Abstract

When impinged by an arbitrary laser beam, lossless and homogeneous negative refractive index (NRI) spherical particles refract and reflect light in an unusual way, giving rise to different scattered and internal fields when compared to their equivalent positive refractive index particles. In the generalized Lorenz–Mie theory, the scattered fields are dependent upon the Mie scattering coefficients, whose values must reflect the metamaterial behavior of an NRI scatterer, thus leading to new optical properties such as force and torque. In this way, this work is devoted to the analysis of both radial and longitudinal optical forces exerted on lossless and simple NRI particles by zero-order Bessel beams, revealing how the force profiles are changed whenever the refractive index becomes negative.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  2. A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
    [CrossRef]
  3. A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
    [CrossRef]
  4. A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
    [CrossRef]
  5. A. Ashkin and J. M. Dziedzic, “Optical levitation in high vacuum,” Appl. Phys. Lett. 28, 333–335 (1976).
    [CrossRef]
  6. A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).
    [CrossRef]
  7. A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19, 660–668 (1980).
    [CrossRef] [PubMed]
  8. 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]
  9. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
    [CrossRef] [PubMed]
  10. 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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
    [CrossRef] [PubMed]
  11. 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, 795–799(1996).
    [CrossRef] [PubMed]
  12. G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48, 15–19 (2007).
    [CrossRef]
  13. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
    [CrossRef] [PubMed]
  14. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
    [CrossRef]
  15. 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, 171–176(2004).
    [CrossRef] [PubMed]
  16. 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]
  17. L. A. Ambrosio and H. E. Hernández-Figueroa, “Inversion of gradient forces for high refractive index particles in optical trapping,” Opt. Express 18, 5802–5808 (2010).
    [CrossRef] [PubMed]
  18. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [CrossRef]
  19. V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
    [CrossRef]
  20. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
    [CrossRef] [PubMed]
  21. G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
    [CrossRef]
  22. G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. 13, 97–103 (1982).
    [CrossRef]
  23. B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
    [CrossRef]
  24. G. Gouesbet, G. Gréhan, and B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. 16, 83–93 (1985).
    [CrossRef]
  25. G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. 19, 35–48 (1988).
    [CrossRef]
  26. 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).
    [CrossRef]
  27. K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
    [CrossRef]
  28. 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).
    [CrossRef]
  29. 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).
    [CrossRef]
  30. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  31. 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, 4184–4187 (2000).
    [CrossRef] [PubMed]
  32. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  33. N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microwave Theory Tech. 53, 1535–1556 (2005).
    [CrossRef]
  34. N. Engheta and R. Ziolkowski, Metamaterials—Physics and Engineering Explorations (IEEE, Wiley-Interscience, Wiley & Sons, 2006).
  35. C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (IEEE, Wiley-Interscience, Wiley & Sons, 2006).
  36. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623(2005).
    [CrossRef]
  37. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  38. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  39. S. Zouhdi, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modeling, Applications (Springer, NATO, 2008).
  40. 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, 21918–21924 (2009).
    [CrossRef] [PubMed]
  41. L. A. Ambrosio and H. E. Hernández-Figueroa, “Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz–Mie theory,” Biomed. Opt. Express 1, 1284–1301 (2010).
    [CrossRef]
  42. L. A. Ambrosio and H. E. Hernández-Figueroa, “Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime,” Opt. Express 18, 24287–24292 (2010).
    [CrossRef] [PubMed]
  43. M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 11428–11443 (2010).
    [CrossRef] [PubMed]
  44. L. A. Ambrosio and H. E. Hernández-Figueroa, “Integral localized approximation description of ordinary Bessel beams in the generalized Lorenz–Mie theory and application to optical forces,” Biomed. Opt. Express 2, 1893–1906 (2011).
    [CrossRef] [PubMed]
  45. G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972–13987 (2007).
    [CrossRef] [PubMed]
  46. C. F. Bohren and D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, Wiley & Sons, 1983).
  47. 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).
  48. B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances in small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327–334 (2008).
    [CrossRef]
  49. “Non-Rayleigh limit of the Lorenz–Mie solution and suppression of scattering by spheres of negative refractive index,” Phys. Rev. A 80, 013808 (2009).
    [CrossRef]
  50. L. A. Ambrosio and H. E. Hernández-Figueroa are preparing a manuscript to be called “The Mie scattering coefficients for double-negative spherical particles: emphasizing the metamaterial.”
  51. 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).
    [CrossRef]

2011

2010

2009

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, 21918–21924 (2009).
[CrossRef] [PubMed]

“Non-Rayleigh limit of the Lorenz–Mie solution and suppression of scattering by spheres of negative refractive index,” Phys. Rev. A 80, 013808 (2009).
[CrossRef]

2008

2007

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972–13987 (2007).
[CrossRef] [PubMed]

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

2006

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

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

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

2005

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

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623(2005).
[CrossRef]

2004

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

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

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, 171–176(2004).
[CrossRef] [PubMed]

2002

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

2001

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

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

2000

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, 4184–4187 (2000).
[CrossRef] [PubMed]

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

1998

1997

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

1996

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, 795–799(1996).
[CrossRef] [PubMed]

1995

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).

