Abstract

A tightly focused, linearly polarized laser beam, so-called optical tweezers, is proven to be a useful micromanipulation tool. It is known that there is a stiffness asymmetry in the direction perpendicular to the optical axis inherited from the polarization state of the laser. In this Letter, we report our experimental results of stiffness asymmetry for different bead sizes measured at the optimal trapping condition. We also provide the results of our generalized Lorenz–Mie based calculations, which are in good agreement with our experimental results. We also compare our results with previous reports.

© 2012 Optical Society of America

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2011

S. N. S. Reihani, S. A. Mir, A. C. Richardson, and L. B. Oddershede, J. Opt. 13, 105301 (2011).
[CrossRef]

A. Mahmoudi and S. N. S. Reihani, Opt. Express 19, 14794 (2011).
[CrossRef]

2010

P. M. Bendix, S. N. S. Reihani, and L. B. Oddershede, ACS Nano 4, 2256 (2010).
[CrossRef]

2007

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

S. N. S. Reihani and L. B. Oddershede, Opt. Lett. 32, 1998 (2007).
[CrossRef]

F. Borghese, P. Denti, R. Saija, and M. A. Iatí, Opt. Express 15, 11984 (2007).
[CrossRef]

2006

2005

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef]

2004

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

1986

Ashkin, A.

Bendix, P. M.

P. M. Bendix, S. N. S. Reihani, and L. B. Oddershede, ACS Nano 4, 2256 (2010).
[CrossRef]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Bjorkholm, J. E.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Borghese, F.

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Chu, S.

Denti, P.

Dziedzic, J. M.

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Hansen, T. M.

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef]

Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Iatí, M. A.

Knöner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Mahmoudi, A.

Mansuripur, M.

Mir, S. A.

S. N. S. Reihani, S. A. Mir, A. C. Richardson, and L. B. Oddershede, J. Opt. 13, 105301 (2011).
[CrossRef]

Moloney, J. V.

Nieminen, T. A.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Oddershede, L. B.

S. N. S. Reihani, S. A. Mir, A. C. Richardson, and L. B. Oddershede, J. Opt. 13, 105301 (2011).
[CrossRef]

P. M. Bendix, S. N. S. Reihani, and L. B. Oddershede, ACS Nano 4, 2256 (2010).
[CrossRef]

S. N. S. Reihani and L. B. Oddershede, Opt. Lett. 32, 1998 (2007).
[CrossRef]

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef]

Polynkin, P.

Reihani, S. N. S.

A. Mahmoudi and S. N. S. Reihani, Opt. Express 19, 14794 (2011).
[CrossRef]

S. N. S. Reihani, S. A. Mir, A. C. Richardson, and L. B. Oddershede, J. Opt. 13, 105301 (2011).
[CrossRef]

P. M. Bendix, S. N. S. Reihani, and L. B. Oddershede, ACS Nano 4, 2256 (2010).
[CrossRef]

S. N. S. Reihani and L. B. Oddershede, Opt. Lett. 32, 1998 (2007).
[CrossRef]

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef]

Richardson, A. C.

S. N. S. Reihani, S. A. Mir, A. C. Richardson, and L. B. Oddershede, J. Opt. 13, 105301 (2011).
[CrossRef]

Rohrbach, A.

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef]

Rubinsztein-Dunlop, H.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Saija, R.

Sørensen, M. A.

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef]

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Zakharian, A. R.

ACS Nano

P. M. Bendix, S. N. S. Reihani, and L. B. Oddershede, ACS Nano 4, 2256 (2010).
[CrossRef]

J. Opt.

S. N. S. Reihani, S. A. Mir, A. C. Richardson, and L. B. Oddershede, J. Opt. 13, 105301 (2011).
[CrossRef]

J. Opt. A

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef]

Proc. Natl. Acad. Sci. USA

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef]

Rev. Sci. Instrum.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Typical power spectrum of the recorded positional signals at the optimal depth. The corner frequency for x, y, and z directions are 1013, 998, and 332 Hz, respectively. (b) Variation of the trap stiffness as a function of depth for 0.8 μm bead. The solid lines represent Gaussian fit to the data points. The laser power was 27 mW at the sample.

Fig. 2.
Fig. 2.

(a) Lateral and axial cross section of the intensity profile at the focus. The side graphs quantitatively show the spatial variation of the intensity. (b) Stiffness as a function of depth for 0.8 μm polystyrene bead.

Fig. 3.
Fig. 3.

Lateral asymmetry as a function of bead size. Vertical (horizontal) error bars represent standard deviation of the measured values (bead sizes based on the company reports).

Tables (1)

Tables Icon

Table 1. Measured Trap Stiffnesses (Normalized to Laser Power at the Focus; fNnm·mW) in the x (Polarization), y, and z Directions for Different Bead Sizesa

Equations (2)

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E=in1k0f2πein1k0fE0n0n10α02πdθ1dϕsinθ1cosθ1exp(1f02sin2θ1sin2α)Esampleexp[in1k0sinθ1(xcosϕ+ysinϕ)]exp[in4k0cosθ4]exp[in1k0(t2+t3+t4)cosθ1]exp[ik0(n2t2cosθ2+n3t3cosθ3+n4t4cosθ4)],
FζScat=2|E0|216πkv2ReplmplmAlm(p)*Alm(p)illIζ,lmlmppFζExt=2|E0|216πkv2ReplmplmWIlm(p)*Alm(p)illIζ,lmlmppFζ=FζScat+FζExt.

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