Abstract

The unexpected fact that a spherical dielectric particle with refractive index higher than the surrounding medium will not always be attracted towards high intensity regions of the trapping beam is fully demonstrated here using a simple ray optics approach. This unusual situation may happen due to the inversion of gradient forces, as shown here. Therefore, conventional schemes, such the one based on the use of two counter-propagating beams to cancel the scattering forces, will fail to trap the particle. However, effective trapping still can be obtained by adopting suitable incident laser beams.

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References

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  1. 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(5), 288–290 (1986).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. 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]
  4. 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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2009 (1)

2008 (1)

2007 (2)

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48(1), 15 (2007).
[CrossRef]

D. R. Burnham, G. D. Wright, N. D. Read, and D. McGloin, “Holographic and single beam optical manipulation of hyphal growth in filamentous fungi,” J. Opt. A, Pure Appl. Opt. 9(8), S172–S179 (2007).
[CrossRef]

2006 (1)

A. Virag and S. D. Harris, “The Spitzenkörper: a molecular perspective,” Mycol. Res. 110(1), 4–13 (2006).
[CrossRef]

2005 (2)

C. G. Reynaga-Peña and S. Bartnicki-García, “Cytoplasmic contractions in growing fungal hyphae and their morphogenetic consequences,” Arch. Microbiol. 183(4), 292–300 (2005).
[CrossRef] [PubMed]

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]

2004 (1)

1997 (1)

1996 (1)

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

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]

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]

1986 (1)

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.

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48(1), 15 (2007).
[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]

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(5), 288–290 (1986).
[CrossRef] [PubMed]

Bartnicki-García, S.

C. G. Reynaga-Peña and S. Bartnicki-García, “Cytoplasmic contractions in growing fungal hyphae and their morphogenetic consequences,” Arch. Microbiol. 183(4), 292–300 (2005).
[CrossRef] [PubMed]

Berns, M. W.

W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photo-refractive phase conjugation,” J. Opt. Soc. Am. B 14(4), 697–704 (1997).
[CrossRef]

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]

Bjorkholm, J. E.

Burnham, D. R.

D. R. Burnham, G. D. Wright, N. D. Read, and D. McGloin, “Holographic and single beam optical manipulation of hyphal growth in filamentous fungi,” J. Opt. A, Pure Appl. Opt. 9(8), S172–S179 (2007).
[CrossRef]

Bustamante, C.

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

Chiou, A. E.

Chu, S.

Cojoc, D.

Coppey-Moisan, M.

Cui, Y.

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

Daria, V. R.

Di Fabrizio, E.

Dogterom, M.

Durieux, C.

Dziedzic, J. M.

Emiliani, V.

Ferrari, E.

Garbin, V.

Glückstad, J.

Harris, S. D.

A. Virag and S. D. Harris, “The Spitzenkörper: a molecular perspective,” Mycol. Res. 110(1), 4–13 (2006).
[CrossRef]

Hernández-Figueroa, H. E.

McGloin, D.

D. R. Burnham, G. D. Wright, N. D. Read, and D. McGloin, “Holographic and single beam optical manipulation of hyphal growth in filamentous fungi,” J. Opt. A, Pure Appl. Opt. 9(8), S172–S179 (2007).
[CrossRef]

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]

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(1), 15 (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. U.S.A. 86(12), 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(1), 15 (2007).
[CrossRef]

D. R. Burnham, G. D. Wright, N. D. Read, and D. McGloin, “Holographic and single beam optical manipulation of hyphal growth in filamentous fungi,” J. Opt. A, Pure Appl. Opt. 9(8), S172–S179 (2007).
[CrossRef]

Reynaga-Peña, C. G.

C. G. Reynaga-Peña and S. Bartnicki-García, “Cytoplasmic contractions in growing fungal hyphae and their morphogenetic consequences,” Arch. Microbiol. 183(4), 292–300 (2005).
[CrossRef] [PubMed]

Rodrigo, P. J.

Smith, S. B.

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

Sonek, G. J.

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]

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.

Virag, A.

A. Virag and S. D. Harris, “The Spitzenkörper: a molecular perspective,” Mycol. Res. 110(1), 4–13 (2006).
[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]

Wang, W.

Wright, G. D.

