MINISTRY OF EDUCATION AND TRAINING MINISTRY OF DEFENCE ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY HOANG DINH HAI STUDY THE INFLUENCE OF SOME PARAMETERS ON THE OPTICAL TWEEZERS USING TW
Trang 1MINISTRY OF EDUCATION AND TRAINING MINISTRY OF DEFENCE
ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY
HOANG DINH HAI
STUDY THE INFLUENCE OF SOME PARAMETERS ON THE OPTICAL TWEEZERS USING TWO COUNTER PROPAGATION GAUSSIAN PULSE BEAMS
Speciality: Optics Code: 62 44 01 09
PH.D THESIS SUMMARY
HA NOI - 2014
Trang 2TO BEE COMPLETED AT ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY
MINISTRY OF DEFENCE
Scientific supervisor: Ho Quang Quy Assoc Prof Dr
Reviewer 1: Trinh Dinh Chien Assoc Prof Dr
Hanoi National University
Reviewer 2: Do Quoc Hung Assoc Prof Dr
University of Military Techniques
Reviewer 3: Pham Vu Thinh Dr
Academy of Military Science and Technology
to be presented and defended the thesis Examining committee of Academy of Military Science and Technology at h 2014
The thesis can be found at:
- Library of Academy of Military Science and Technology
- Vietnam National Library
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PREFACE
In 1971, Ashkin has discovered the way in order to balance between the light pressure and gravity of the dielectric particle of size about 20 µm [6] He and his colleagues continue to pursue the field of optical trapping for small particles with different sizes His works are mainly interested in trapping atoms, colloidal particles They are classified into two categories: atom cooling by laser and optical trapping In 1968, Ashkin and his colleagues published the first result using a beam optical trap to keep the particles having diameters ranging from 25 nm to 10 µm at a certain point
in water The device Ashkin used to trap the particles, later called optical tweezers, and this method is called optical trapping
The theory of optical trapping mainly calculates the force acting on particles in different embedding medium Calculation of the optical force acting on the particles is directly related to its regime If particle’s size is much smaller than the wavelength of the laser light, it is used a Rayleigh regime , in contrast, optical geometry regime for particle size is larger than the wavelength of laser light or Mie regime for particle size is equivalent to the laser wavelength Many works have been interested in the effects of tweezers parameters on the optical force However, the previous theoretical work on optical forces was only for a plane wave, which is applied to the laser beam emitted from the cavity plane mirror in continuous regime In current practice, the Gaussian laser beam is mainly emitted from the spherical mirror cavity and modulated pulses Thus, many authors have calculated for using “Gaussian” laser tweezers since
2005
Zhao and colleagues published the results of optical force calculating for a Gaussian pulse beam Agree with the first conclusion, M Kawano and his colleagues (2008) have proposed an optical tweezers using two laser beams in the opposite direction and then in 2009 H.Q.Quy and M.V.Luu have studied the optical force of the two counter-propagating Gaussian beams However, an accurate analysis of the stability of the particles in the trap region and the parameters’ effect on the stability of the particles are still left open
In addition, the application of optical tweezers to study living cells showed that the position of the cell is not completely retained during trap process, it fluctuates in a certain limit around the trap center This indicates the stiffness or the elasticity of optical tweezers have a certain value The stiffness is the ratio of the force acting on the particles and the particle’s fluctuation deviation from its trap center Therefore, the
Trang 42 durability of the trap depends on the force, particle size and embedding medium conditions
Hence, it can be stated that the particles trapped in optical tweezers are unstable but moving in a certain region, and in certain duration
From the research results of theory and experience mentioned above, the research of the effect of the optical tweezers parameters on the stability of the particles is essential First, it can provide some scientific conclusions to guide empirical studies by means of simulation, applied for particle trap
This is the content mentioned in my thesis "Study on the effect of some parameters on the optical tweezers using two counter-propagating Gaussian pulse beams."
