1996 (1)

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[PubMed]

1994 (4)

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).
[PubMed]

1990 (1)

1988 (2)

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).

G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz-Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).

1987 (1)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[PubMed]

1982 (1)

G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).

1980 (1)

1977 (1)

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).

1976 (1)

A. Ashkin and J. M. Dziedzic, “Optical levitation in high vacuum,” Appl. Phys. Lett. 28, 333–335 (1976).

1974 (1)

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).

1971 (1)

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).

1968 (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 4, 509–514 (1968).

1908 (1)

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).

Ambrosio, L. A.

Arlt, J.

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).

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).
[PubMed]

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19(5), 660–668 (1980).
[PubMed]

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).

A. Ashkin and J. M. Dziedzic, “Optical levitation in high vacuum,” Appl. Phys. Lett. 28, 333–335 (1976).

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[PubMed]

Bustamante, C.

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[PubMed]

Cui, Y.

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[PubMed]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19(5), 660–668 (1980).
[PubMed]

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).

A. Ashkin and J. M. Dziedzic, “Optical levitation in high vacuum,” Appl. Phys. Lett. 28, 333–335 (1976).

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).

Engheta, N.

N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).

Gouesbet, G.

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
[PubMed]

G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).

K. F. Ren, G. Gréhan, 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).

K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11, 1812–1817 (1994).

G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).

G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz-Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).

G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).

Gréhan, G.

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
[PubMed]

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).

K. F. Ren, G. Gréhan, 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).

K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11, 1812–1817 (1994).

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).

G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz-Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).

G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).

Halas, N. J.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
[PubMed]

Heckenberg, N. R.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Antireflection coating for improved optical trapping,” J. Appl. Phys. 103, 093119 (2008).

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

Hernández-Figueroa, H. E.

Hirsch, L. R.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
[PubMed]

Hu, Y.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Antireflection coating for improved optical trapping,” J. Appl. Phys. 103, 093119 (2008).

Knöener, G.

Lock, J. A.

Maheu, B.

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).

G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz-Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).

Mie, G.

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[PubMed]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[PubMed]

Nieminen, T. A.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Antireflection coating for improved optical trapping,” J. Appl. Phys. 103, 093119 (2008).

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

O’Neal, D. P.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
[PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[PubMed]

Payne, J. D.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
[PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[PubMed]

Polaert, H.

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).

Poon, W. C. K.

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).

Read, N. D.

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).

Ren, K. F.

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
[PubMed]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11, 1812–1817 (1994).

K. F. Ren, G. Gréhan, 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).

Rubinsztein-Dunlop, H.

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Antireflection coating for improved optical trapping,” J. Appl. Phys. 103, 093119 (2008).

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[PubMed]

Smith, S. B.

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[PubMed]

Stilgoe, A. B.

Veselago, V. G.

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 4, 509–514 (1968).

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[PubMed]

West, J. L.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
[PubMed]

Wright, G. D.

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).

Ziolkowski, R.

N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).

Appl. Opt. (2)

Appl. Phys. Lett. (4)

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).

A. Ashkin and J. M. Dziedzic, “Optical levitation in high vacuum,” Appl. Phys. Lett. 28, 333–335 (1976).

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).

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).
[PubMed]

Cancer Lett. (1)

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004).
[PubMed]

IEEE Trans. Microw. Theory Tech. (1)

N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).

J. Appl. Phys. (1)

Y. Hu, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Antireflection coating for improved optical trapping,” J. Appl. Phys. 103, 093119 (2008).

J. Opt. (Paris) (3)

G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).

G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz-Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).

J. Opt. Soc. Am. A (4)

Mycoscience (1)

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).

Opt. Commun. (2)

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).

K. F. Ren, G. Gréhan, 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).

Opt. Express (3)

Phys. Rev. Lett. (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[PubMed]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[PubMed]

Science (3)

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996).
[PubMed]

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 4, 509–514 (1968).

Other (6)

K. R. Fen, Diffusion des Faisceaux Feuille Laser par une Particule Sphérique et Applications aux Ecoulements Diphasiques (Ph.D thesis, Faculté des Sciences de L’Université de Rouen, 1995).

