Abstract

Ordinary Bessel beams are described in terms of the generalized Lorenz-Mie theory (GLMT) by adopting, for what is to our knowledge the first time in the literature, the integral localized approximation for computing their beam shape coefficients (BSCs) in the expansion of the electromagnetic fields. Numerical results reveal that the beam shape coefficients calculated in this way can adequately describe a zero-order Bessel beam with insignificant difference when compared to other relative time-consuming methods involving numerical integration over the spherical coordinates of the GLMT coordinate system, or quadratures. We show that this fast and efficient new numerical description of zero-order Bessel beams can be used with advantage, for example, in the analysis of optical forces in optical trapping systems for arbitrary optical regimes.

© 2011 OSA

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  2. G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
  3. 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).
  4. 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).
  5. G. Gouesbet, G. Gréhan, and B. Maheu, “On the generalized Lorenz-Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).
  6. 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(6), 998–1007 (1990).
    [CrossRef]
  7. K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
    [CrossRef] [PubMed]
  8. J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
    [CrossRef]
  9. G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: A perspective,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1223–1238 (2009).
    [CrossRef]
  10. G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
    [CrossRef]
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    [CrossRef]
  13. 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(9), 2516–2525 (1994).
    [CrossRef]
  14. 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(4-6), 343–354 (1994).
    [CrossRef]
  15. H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1-3), 169–179 (1998).
    [CrossRef]
  16. 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(5), 1284–1301 (2010).
    [CrossRef] [PubMed]
  17. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
    [CrossRef]
  18. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
    [CrossRef] [PubMed]
  19. V. Garcés-Chávez, 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(18), 4001–4003 (2004).
    [CrossRef]
  20. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
    [CrossRef] [PubMed]
  21. A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003).
    [CrossRef]
  22. G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15(21), 13972–13987 (2007).
    [CrossRef] [PubMed]
  23. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
  28. F. Corbin, G. Gréhan, and G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Sys. Characterization. 8(1-4), 222–228 (1991).
    [CrossRef]
  29. G. Gouesbet, J. A. Lock, and G. Gréhan, “Partial-wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34(12), 2133–2143 (1995).
    [CrossRef] [PubMed]
  30. G. Gouesbet, “Validity of the localized approximations for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am. A 16(7), 1641–1650 (1999).
    [CrossRef]

2011 (1)

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[CrossRef]

2010 (1)

2009 (2)

J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
[CrossRef]

G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: A perspective,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1223–1238 (2009).
[CrossRef]

2007 (1)

2004 (2)

V. Garcés-Chávez, 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(18), 4001–4003 (2004).
[CrossRef]

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

2003 (1)

A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003).
[CrossRef]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[CrossRef]

1999 (1)

1998 (2)

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
[CrossRef] [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(1-3), 169–179 (1998).
[CrossRef]

1995 (1)

1994 (4)

1991 (1)

F. Corbin, G. Gréhan, and G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Sys. Characterization. 8(1-4), 222–228 (1991).
[CrossRef]

1990 (1)

1989 (1)

G. Gouesbet, G. Gréhan, and B. Maheu, “On the generalized Lorenz-Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).

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)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

1982 (1)

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

1908 (1)

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–452 (1908).
[CrossRef]

Afanas’ev, A. A.

A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003).
[CrossRef]

Ambrosio, L. A.

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[CrossRef]

Block, S. M.

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

Corbin, F.

F. Corbin, G. Gréhan, and G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Sys. Characterization. 8(1-4), 222–228 (1991).
[CrossRef]

Dholakia, K.

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15(21), 13972–13987 (2007).
[CrossRef] [PubMed]

V. Garcés-Chávez, 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(18), 4001–4003 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 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(4-6), 239–245 (2001).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Ermolaev, I. E.

A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003).
[CrossRef]

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[CrossRef]

Garcés-Chávez, V.

V. Garcés-Chávez, 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(18), 4001–4003 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Gouesbet, G.

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[CrossRef]

G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: A perspective,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1223–1238 (2009).
[CrossRef]

J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
[CrossRef]

G. Gouesbet, “Validity of the localized approximations for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am. A 16(7), 1641–1650 (1999).
[CrossRef]

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1-3), 169–179 (1998).
[CrossRef]

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

G. Gouesbet, J. A. Lock, and G. Gréhan, “Partial-wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34(12), 2133–2143 (1995).
[CrossRef] [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(9), 2516–2525 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11(6), 1812–1817 (1994).
[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(9), 2503–2515 (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(4-6), 343–354 (1994).
[CrossRef]

F. Corbin, G. Gréhan, and G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Sys. Characterization. 8(1-4), 222–228 (1991).
[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(6), 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, and B. Maheu, “On the generalized Lorenz-Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).

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).

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

Gréhan, G.

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[CrossRef]

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998).
[CrossRef] [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(1-3), 169–179 (1998).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Partial-wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34(12), 2133–2143 (1995).
[CrossRef] [PubMed]

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(4-6), 343–354 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11(6), 1812–1817 (1994).
[CrossRef]

F. Corbin, G. Gréhan, and G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Sys. Characterization. 8(1-4), 222–228 (1991).
[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(6), 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, and B. Maheu, “On the generalized Lorenz-Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).