1994

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]

1990

1989

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [PubMed]

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. 19, 35–48 (1988).
[CrossRef]

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

1987

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

1986

1985

G. Gouesbet, G. Gréhan, and B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. 16, 83–93 (1985).
[CrossRef]

1983

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

1982

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

1980

1977

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

1976

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

1974

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

1971

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

1970

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

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

1968

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

1908

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623(2005).
[CrossRef]

Ambrosio, L. A.

Andrews, J. J.

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [PubMed]

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).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

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

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]

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

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

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

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

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

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

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

Berns, M. W.

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Block, S. M.

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

Bohren, C. F.

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

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, 795–799(1996).
[CrossRef] [PubMed]

Caloz, C.

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

Chantada, L.

Chu, S.

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, 795–799(1996).
[CrossRef] [PubMed]

Dholakia, K.

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972–13987 (2007).
[CrossRef] [PubMed]

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Dziedzic, J. M.

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

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]

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

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

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

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

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

Engheta, N.

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

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

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623(2005).
[CrossRef]

Fen, K. R.

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).

Garces-Chavez, V.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

García-Cámara, B.

Gómez-Medina, R.

González, F.

Gouesbet, G.

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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

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

G. Gouesbet, G. Gréhan, and B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. 16, 83–93 (1985).
[CrossRef]

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

Gréhan, G.

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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

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

G. Gouesbet, G. Gréhan, and B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. 16, 83–93 (1985).
[CrossRef]

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

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, 171–176(2004).
[CrossRef] [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, 171–176(2004).
[CrossRef] [PubMed]

Huffmann, D. R.

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

Itoh, T.

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

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

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).
[CrossRef]

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

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

G. Gouesbet, G. Gréhan, and B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. 16, 83–93 (1985).
[CrossRef]

McGloin, D.

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15, 13972–13987 (2007).
[CrossRef] [PubMed]

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

Milne, G.

Moreno, F.

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, 4184–4187 (2000).
[CrossRef] [PubMed]

Neuman, K. C.

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

Nieto-Vesperinas, M.

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, 171–176(2004).
[CrossRef] [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, 4184–4187 (2000).
[CrossRef] [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, 171–176(2004).
[CrossRef] [PubMed]

Pendry, J. B.

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

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).
[CrossRef]

Profeta, G. A.

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [PubMed]

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).
[CrossRef]

Ren, K. F.

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

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).
[CrossRef]

Roskey, D.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

Sáenz, J. J.

Saiz, J. M.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [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, 4184–4187 (2000).
[CrossRef] [PubMed]

Shelby, R. A.

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

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Sihvola, A.

S. Zouhdi, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modeling, Applications (Springer, NATO, 2008).

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [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, 4184–4187 (2000).
[CrossRef] [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, 795–799(1996).
[CrossRef] [PubMed]

Summers, M. D.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

Tromberg, B. J.

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Videen, G.

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, 4184–4187 (2000).
[CrossRef] [PubMed]

Vinogradov, A. P.

S. Zouhdi, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modeling, Applications (Springer, NATO, 2008).

Volke-Sepulveda, K.

Walter, R. J.

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [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, 171–176(2004).
[CrossRef] [PubMed]

Wright, E. M.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

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).
[CrossRef]

Wright, W. H.

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [PubMed]

Zemánek, P.

Ziolkowski, R.

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

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

Zouhdi, S.

S. Zouhdi, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modeling, Applications (Springer, NATO, 2008).

Ann. Phys.

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

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

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

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

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85, 4001–4003 (2004).
[CrossRef]

Biomed. Opt. Express

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]

Cancer Lett.

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, 171–176(2004).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech.