N. Engheta and R. Ziolkowski, Metamaterials – Physics and Engineering Explorations (IEEE press, Wiley-Interscience, John Wiley & Sons, 2006).

C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (IEEE press, Wiley-Interscience, John Wiley & Sons, 2006).

C. F. Bohren, and D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, John Wiley & Sons, 1983).

M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” in Proceedings of the National Academy of Science of the United States of America86, (1989), pp. 7914–7918.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” in Proceedings of the National Academy of Science of the United States of America94, (1997), pp. 4853–4860.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

Normalized (over nmP/c) individual transverse force Fy as a function of both θi and np for a circularly polarized ray over (a) a PRI and (c) a NRI particle. The difference observed between these two cases leads to new trapping phenomena for nrel < 0. (b) and (d) are the contour plots of (a) and (c), respectively.

Fig. 2
Fig. 2

Normalized (over nmP/c) individual transverse force Fy as a function of θi for (a) nrel = 1.2 (dotted) and −1.2 (solid) and (b) nrel = 0.8 (dotted) and −0.8 (solid). Force profiles can significantly vary for NRI and PRI particles possessing the same (in modulus) electromagnetic parameters. In (b), total reflection occurs for θi > 0.9273 rad.

Fig. 3
Fig. 3

(a) Ftransverse as a function of both nrel and r for a PRI particle under the influence of a focused Gaussian beam with w 0 = 1000 nm. The particle has a radius a = 10λ, where λ = 1064 nm is the wavelength of the beam. When nrel = 1, Ftransverse is always zero, as expected. (b) The contour plot of (a). Arbitrary units are adopted.

Fig. 4
Fig. 4

(a) Ftransverse as a function of both nrel and r for a NRI particle under the influence of the same laser beam and electromagnetic parameters as in Fig. 3. (b) The contour plot of (a). The same arbitrary units of Fig. 3 are adopted.

Fig. 5
Fig. 5

Real (solid, red) and imaginary (dashed, blue) parts of the Mie scattering coefficient an as a function of the size parameter x for nrel = 1.33 and (a) n = 1, (b) n = 4, (c) n = 9 and (d) n = 16. In the framework of the GLMT, the coefficients an and bn modulates the phase and amplitude of the scattered fields.

Fig. 6
Fig. 6

Real (solid, red) and imaginary (dashed, blue) parts of the Mie coefficient an as a function of x for a NRI particle with nrel = −1.33 and (a) n = 1, (b) n = 4, (c) n = 9 and (d) n = 16. Different phase and amplitudes are observed in comparison with Fig. 5, so that the scattered fields will also be different.

Fig. 7
Fig. 7

Longitudinal radiation pressure cross-section Cpr,z as a function of z 0 for x 0 = y 0 = 0 for (a) nrel = 1.5 and (c) nrel = 1/1.33. (b) and (d) are the NRI analogues of (a) and (c), respectively.

Fig. 8
Fig. 8

(a) Cpr,z for several values of nrel assuming a PRI particle with radius a = 3.75 μm immersed on a focused Gaussian beam with λ = 0.3682 μm and w 0 = 1.8 μm. The same relative refractive indices were used in (b) for a NRI particle with the same radius as (a). The beam is shifted along its optical axis, i.e., x 0 = y 0 = 0.

Fig. 9
Fig. 9

(a) Cpr,x for several diameters of a PRI particle with nrel = 1.5. The beam is shifted along x with y 0 = z 0 = 0, x 0 being the transverse distance between the optical axis and the centre of the particle. (b) The NRI analogue with nrel = −1.5.

Fig. 10
Fig. 10

(a) Cpr,z for a NRI particle with nrel = −1 and four different size parameters. The incident beam is a focused Gaussian beam with λ = 1064 nm and w 0 = 1.0 μm. The beam is shifted along its optical axis, i.e., x 0 = y 0 = 0.

Fig. 11
Fig. 11

Cpr,x for several diameters of a PRI particle with (a) nrel = 0.5 and (b) nrel = −0.5. This corresponds to Fig. 9 but now for |nrel | < 1.

