Abstract

Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geo-metrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n| > 1 to |n| < 1, thus revealing new and interesting trapping properties.

© 2010 OSA

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  1. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
    [CrossRef] [PubMed]
  2. R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
    [CrossRef] [PubMed]
  3. 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. U.S.A. 86(12), 4539–4543 (1989).
    [CrossRef] [PubMed]
  4. V. Emiliani, D. Cojoc, E. Ferrari, V. Garbin, C. Durieux, M. Coppey-Moisan, and E. Di Fabrizio, “Wave front engineering for microscopy of living cells,” Opt. Express 13(5), 1395–1405 (2005).
    [CrossRef] [PubMed]
  5. 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).
    [CrossRef] [PubMed]
  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. A. van der Horst, P. D. J. van Oostrum, A. Moroz, A. van Blaaderen, and M. Dogterom, “High trapping forces for high-refractive index particles trapped in dynamic arrays of counterpropagating optical tweezers,” Appl. Opt. 47(17), 3196–3202 (2008).
    [CrossRef] [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).
    [CrossRef] [PubMed]
  9. 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).
    [CrossRef] [PubMed]
  10. 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 (to be published).
    [PubMed]
  11. 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]
  12. 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]
  13. 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]
  14. V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
    [CrossRef]
  15. L. A. Ambrosio, and H. E. Hernández-Figueroa are preparing a manuscript to be called “Integral localized approximation description of ordinary Bessel beams in the generalized Lorenz-Mie theory and application to optical forces.”
  16. L. A. Ambrosio, and H. E. Hernández-Figueroa, “Integral localized approximation description of v-th order Bessel beams in the generalized Lorenz-Mie theory and applications to optical trapping,” in Proceedings of PIERS2011in Marrakesh (to be published).

2010 (1)

2009 (1)

2008 (1)

2005 (1)

2004 (1)

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]

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]

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).
[CrossRef] [PubMed]

1991 (1)

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

1987 (1)

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

1968 (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

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]

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).
[CrossRef] [PubMed]

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

Berns, M. W.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
[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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

Cheng, S.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
[CrossRef] [PubMed]

Cojoc, D.

Coppey-Moisan, M.

Dholakia, K.

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]

Di Fabrizio, E.

Dogterom, M.

Durieux, C.

Dziedzic, J. M.

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

Emiliani, V.

Ferrari, E.

Garbin, V.

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.

Gréhan, G.

Hernández-Figueroa, H. E.

Maheu, B.

McGloin, 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]

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]

Moroz, A.

Numajiri, Y.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
[CrossRef] [PubMed]

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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

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]

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]

Steubing, R. W.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
[CrossRef] [PubMed]

Summers, M. 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]

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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

van Blaaderen, A.

van der Horst, A.

van Oostrum, P. D. J.

Veselago, V. G.

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

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).
[CrossRef]

Wright, W. H.

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
[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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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]

Biomed. Opt. Express (1)

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 (to be published).
[PubMed]

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).
[CrossRef] [PubMed]

Cytometry (1)

R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12(6), 505–510 (1991).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Nature (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]

Opt. Commun. (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]

Opt. Express (3)

Proc. Natl. Acad. Sci. U.S.A. (1)

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. U.S.A. 86(12), 4539–4543 (1989).
[CrossRef] [PubMed]

Science (1)

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

Sov. Phys. Usp. (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Other (2)

L. A. Ambrosio, and H. E. Hernández-Figueroa are preparing a manuscript to be called “Integral localized approximation description of ordinary Bessel beams in the generalized Lorenz-Mie theory and application to optical forces.”

L. A. Ambrosio, and H. E. Hernández-Figueroa, “Integral localized approximation description of v-th order Bessel beams in the generalized Lorenz-Mie theory and applications to optical trapping,” in Proceedings of PIERS2011in Marrakesh (to be published).

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Figures (6)

Fig. 2
Fig. 2

A v = 0 Bessel beam (solid line) and Fg for several values of n (np ). The surrounding media has nm = 1.33. Note that, as expected, in trapping DPS spherical particles, Fg inverts sign when n goes from n < 1 to n > 1.

Fig. 1
Fig. 1

Coordinate system for trapping a DNG spherical particle using a v-th order Bessel beam.

Fig. 3
Fig. 3

Same results as in Fig. 2 for a DNG particle. For all five relative refractive indices depicted, the points of stable equilibrium are about the same, located at distances close to nulls of intensity (again, the intensity profile is shown as a solid line).

Fig. 4
Fig. 4

A v = 3 Bessel beam (solid line) and Fx for four values of n. Again, nm = 1.33. Negative values of Fx means a gradient force pulling the particle towards the optical axis of the beam. For a DPS particle, the points of stable equilibrium depends upon n being higher or less (but higher than zero) than one.

Fig. 5
Fig. 5

A v = 3 Bessel beam (solid line) and Fx for four values of n. Again, nm = 1.33. For this DNG particle, points of stable equilibrium are seen at ρ 0 ≈0, 76, 117 μm regardless of |n| being higher or less than one.

Fig. 6
Fig. 6

(a) Fx as a function of the displacement ρ 0 and n for a particle of radius a = 10λ, where λ = 1064 nm is the wavelength of our zero-order Bessel beam with an axicon angle θ = 0.0141 rad (spot of Δρ = 28.89 μm). (b) A contour plot of (a).

Equations (2)

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P ( r , θ , ϕ ) = | J v ( k ρ r 2 sin 2 θ + ρ 0 2 2 r ρ 0 sin θ cos ( ϕ ϕ 0 ) ) | 2
F g = n m P ( r , θ , ϕ ) c { R sin 2 θ i T 2 [ sin ( 2 θ i + 2 θ t ) + R sin 2 θ i ] 1 + R 2 + 2 R cos 2 θ t }

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