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Numerical modeling of optical levitation and trapping of the “stuck” particles with a pulsed optical tweezers

Jian-liao Deng, Qing Wei, Yu-zhu Wang, and Yong-qing Li

Open Access Open Access

Abstract

We present the theoretical analysis and the numerical modeling of optical levitation and trapping of the stuck particles with a pulsed optical tweezers. In our model, a pulsed laser was used to generate a large gradient force within a short duration that overcame the adhesive interaction between the stuck particles and the surface; and then a low power continuous-wave (cw) laser was used to capture the levitated particle. We describe the gradient force generated by the pulsed optical tweezers and model the binding interaction between the stuck beads and glass surface by the dominative van der Waals force with a randomly distributed binding strength. We numerically calculate the single pulse levitation efficiency for polystyrene beads as the function of the pulse energy, the axial displacement from the surface to the pulsed laser focus and the pulse duration. The result of our numerical modeling is qualitatively consistent with the experimental result.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Schematics of the pulsed optical tweezers

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Fig. 2.
Fig. 2. (a) The beads were stuck on the surface. (b) The marked bead was levitated with a pulse and moved to the focus.

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Fig. 3.
Fig. 3. The position h of the bead versus time at the different pulse energy. Curve a is for E=1.1×10-5Ns/m; b for E=7×10-7Ns/m; c for E=0.

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Fig. 4.
Fig. 4. The levitation efficiency versus the E with a fixed z0=6µm andτ=45µs.

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Fig. 5.
Fig. 5. The dependence of the levitation efficiency on the displacement z0 with the fixed E=1.1×10-6Ns/m and τ=45µs.

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Fig. 6.
Fig. 6. The dependence of the levitation efficiency on the pulse duration τ with the fixed E=1.1×10-6Ns/m and z0=6µm.

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Equations (12)

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I ( x , y , z , t ) = I 0 ω 0 2 ω ( z ) 2 exp ( − 2 ( x 2 + y 2 ) ⁄ ω ( z ) 2 )
+ 2 U τ π ω 0 2 ω ( z ) 2 exp ( − ( t ⁄ τ ) 2 ) exp ( − 2 ( x 2 + y 2 ) ⁄ ω ( z ) 2 ) ,
ω ( z ) = ω 0 ( 1 + ( z ⁄ z s ) 2 ) 1 ⁄ 2 ,
F cw = − k z z ( 1 + ( z ⁄ z s ) 2 ) 2 ,
F cw = − k z z ( 1 + ( z ⁄ z s ) 2 ) 2 exp ( − ( z z s ) 4 )
F pulse = − 2 E τ π z ( 1 + ( z ⁄ z s ) 2 ) 2 exp ( − ( t ⁄ τ ) 2 ) exp ( − ( z z s ) 4 )
m z ̈ = F cw + F pulse + F S + F V ,
F V = − Aa 6 h 2 f ( p ) ,
F S = − 6 π a η λ z ˙ = − D z ˙
λ = 1 1 − 9 8 ( a h + a ) + 1 2 ( a h + a ) 3 .
p { A } = 1 2 π σ e − ( A − ζ ) 2 ⁄ 2 σ 2 ,
P { A } = 1 2 π σ ∫ − ∞ A e − ( t − ζ ) 2 ⁄ 2 σ 2 dt = Φ ( A − ζ σ ) ,
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