Fig. 12
Fig. 12

(a) Cpr,y for several diameters of a PRI particle with nrel = 1.5. The beam is shifted along y with x 0 = z 0 = 0, y 0 being the transverse distance between the optical axis (beam waist centre) and the centre of the particle. (b) The NRI analogue with nrel = −1.5.

Fig. 13
Fig. 13

Cpr,y for several diameters of a PRI particle with (a) nrel = 0.5 and (b) nrel = −0.5. This corresponds to Fig. 12 but now for |nrel | < 1.

Fig. 14
Fig. 14

Normalized (over nmP/c) individual transverse force Ftransverse as a function of θi for both nrel = −1.5 (dotted) and −0.5 (solid). For the last case, total reflection occurs for θi > 0.5236 rad.

Fig. 15
Fig. 15

Cpr,x as a function of the displacement x 0 and the relative refractive index nrel for a NRI particle with d = 40 μm.

Equations (13)

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

a n = μ n r e l ψ n ( n r e l x ) ψ n ( x ) μ p ψ n ( x ) ψ n ( n r e l x ) μ n r e l ψ n ( n r e l x ) ξ n ( x ) μ p ξ n ( x ) ψ n ( n r e l x )
b n = μ p ψ n ( n r e l x ) ψ n ( x ) μ n r e l ψ n ( x ) ψ n ( n r e l x ) μ p ψ n ( n r e l x ) ξ n ( x ) μ n r e l ξ n ( x ) ψ n ( n r e l x )
g n , T E m = Z n m 2 π H 0 0 2 π G ^ [ H r ( r , θ , ϕ ) ] e i m ϕ d ϕ
g n , T M m = Z n m 2 π E 0 0 2 π G ^ [ E r ( r , θ , ϕ ) ] e i m ϕ d ϕ
g n , T E m = k n m 2 i F D a v i s ( n + 1 / 2 , π / 2 ) j = 0 p = 0 j Ψ j , p D a v i s ( n + 1 / 2 , π / 2 ) ( δ j 2 p + 1 , m δ j 2 p 1 , m )
g n , T M m = k n m 2 F D a v i s ( n + 1 / 2 , π / 2 ) j = 0 p = 0 j Ψ j , p D a v i s ( n + 1 / 2 , π / 2 ) ( δ j 2 p + 1 , m + δ j 2 p 1 , m ) ,
C p r , z = λ 2 π n = 1 p = n n ( 1 ( n + 1 ) 2 ( n + 1 + | p | ) ! ( n | p | ) ! Re [ ( a n + a n + 1 2 a n a n + 1 ) g n , T M p g n + 1 , T M p + ( b n + b n + 1 2 b n b n + 1 ) g n , T E p g n + 1 , T E p ] + p 2 n + 1 n 2 ( n + 1 ) 2 ( n + | p | ) ! ( n | p | ) ! Re [ i ( 2 a n b n a n b n ) g n , T M p g n , T E p ] ) ,
C = λ 2 2 π p = 1 n = p m = p 1 0 ( ( n + | p | ) ! ( n | p | ) ! [ ( S m , n p 1 + S n , m p 2 U m , n p 1 2 U n , m p ) ( 1 m 2 δ m , n + 1 1 n 2 δ n , m + 1 ) + 2 n + 1 n 2 ( n + 1 ) 2 δ n , m ( T m , n p 1 T n , m p 2 V m , n p 1 + 2 V n , m p ) ] ) ,
( C p r , x C p r , y ) = ( Re ( C ) Im ( C ) )
U n , m p = a n a m g n , T M p g m , T M p + 1 + b n b m g n , T E p g m , T E p + 1 ,
V n , m p = i b n a m g n , T E p g m , T M p + 1 i a n b m g n , T M p g m , T E p + 1 ,
S n , m p = ( a n + a m ) g n , T M p g m , T M p + 1 + ( b n + b m ) g n , T E p g m , T E p + 1 ,
T n , m p = i ( b n + a m ) g n , T E p g m , T M p + 1 i ( a n + b m ) g n , T M p g m , T E p + 1 .

Metrics