The layout of the thesis:
Chapter 1 Overview of optical tweezers using two Gaussian pulse beams in the opposite direction
This chapter introduces some concepts of optical force and optical tweezers’ configuration using two Gaussian pulse beams in the opposite direction and Brownian motion Through this analysis a number of factors affecting the stability of the particles in a fluid under the influence of optical tweezers using two Gaussian pulse beams in the opposite direction
Chapter 2 The dynamic process of particle
This chapter simulated particle’s kinetic process in fluids using Langevin equation with Brown force and optical force impact The analysis of these two forces’s competition in a pulse regime and the formation of trapping time
Chapter 3 Effect of parameters on particle's dynamic process
This chapter analyzes the impact of parameters such as initial position of the particle, the total energy and the beam waist radius, particle’s radius to its shift speed toward the tweezers’ center as well as its deviation at the trap center
Chapter 4 The influence of the parameters on the stable region
This chapter proposed the concept of space - time stability region of the particle in the optical tweezers Considered the influence of optical tweezers parameters, the thermo-mechanic parameters of fluid and particle
on the stability region Then, we analyzed and selected suitable parameters for the best space - time stability region
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Chapter 1 OVERVIEW OF OPTICAL TWEEZERS USING TWO
GAUSS PULSE BEAMS IN THE OPPOSITE DIRECTION 1.1 Optical force
Photon with the wavelength of λ has a momentum as follows:
It is usually decomposed into two components: the gradient force and scattering force
Figure 1.1 Light rays are
refracted at the interface of dielectric particles
Assuming the dielectric particle has a size a smaller than the
wavelength of light (a<<λ), it can be considered as a dipole interacting with the light field, the force on the particle is the Lorentz force due to the effect of electric field gradient as shown in Figure 1.3 The interaction of light and particle is considered in the Rayleigh regime, the beam has Gaussian spatial contribution, Lorentz force toward the focal point and is defined as follows [17]:
Figure 1.3 Forces on dielectric
particles in the Rayleigh regime
Using the Rayleigh approximation (ignoring absorption phenomena and particles as small-spherical microspheres), then we write the gradient
Trang 64 force as:
where c is the velocity of light in vacuum, and I is the intensity of the laser
beam Force component scattering along the direction of light propagation
Figure 1.5 Diagram of optical traps use two counter-propagation
Gaussian pulse beams:
a Diagram of two counter-propagation Gaussian pulse beams; b Plane
of trap center; c Optical diagram
1.2.2 Total intensity of two counter-propagating Gaussian pulse beams
The electric field of a Gaussian pulse beam [17] can be represented
by the following formula:
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U E
2 2 2
0
W 2
zk P
2
W exp 2
2
W exp 2
(1.19)
Considering two completely coherent beams and independent
Trang 86 propagating with polarization perpendicular to each other, so the total intensity of the field E l2and E r2 can be described by the following expression:
( z, , , ) l( z, , , ) r( z, , , )
I ρ z t d =I ρ z t d +I ρ z t d (1.20)
1.2.3 The influence of the distance d to the total intensity distribution
As we have analyzed in the optical configuration of two Gaussian pulses in the opposite direction, from the formula (1.18), (1.19) and (1.20) the distance between the two beam waists of the beam is one of the parameters affect the total intensity of the beams Especially this parameter greatly affects the intensity distribution in the overlapping area, the region has a significant influence on trapping efficiency Therefore, examining the influence of this parameter on the overall intensity is very important
Figure 1.7 Total intensity distribution with different values of the
distance d between the two beam waists: 15 µ m (a), 10 µ m (b),
5 µ m (c) and 0 µ m (d)
1.2.4 The influence of the beam waist W 0 on the total intensity distribution
Figure 1.8 Total intensity distribution with different values of waist radius
W0 side: 2 µ m (a), 1.5 µ m (b), 1 µ m (c) and 0.5 µ m (d)
1.2.5 Optical forces on dielectric particles
Trang 97 The force follow the propagation axis:
ɶ ɶ
presented above (Figure 1.9),
Figure 1.9 Optical power distribution along the phase plane (z, t) for different
values of waist radius W 0 : 0,5 µ m (a); 1 µ m (b); 1.5 µ m (c) and 2 µ m (d).