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).

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

Hernández-Figueroa, H. E.

Kurochkin, Y. A.

A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003).
[CrossRef]

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(6), 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, and B. Maheu, “On the generalized Lorenz-Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).

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).

McGloin, D.

G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15(21), 13972–13987 (2007).
[CrossRef] [PubMed]

V. Garcés-Chávez, 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(18), 4001–4003 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garcés-Chávez, 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(18), 4001–4003 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–452 (1908).
[CrossRef]

Mikhnevich, S. Y.

A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003).
[CrossRef]

Milne, G.

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef] [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(1-3), 169–179 (1998).
[CrossRef]

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).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11(6), 1812–1817 (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(4-6), 343–354 (1994).
[CrossRef]

Roskey, D.

V. Garcés-Chávez, 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(18), 4001–4003 (2004).
[CrossRef]

Rubinov, A. N.

A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003).
[CrossRef]

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 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(4-6), 239–245 (2001).
[CrossRef]

Summers, M. D.

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[CrossRef]

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Wright, E. M.

V. Garcés-Chávez, 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(18), 4001–4003 (2004).
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V. Garcés-Chávez, 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(18), 4001–4003 (2004).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Geometrical description of an ordinary Bessel beam propagating parallel to + z (out of the page). The optical axis makes an angle ϕ 0 relative to the x-axis and is displaced ρ 0 from the origin O of the coordinate system.

Fig. 2
Fig. 2

Ex -field intensity profile for a Bessel beam with λ = 1064 nm, θa = 0.0141 rad and displaced (a) ρ 0 = 0, (b) ρ 0 = 30 μm, (c) ρ 0 = 60 μm and (d) ρ 0 = 90 μm along x. The accuracy of the ILA for increasing x depends on increasing the number of BSCs entering superposition (18) and (19). In all cases, mmax = 15.

Fig. 3
Fig. 3

(a) 3D and (b) 2D Ey-field intensity profile for an on-axis x-polarized Bessel beam with λ = 500 nm, Δρ = 10.0 μm (θa ≈ 1.1°). The Fortran code was run by imposing nmax = 1800 (non-zero BSCs occur only for |m| = 1). (c) and (d) are the corresponding Ez-field.

Fig. 4
Fig. 4

.a) 3D and (b) 2D Ey-field intensity profile for an off-axis (ρ0 = 5 μm and ϕ0 = π/2) x-polarized Bessel beam with λ = 532 nm, Δρ = 2.336 μm (θa = 5°, representing a limiting angle for the paraxial approximation). The Fortran code was run by imposing nmax = and mmax = 15. (c) and (d) show the corresponding Ez-field.

Fig. 5
Fig. 5

Normalized force profile exerted on a dielectric simple particle of relative refractive index nrel = 1.1. The field intensity of the zero-order Bessel beam is also shown as a solid line. All parameters of the incident beam are the same as those of Fig. 2. Positive Fx/Fmax means an attractive force towards the optical axis of the beam.

Fig. 6
Fig. 6

Radiation pressure cross-section Cpr,x (solid) for an x-polarized Bessel beam displaced along x using the ILA. The beam has λ = 802.7 nm and Δρ ≈2.35 μm in water (nm = 1.33). The beam intensity is shown as a dotted line. The silicon spheres have a refractive index np = 1.4496 and radii a = 1.15 μm (a), 2.15 μm (b), 2.50 μm (c) and 3.42 μm (d). Points of stable equilibrium are close to those predicted in Ref. [21], where a quadrature scheme was adopted for numerically implementing the GLMT.

Tables (2)

Tables Icon

Table 1 Beam-shape coefficients g n , T M 1 evaluated by quadratures (methods F1 and F2) and using the integral localized approximation ILA for an on-axis (ρ 0 = ϕ 0 = 0) zero-order Bessel beam with λ = 1064 nm and θa = 0.0141 rad a

Tables Icon

Table 2 Elapsed time (in seconds) for computing the BSC’s g n , T M 1 of an on-axis (ρ 0 = ϕ 0 = 0) zero-order Bessel beam with λ = 1064 nm and θa = 0.0141 rad a

Equations (19)

