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The influence of the mechanical parameters as the radius of dielectric particle, viscosity of surrounding fluid on the usefulness of optical trap using pulsed Gaussian beam is simulated

The Influence of Parameters of the Dielectric and Fluid

on Usefulness of the Optical Trap

Ho Quang Quy 1 , Hoang Dinh Hai 2 , Phan Si Chau 3 , Do Ich Tinh 3 , Doan Hoai Son 3 , Mai Van Luu 3

1 Institute of Applied Physics, NEWTECHPRO, VAST, 8 Hoang Quoc Viet, Hano, Vietnam.

hoquy1253@yahoo.com

2 Pedagogical College of Nghe An, Vietnam.

3 Faculty of Physics, Vinh University, Vietnam.

Abstract: In this article the stable process of the dielectric particle in optical trap is

investigated The influence of the mechanical parameters as the radius of dielectric particle, viscosity of surrounding fluid on the usefulness of optical trap using pulsed Gaussian beam is simulated and discussed.

Key words: Optical trap, Pulsed Gaussian beam, Optical force, Brownian motion.

1 Introduction

In 1970, Ashkin [1] first demonstrated the optical trapping of particles using the radiation force produced by the focused continuous-wave (CW) Gaussian beam Since then the optical trap and tweezers has been a powerful tool for manipulating dielectric particles [2, 3]

In works [4-7], the discussions about stability of the optical trap and the tweezers as well as the effectively controlling dielectric particles like gold nanoparticles and live membrane, have been conducted taking into account of Brownian force But, the stabilizing process during the pulsing of the optical beam and the absolutely-stable conditions of dielectric particles were not clear Therefore, it is desirable to advance the studies of above questions for the pulsing optical trap

Up to now, we have paid attention to optical trap using counter-propagating pulsed Gaussian beams [8] and after discussing about its stability in general, but not in detail

So, in this paper the stable process during pulsing time of optical tweezer using pulsed Gaussian beam and influence of mechanical parameters on its stability and usefulness are interested This paper is organized as follows: In Sec II we introduce the set of Langevin equations concerning thermal fluctuations of the probe with appearance of the Gradient optical force acting on dielectric nano particles in the optical tweezer pulsed Gaussian beams (PGB),; In section III, we present the radial variances of glass nano particles in water, which are trapped by picoseconds PGB and the discussions about stability of them and usefulness of tweezer

2 Theory

Two PGBs with the total energy, U, duration time, τ, and beam waist, W 0 , are considered to trap fluctuating dielectric nano particles with radius, a, refractive index, n1 in

the fluid with viscosity, γ, and refractive index n2 , which is placed at z=0 (Fig.1) We consider the gradient optical force is induced by PGB acting on a Rayleigh dielectric particle The polarization direction of the electric field is assumed to be along the xaxis

For simplicity, we assume that the radius (a) of the particle is much smaller than the

point dipole We also assume that the refractive index of the dielectric particle is n1 and

2

n >>

Assuming a low Reynold's number regime [9], the Brownian motion of the dielectric in the optical force field is described by a set of Langevin equations as follows:

( )t F grad,ρ ( )t 2D h t( )

where ρr( )t = x t y t( ) ( ),  is the dielectric particle’s position in the fluid plate, γ =6 aπ η is

its friction coefficient, η is the fluid viscosity, 2D h tγ r( ) = 2D h t h tγ  x( ) ( ), y  is a vector

of independent white Gaussian random processes describing the Brownian force forces,

/

B

D k T= γ is the diffusion coefficient, T is the absolute temperature, and k B is the Boltzmann constant, Fgrad, ρ is the gradient optical force acting on dielectric particle, which is given by [4,8]

where is the scattering cross section, 4 3[ ( 2 1) (/ 2 2) ]

0

2

ρ ˆ is the unit radial vector, ρ ρ % = /W0, W0 is the waist radius of Gaussian beam at the plane

0

z= ,m=n1/ n2, and I is the intensity distribution for the PGB as follows [4]:

[ 2~2] [exp 2~ 2]

exp )

where ( )3/ 2 2

0

2 2 /

P= U  π W τ 

 , and ~ t t = / τ, , k =2π/λ is the wave number

We compute the two-dimensional motion and the radial variance (position) of a dielectric particle in fluid using the Brownian dynamic simulation method A particle/bead-spring model is employed to represent the dielectric particle, and the following equation of motion is computed for each particle:

Fig 1 (a) The schematic of optical trap.