1.2.7 Effect of pulse width ττττ on the distribution of vertical optical force
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Figure 1:10 Longitudinal distribution of optical force in the phase plane (z,
t) for different values of the pulse widths τ: 0,5ps (a); 1ps (b); 1,5ps (c) and
2ps (d)
1.2.8 The influence of the distance of two beam waists d to the longitudinal optical force
Figure 1:11 The distance’s influence d to the longitudinal distribution of
optical force: d = 5 µ m (a), d = 10 µ m (b), d = 15 µ m (c), d = 20 µ m (d)
1.2.9 Influence of waist radius W 0 to the transverse optical force
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y
Figure 1.13 Potential hole that
created by a transeverse force
Figure 1.14 Optical trnasverse forces
depend on beam waist radii: t=1τ, d=10µm at the position z = 0µm
1.2.10 The influence of the distance of two beam waists d to transverse optical force
Figure 1.15 Distribution of transverse optical force F grad in the plane (ρ,t) for different values of d: 1 µm (a), 5 µm (b), 10 µm (c) and 15 µm (d)
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1.2.11 The influence of pulse width on the transverse optical force
Figure 1.16 Transverse optical force, F grad in phase plane (ρ,t) for different pulse widths of τ: 0,5 ps (a); 1ps (b) and 1,5 ps (c)
1.3 Brownian motion of dielectric particles in fluid
The particles move in orbits like as figure 1.17 is defined as a Brown particle
1.4 Factors affecting the stability of optical trap
1.4.1 The requirement of stability
We know that in order to study the characteristics and properties of a dielectric particle in fluid or a cold atom in a cold chamber (cryotrap) must be positioned it in a given area (stable region as small as possible) The particle’s stability is not only in space (stability in a given space) but
in time (stability in a desired time duration)
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1.4.2 Factors affecting the stability of the particle in the trap process
- The energy of the laser
beam;
- Laser pulse duration;
- The laser beam waist (spatial
distribution of the laser beam);
- The gap between the two waist sides
- Characteristics of the particle (size, refractive index)
- Characteristics of the fluid (viscosity, refractive index, temperature)
Optical force is the light pressure acting on the material, however, it
is weak for the incoherent light
Laser beam is coherent, orientation, the average power (E=1µJ) may also impact on the particle with a force of about 0,01÷30 pN, equivalent to the interaction between macromolecules in DNA sequence, depending on the numerical aperture of the objective system
Due to those forces, laser beams having intensity gradient will pull particle in areas with high intensity when embedded in a smaller refractive index medium and drag it in low-intensity regions when embedded in larger refractive index medium (optical gradient force ) and push it in the direction of particle propagation (optical scattering force) Optical system uses a focused laser beam (generated gradient magnitude ) to keep particle embedded in a fluid called optical tweezers
Optical force acting on the particles are three different regimes depending on the ratio between the laser wavelength λ and particle radius
a (assume that particles have microspheric shape) Geometry regime is applied for a>>λ, Rayleigh regime a<<λ and the Mie one a∼λ Optical tweezers used two counter-propagating Gaussian pulse beams having polarization to be perpendicular each other to enhance the optical force and avoid scattering forces In this optical tweezers, the intensity of the laser is the sum of two beams and optical force acting on the particle generated from this total intensity Therefore, the value and distribution of optical force in time-space depends on the structure parameters of tweezers such as beam energy, beam waist radius, the distance within beam waists, pulse width ,etc In addition, the optical force depends on the particle radius, viscosity of the fluid
These parameters not only directly affect on the optical force and its distribution but also affects the dynamics of particles in the fluid and the stability of tweezers (or the stability of the particle in space - time )
Trang 1412 The dynamic process of particles in fluid will be Brownian motion if having no external field effect In optical tweezers, the particle is affected
by Brownian force and optical force control (considered as external forces), therefore, the dynamics of particles is described by the Langevin equation with the effect of the two forces said above Dynamics of particles in a fluid under the action of optical forces will determine the stability of optical tweezers
Chapter 2 DYNAMIC PROCESS OF PARTICLE 2.1 Lagevin equation for the general case
To study the motion of particles in fluid, we start from the classical Newton's second law [24]
F =F +F =F ρ+F +F =F ρ +F (2.11)
To examine the effect of these factors, we select the simulation of the motion of particles, from which we consider meaning of physical phenomena Simulation algorithm will be introduced in the following section
2.3 Algorithm and simulation procedure
We study two-dimensional motion (in the plane) and the position of the glass particle in water by means of Brownian kinetic method Fluid sample is used to describe the motion of particle and therefore, the
Trang 1513 following equations of motion for each particle is calculated on the focal plane [17], [24]:
rad, ( ( ))(t t) ( )t F g ρ ρ t t 2 ( )D t h t
= Using (2.18) we found the position
of the particle in the trap ρ(t1)=ρ(0+δt), which is calculated δρ after the period δt Then, instead of ρ(t1) and t1 into the formula (2.13)÷(2.15)
we calculate the optical force Fgrad,ρ =F(t1,ρ( )t1 ) This process continues until the moment t n =6τ Using Matlab program, simulation has been carried out The dynamic process of particle in the tweezers was simulated through orbital motion of particle in the pulse duration and the effect of the laser beam parameters, fluid environment to orbit and orbital speed changes
2.4 Brown motion in the focal plane
Figure 2.1 Brownian motion of glass particle in the water from a beam
axis around ρ0 = 1(µm) with different simulation time steps:
a) δt=6 / 2000τ ,b) δt=6 / 4000τ ,c) δt=6 / 8000τ , d)δt=6 / 10000τ However, the motion shape and different random.simulation time steps
Figure 2.2 Brownian motion of glass particle in the water from a beam
axis around ρ0 = 0 (µm) with simulation time steps:
a) δt=6 / 2000τ , b) δt=6 / 4000τ , c) δt=6 / 8000τ , d) δt=6 / 10000τ