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E ( ρ , ϕ , z ) = { x ^ y ^ } E 0 J 0 ( k ρ ρ 2 + ρ 0 2 2 ρ ρ 0 cos ( ϕ ϕ 0 ) ) e i k z z
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 , T E m = Z n m 2 π H 0 0 2 π G ^ [ H r ( r , θ , ϕ ) ] exp ( 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 ) ] exp ( i m ϕ ) d ϕ
Z n 0 = 2 n ( n + 1 ) i 2 n + 1 ,              m = 0
Z n m = ( 2 i 2 n + 1 ) | m | 1 ,             m 0.
g n , T M 0 { x y } = i 2 n ( n + 1 ) 2 π ( 2 n + 1 ) 0 2 π J 0 [ sin θ a ( n + 1 / 2 ) 2 + ρ 0 2 k 2 2 ( n + 1 / 2 ) ρ 0 cos ( ϕ ϕ 0 ) ] { cos ϕ sin ϕ } d ϕ
J 0 [ ϖ 2 + ξ 2 2 ϖ ξ cos ( ϕ ϕ 0 ) ] = p = 0 ε p J p ( ϖ ) J p ( ξ ) cos [ p ( ϕ ϕ 0 ) ]
g n , T M 0 { x y } = i 2 n ( n + 1 ) 2 π ( 2 n + 1 ) 0 2 π p = 0 ε p J p ( sin θ a ( n + 1 / 2 ) ) J p ( ρ 0 k sin θ a ) cos [ p ( ϕ ϕ 0 ) ] { cos ϕ sin ϕ } d ϕ = i 2 n ( n + 1 ) 2 π ( 2 n + 1 ) p = 0 ε p J p ( sin θ a ( n + 1 / 2 ) ) J p ( ρ 0 k sin θ a ) 0 2 π cos [ p ( ϕ ϕ 0 ) ] { cos ϕ sin ϕ } d ϕ = i 2 n ( n + 1 ) 2 π ( 2 n + 1 ) p = 0 ε p J p ( sin θ a ( n + 1 / 2 ) ) J p ( ρ 0 k sin θ a ) { cos p ϕ 0 0 2 π { cos ( p 1 ) ϕ + cos ( p + 1 ) ϕ 2 0 } d ϕ + sin p ϕ 0 0 2 π { 0 cos ( p 1 ) ϕ cos ( p + 1 ) ϕ 2 } d ϕ } = 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 } ,
g n , T M m 0 { x y } = 1 2 π ( 2 i 2 n + 1 ) | m | 1 p = 0 ε p J p ( sin θ a ( n + 1 / 2 ) ) J p ( ρ 0 k sin θ a ) [ cos p ϕ 0 0 2 π { cos p ϕ cos m ϕ cos ϕ i cos p ϕ sin m ϕ sin ϕ } d ϕ + sin p ϕ 0 0 2 π { i sin p ϕ sin m ϕ cos ϕ sin p ϕ cos m ϕ sin ϕ } d ϕ ]
            = 1 2 π ( 2 i 2 n + 1 ) | m | 1 p = 0 ε p J p ( sin θ a ( n + 1 / 2 ) ) J p ( ρ 0 k sin θ a ) [ cos p ϕ 0 0 2 π { cos p ϕ cos | m | ϕ cos ϕ i cos p ϕ sin | m | ϕ sin ϕ } d ϕ + sin p ϕ 0 0 2 π { i sin p ϕ sin | m | ϕ cos ϕ sin p ϕ cos | m | ϕ sin ϕ } d ϕ ]             = 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 ] ] ,
g n , T E 0 { x y } = i 2 n ( n + 1 ) ( 2 n + 1 ) J 1 ( sin θ a ( n + 1 / 2 ) ) J 1 ( ρ 0 k sin θ a ) { sin ϕ 0 cos ϕ 0 } ,
g n , T E m 0 { x y } = 1 2 ( 2 i 2 n + 1 ) | m | 1 [ { i 1 } 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 ] + { ± i 1 } 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 ] ] ,
g n , T E m = 1 4 π ( i n 1 ) R j n ( R ) ( n | m | ) ! ( n + | m | ) ! 0 π sin θ d θ 0 2 π d ϕ P ( cos θ ) n | m | exp ( i m ϕ ) H r ( R , θ , ϕ ) H 0
g n , T M m = 1 4 π ( i n 1 ) R j n ( R ) ( n | m | ) ! ( n + | m | ) ! 0 π sin θ d θ 0 2 π d ϕ P ( cos θ ) n | m | exp ( i m ϕ ) E r ( R , θ , ϕ ) E 0
E r ( R , θ , ϕ ) = i E 0 n = 1 ( i ) n ( 2 n + 1 ) j n ( R ) R m = n n g n , T M m π n | m | ( θ ) sin θ exp ( i m ϕ )
E θ ( R , θ , ϕ ) = E 0 n = 1 ( i ) n ( 2 n + 1 ) n ( n + 1 ) { j n ( R ) m = n n g n , T E m i m π n | m | ( θ ) exp ( i m ϕ ) + i [ j n 1 ( R ) n R j n ( R ) ] m = n n g n , T M m τ n | m | ( θ ) exp ( i m ϕ ) } E ϕ ( R , θ , ϕ ) = E 0 n = 1 ( i ) n ( 2 n + 1 ) n ( n + 1 ) { j n ( R ) m = n n g n , T E m τ n | m | ( θ ) exp ( i m ϕ ) + i [ j n 1 ( R ) n R j n ( R ) ] m = n n g n , T M m i m π n | m | ( θ ) exp ( i m ϕ ) }
E x ( x , y , z ) = { E r ( r = | x | = | ρ 0 | , θ = π 2 , ϕ = 0 ) ,          i f   x > 0 E r ( r = | x | = | ρ 0 | , θ = π 2 , ϕ = π ) ,       i f   x < 0

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