(b) The motion with radial variance of particle in the fluid plate.

Pulsed laser beam Focus lens

Radial Variance ρ

Z

Y

( ) ( ) , ( ( ) ) ( ) ( )

2

grad

γ

r

where δt is the time increment of the simulation, h tr( ) is a random vector whose components are chosen from the range [-1, 1] in each time step Frgrad,ρ(ρr( )t ) in Eq (2)

describes the gradient optical force acting on the particle located at position ρ at time t For example, at beginning time t=0, the dielectric particle is assumed to locate at the position

(t 0) W0

ρ = = , where W0 is the beam waist, then we understand that the gradient optical force Fgrad,ρ(W0,t) acts on the particle, which will be located at position W+ ∆ρ after a

time incrementδt

3 Simulated Results

We interest only on the radial variance of glass particle in the pulsing time (this parameter describes the stability of particle), so the simulation will be computed from

beginning moment t=-3τ (or t=0) to ending moment t=3τ (or t=6τ) of the optical pulse In

following numerical simulation we choose fixed parameters as follows: The laser beam with wavelength, λ = 1 064 µm, duration, τ = 1ps, beam waist, U = 0 1 µJ , total energy,

J

U = 0 1 µ ; The glass particle with refractive index, n1 = 1 592, radius, a= ( 2 ÷ 20 )nm; The fluids have been changed from alcohol methyl with viscosity, ηalcohol methyl, =0.59mPa s , to water, ηwater =1.00(mPa s ), alcohol ethyl, ηalcohol ethyl, =1.1(mPa s ), and

η = The refractive index of the fluid at temperature of 20oC is determined by [11]

( )

2

4

2

1 1/

2

a n

where

*

T

T

T

ρ ρ ρ

λ

= a0 =0.24425773, a1=0.00974634476,

2 0.00373234996

a = − , a3 =0.000268678472, a4 =0.0015892057, a5 =0.00245934259 , a6 =0.90070492, a7 = −0.0166626219, λ =UV 0.229202, T* =273.15K,

* 1000 kg m 3

ρ = − , λ =* 589nm, λ =IR 5.432937

Considering the temperature of the fluid is fixed at 20oC and mass density is chosen

to be ρ =1000 kg m− 3, and wave length of laser λ = 1 064 µm , using (5) we have n2 =

1.289

From curves in Fig.2, which discribes the dependence of the stable radius and stable time of patricle in trap, we can see that, with fixed optical parameters, the stability of particle in trap is higher when the radius of particle is shorter In detail, when trapped particle has radius of (14 ÷ 20)nm, the stable radius ρs ≈ 25nm and stable time

ps

s ≈ 3 3

τ It means that the particle oscillates around its center, and the designed optical

However, the above-mentioned stable conditions changes in different fluid From Fig.3, we can see the dependence of stable radius and stable time on viscosity of fluid The same particle, which is mixed in fluid with high viscosity, will be more stable than one, which is mixed in fluid with low viscosity It is of course that in the fluid with high viscosity, the vividity of particle is lower, and then the Brownian force is lower

In general, to have the stability of dielectric particle in given optical trap, it is convenient to choose a suitable particle, and to mix it in a suitable fluid

4 Conclusion

From above results, we can conlude that: First, the stability of dielectric particle in optical trap depends not only on optical parameters, but also on mechanical parameters as radius of particle, viscosity of fluid, ; Second, one designed optical trap will be useful with the suitable particle, which is mixed in suitable fuid

a [nm]

ρ s

Fig.2 Left: ρs vs a; Right: τs vs a.

with: , ,, , T=20 o C

a [nm]

τ s[

ρ s

- 8 m

Fig.3 Left: τs vs γ; Right: ρs vs γ

with: , ,, , T=20 o C

τ s[

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