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

J. Opt.

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

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

G. Gouesbet, G. Gréhan, and B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. 16, 83–93 (1985).
[CrossRef]

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

J. Opt. Soc. Am. A

Mycoscience

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

Nature

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

Opt. Commun.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

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).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

“Non-Rayleigh limit of the Lorenz–Mie solution and suppression of scattering by spheres of negative refractive index,” Phys. Rev. A 80, 013808 (2009).
[CrossRef]

Phys. Rev. E

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623(2005).
[CrossRef]

Phys. Rev. Lett.

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, 4184–4187 (2000).
[CrossRef] [PubMed]

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

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

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

Proc. Natl. Acad. Sci. USA

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

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,” Proc. Natl. Acad. Sci. USA 86, 4539–4543 (1989).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

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

Science

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, 795–799(1996).
[CrossRef] [PubMed]

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

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

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Other

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

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

S. Zouhdi, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modeling, Applications (Springer, NATO, 2008).

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

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).

L. A. Ambrosio and H. E. Hernández-Figueroa are preparing a manuscript to be called “The Mie scattering coefficients for double-negative spherical particles: emphasizing the metamaterial.”

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 (7)

Fig. 1
Fig. 1

C pr , z (solid blue curve) as a function of ρ 0 = x 0 for a / λ = ( a ) 0.01 , (b) 0.1, (c) 1, (d) 5, (e) 10, and (f) 20. The NRI particle and the host medium are matched ( n rel = 1 , n m = 1.33 ). The axial force is always repulsive ( C pr , z is positive), and weaker radiation pressure cross sections act on smaller particles, the profile resembling that of the BB intensity (dashed red curve), as expected. In all cases, a three-dimensional trap is impossible.

Fig. 2
Fig. 2

C pr , z as a function of both x 0 and n p . (a) , (b) 3D views for a / λ = 0.01 with 0 < n p < 4 and 4 < n p < 0 , respectively. (c), (d) Equivalent to (a), (b) for a / λ = 20 . Dashed lines are placed at n p = ± 1.33 ( n rel = ± 1 ), where C pr , z = 0 for PRI particles.

Fig. 3
Fig. 3

Mie scattering coefficients a 1 and b 1 for a / λ = 0.01 , λ = 1064 nm . (a), (b) PRI particle, evidencing the matched condition n rel = 1 , where scattered fields are zero and no optical forces are exerted. (c), (d) NRI particle, where a resonance of a 1 at n rel 1.41 increases the optical forces by many orders of magnitude.

Fig. 4
Fig. 4

Same as Fig. 2 but for a / λ = 0.1 [(a), (b)] and 10 [(c), (d)].

Fig. 5
Fig. 5

C pr , x (solid blue curve) as a function of ρ 0 = x 0 for a / λ = ( a ) 0.01 , (b) 0.1, (c) 1, (d) 5, (e) 10, and (f) 20. The NRI particle and the host medium are matched ( n rel = 1 , n m = 1.33 ), and positive values represent an attractive force toward the optical axis. The Bessel intensity profile is represented by a dashed (red) curve. For (a)–(e), stable equilibrium occurs at high-intensity regions of the beam. In (f), the particle will be under stable equilibrium only when located at one of the low-intensity rings.

Fig. 6
Fig. 6

C pr , x as a function of both x 0 and n p . (a), (b) 3D views for a / λ = 0.01 with 0 < n p < 4 and 4 < n p < 0 , respectively. (c), (d) Equivalent to (a), (b) for a / λ = 20 . The dashed lines at | n p | = 1.33 ( | n rel | = 1 ) in (b), (d) correspond to the cut views (a), (f) of Fig. 5, when C pr , x = 0 for PRI particles.

Fig. 7
Fig. 7

Same as Fig. 6 but for a / λ = 0.1 [(a), (b)] and 10 [(c), (d)]. The dashed lines at | n p | = 1.33 ( | n rel | = 1 ) in (b), (d) correspond to the cut views (b), (e) of Fig. 5.

Equations (15)