D. R. Burnham, G. D. Wright, N. D. Read, and D. McGloin, “Holographic and single beam optical manipulation of hyphal growth in filamentous fungi,” J. Opt. A, Pure Appl. Opt. 9(8), S172–S179 (2007).
[CrossRef]

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48(1), 15 (2007).
[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)

Arch. Microbiol. (1)

C. G. Reynaga-Peña and S. Bartnicki-García, “Cytoplasmic contractions in growing fungal hyphae and their morphogenetic consequences,” Arch. Microbiol. 183(4), 292–300 (2005).
[CrossRef] [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. A, Pure Appl. Opt. (1)

D. R. Burnham, G. D. Wright, N. D. Read, and D. McGloin, “Holographic and single beam optical manipulation of hyphal growth in filamentous fungi,” J. Opt. A, Pure Appl. Opt. 9(8), S172–S179 (2007).
[CrossRef]

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

Mycol. Res. (1)

A. Virag and S. D. Harris, “The Spitzenkörper: a molecular perspective,” Mycol. Res. 110(1), 4–13 (2006).
[CrossRef]

Mycoscience (1)

G. D. Wright, J. Arlt, W. C. K. Poon, and N. D. Read, “Experimentally manipulating fungi with optical tweezers,” Mycoscience 48(1), 15 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

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 (2)

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

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

Other (2)

N. D. Read, Fungal Cell Biology Group, Institute of Cell Biology, University of Edinburgh, Rutherford Building, Edinburgh EH9 3JH, UK (personal communication, 2009).

W. Poon, School of Physics & Astronomy, University of Edinburgh, Edinburgh, EH9 3JZ, UK (personal communication, 2009).

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Figures (6)

Fig. 1
Fig. 1

(a). Ray optics analysis showing an incident ray R1 and its first two refracted rays R2 and R3. Looking at the momentum transfer without considering the infinite series of refracted/reflected rays which appears as a consequence of R1 leads to an erroneous interpretation and to the conclusion that the particle would experience a force directed to the high intensity region, i.e., to the centre of the beam. (b). the complete picture taking into account the infinite series of refracted/reflected rays.

Fig. 2
Fig. 2

Reflectivity for nm = 1.33 and np = 1.6, 2.4, 3.2 and 4.0 for (a) perpendicular polarization and (b) parallel polarization. If the laser is designed for case (b), then the incident rays can be chosen so that only the contribution of those with incidence angles close to regions of low reflectivity are relevant.

Fig. 3
Fig. 3

(a) Gradient Force (normalized over nmP/c) for a single ray and its dependence on both incident angle and refractive index. (b) The equivalent contour plot, emphasizing the gradient zero-force line. As the refractive index increases, Fg becomes positive, i.e., repulsive, indicating the trapping impossibility.

Fig. 4
Fig. 4

Gradient (a) and scattering (b) total forces for a circularly polarized TEM00 Gaussian beam as functions of the distance r between the centre of the particle and the beam focus when both are on a horizontal plane perpendicular to the optical axis of the beam. The attractive/repulsive pattern depends on the value of the refractive index np for a fixed nm.

Fig. 5
Fig. 5

(a). Coordinate system for total force numerical calculations. (b) Scattering factor QS and (c) gradient factor Qg as functions of the angle γ between the optical axis of the beam and the vector connecting its focus to the centre of the particle. Higher repulsive scattering total forces are seen as np increases, whereas the gradient total forces become repulsive.

Fig. 6
Fig. 6

Gradient total forces profile for a particle in a zero-order Bessel beam with λ = 1064 nm and a spot of 28.89 μm. The particle has a radius of a = 10.64 μm. For np = 8.0, points at r/a = 2.8 and 6.3 become points of stable equilibrium, and the use of two counter propagating Bessel beams present themselves as excellent alternatives for trapping these high refractive index particles.

Equations (2)

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F S = n m c P n m P R c cos ( π + 2 θ i ) l = 0 n m P c T 2 R l cos ( α + l β ) = n m P c { 1 + R cos 2 θ i T 2 [ cos ( 2 θ i 2 θ t ) + R cos 2 θ i ] 1 + R 2 + 2 R cos 2 θ t } = n m P c Q S ,
F g = n m P R c sin ( π + 2 θ i ) l = 0 n m P c T 2 R l sin ( α + l β ) = n m P 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 } = n m P c Q g ,

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