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

g n , TE 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 , TM m = Z n m 2 π E 0 0 2 π G ^ [ E r ( r , θ , ϕ ) ] e i m ϕ d ϕ ,
E r , { x y } = E 0 J 0 [ sin θ a ( k r ) 2 sin 2 θ + ρ 0 2 k 2 2 ( k r ) ρ 0 sin θ cos ( ϕ ϕ 0 ) ] e i k r cos θ a cos θ sin θ { cos ϕ sin ϕ } ,
H r , { x y } = H 0 cos θ a J 0 [ sin θ a ( k r ) 2 sin 2 θ + ρ 0 2 k 2 2 ( k r ) ρ 0 sin θ cos ( ϕ ϕ 0 ) ] e i k r cos θ a cos θ sin θ { sin ϕ cos ϕ } ,
g n , TM { x y } m = { i 2 n ( n + 1 ) ( 2 n + 1 ) J 1 ( sin θ a ( n + 1 / 2 ) ) J 1 ( ρ 0 k sin θ a ) { cos ϕ 0 sin ϕ 0 } , m = 0 1 2 ( 2 i 2 n + 1 ) | m | 1 [ { 1 i } J | m | 1 ( sin θ a ( n + 1 / 2 ) ) J | m | 1 ( ρ 0 k sin θ a ) × [ cos ( | m | 1 ) ϕ 0 i sin ( | m | 1 ) ϕ 0 ] + { 1 ± i } J | m | + 1 ( sin θ a ( n + 1 / 2 ) ) J | m | + 1 ( ρ 0 k sin θ a ) × [ cos ( | m | + 1 ) ϕ 0 i sin ( | m | + 1 ) ϕ 0 ] ] , m 0 ,
a n m = g n , TM m a n = g n , TM m ψ n ( α ) ψ n ( β ) ε 0 / ε p ψ n ( α ) ψ n ( β ) ψ n ( α ) ψ n ( β ) ε 0 / ε p ψ n ( α ) ψ n ( β ) ,
b n m = g n , TE m b n = g n , TE m ε 0 / ε p ψ n ( α ) ψ n ( β ) ψ n ( α ) ψ n ( β ) ε 0 / ε p ψ n ( α ) ψ n ( β ) ψ n ( α ) ψ n ( β ) ,
C pr , z = λ 2 π n = 1 Re { 1 n + 1 ( A n g n , TM 0 g n + 1 , TM 0 * + B n g n , TE 0 g n + 1 , TE 0 * ) + m = 1 n [ 1 ( n + 1 ) 2 ( n + m + 1 ) ! ( n m ) ! ( A n g n , TM m g n + 1 , TM m * + A n g n , TM m g n + 1 , TM m * + B n g n , TE m g n + 1 , TE m * + B n g n , TE m g n + 1 , TE m * ) + m 2 n + 1 n 2 ( n + 1 ) 2 ( n + m ) ! ( n m ) ! C n ( g n , TM m g n , TE m * g n , TM m g n , TE m * ) ] } ,
C pr , x = Re [ C ] and C pr , y = Im [ C ] ,
C = λ 2 2 π n = 1 { ( 2 n + 2 ) ! ( n + 1 ) 2 F n n + 1 + m = 1 n ( n + m ) ! ( n m ) ! 1 ( n + 1 ) 2 [ F n m + 1 n + m + 1 n m + 1 F n m + 2 n + 1 n 2 ( C n g n , TM m 1 g n , TE m * C n g n , TM m g n + 1 , TE m + 1 * + C n * g n , TE m 1 g n , TM m * C n * g n , TE m g n + 1 , TM m + 1 * ) ] } ,
F n m = A n g n , TM m 1 g n + 1 , TM m * + B n g n , TE m 1 g n + 1 , TE m * + A n * g n + 1 , TM m g n , TM m + 1 * + B n * g n + 1 , TE m g n , TE m + 1 * ,
A n = a n + a n + 1 * 2 a n a n + 1 * B n = b n + b n + 1 * 2 b n b n + 1 * C n = i ( a n + b n + 1 * 2 a n b n + 1 * ) .
a n , NRI m = g n , TM m a n , NRI = g n , TM m ψ n ( α ) ψ n ( | β | ) + ε 0 / | ε p | ψ n ( α ) ψ n ( | β | ) ψ n ( α ) ψ n ( | β | ) + ε 0 / | ε p | ψ n ( α ) ψ n ( | β | ) ,
b n , NRI m = g n , TE m b n , NRI = g n , TE m ε 0 / | ε p | ψ n ( α ) ψ n ( | β | ) + ψ n ( α ) ψ n ( | β | ) ε 0 / | ε p | ψ n ( α ) ψ n ( | β | ) + ψ n ( α ) ψ n ( | β | ) ,
g n , TM m = { i 2 n ( n + 1 ) ( 2 n + 1 ) J 1 ( sin θ a ( n + 1 / 2 ) ) J 1 ( ρ 0 k sin θ a ) , m = 0 1 2 ( 2 i 2 n + 1 ) | m | 1 [ J | m | 1 ( sin θ a ( n + 1 / 2 ) ) J | m | 1 ( ρ 0 k sin θ a ) + J | m | + 1 ( sin θ a ( n + 1 / 2 ) ) J | m | + 1 ( ρ 0 k sin θ a ) ] , m 0 .

Metrics