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 TWO COUNTER PROPAGATION GAUSSIAN PULSE BEAMS Speciality: Optics Code: 62 44 01 09 PH.D. THESIS SUMMARY HA NOI - 201 4 TO 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. 1 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 2 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. 3 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: ˆ in in in in P k k r = =   ℏ ℏ (1.1) When a beam of light enters the medium having refractive index different from its initial medium, light refraction at the contact surface between the two mediums, the photon momentum changes its direction, satisfying the law of momentum conservation (see Figure 1.1). The change in momentum of the photon is transferred to the particle and on the particle acts the force, which was called an optical force. 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]: ( ) ( ) ( ) ( ) ( ) , , , , . , , , , , , P t grad t F z t p z t E z t p z t B z t F F ρ ρ ρ ρ ρ = ⋅∇ + ∂ ×        = +        (1.2) 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 4 force as: 3 2 2 2 1 2 grad a m F I c m π   − = ∇   +   (1.10) 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 is given by: 2 5 6 2 1 3 2 128 1 3 2 scat n a m F I c m π λ   − =   +   (1.11) 1.2. Optical tweezers use two counter-propagating Gaussian pulse beams. 1.2.1. Optical configuration of two counter-propagating Gaussian pulse beams. Diagram of the optical tweezers’ principle using two Gaussian beams in a Decard coordinate system is presented in Figure 1.5 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: ( ) [ ] { } ( ) ( ) ( ) [ ] 2 0 0 0 2 0 2 2 2 2 0 2 2 2 0 2 2 2 2 0 W , , , exp W 2 2 exp W 4 W / exp exp W 4 z ik E z t d xE i kz t ik z kz i k z k t z c k z ρ ω ρ ρ τ = − − +     × −   +       −     × − × −     +         (1.12) where 5 ( ) 2 0 3/ 2 2 2 0 0 4 2 W U E n c ε π τ =     (1.13) The electric field of a Gaussian pulse beam on the left- hand side is: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0 0 0 2 0 2 2 2 2 0 2 2 2 2 0 2 2 2 2 0 W , , , exp W 2 / 2 2 2 / 2 exp W 4 / 2 W / 2 / exp exp W 4 /2 l z z z ik d E z t d xE i k z t ik z d k z d i k z d k t z d c k z d ρ ω ρ ρ τ       = − + −       + +         +   × −   + +       − +         × − × −     + +         (1.14) The electric field of a Gaussian pulse beam on the right- hand side is: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0 0 0 2 0 2 2 2 2 0 2 2 2 2 0 2 2 2 2 0 W , , , exp W 2 / 2 2 2 /2 exp W 4 / 2 W / 2 / exp exp W 4 / 2 r z z z ik d E z t d yE i k z t ik z d k z d i k z d k t z d c k z d ρ ω ρ ρ τ       = − − −       + −         −   × −   + −       + −         × − × −     + −         (1.15) The corresponding magnetic field in crane approximation can write: ( ) ( ) 2 0 , , , , H z t yn cE z t ρ ε ρ ≅   (1.16) Pulse intensity or brightness of a light Gaussian pulse beam is a magnitude’s Poynting vector average over time: ( ) ( ) ( ) 2 22 0 2 2 , , , , , , W2 exp exp 2 1 4 1 4 I z t S z t zI z t zkP z t z z c τ ρ ρ ρ ρ τ ≡ =       = − − −       + +            ɶ ɶ  ɶ ɶ ɶ (1.17) The pulse intensity on the right- hand side is: ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 0 2 , , , , , , exp 1 4 1 4 W exp 2 z l z z t P I z t d S z t d z z d z d z d k t c ρ ρ ρ τ     = = −   + + + +       +     × − −             ɶ  ɶ ɶ ɶ ɶ ɶ ɶ ɶ (1.18) and the pulse intensity on the left- hand side is: ( ) ( ) ( ) ( ) 2 2 2 2 2 0 2 , , , ( , , , ) exp 1 4 1 4 W exp 2 z r z z t P I z t d S z t d z z d z d z d k t c ρ ρ ρ τ     = = −   + − + −       −     × − +             ɶ  ɶ ɶ ɶ ɶ ɶ ɶ ɶ (1.19) Considering two completely coherent beams and independent 6 propagating with polarization perpendicular to each other, so the total intensity of the field 2 l E and 2 r E can be described by the following expression: ( ) ( ) ( ) , , , , , , , , , z l z r z I z t d I z t d I z t d ρ ρ ρ = +    (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. a b c d Figure 1.7. Total intensity distribution with different values of the distance d between the two beam waists: 15 µm (a), 10 µ m (b), 5 µ m (c) and 0 µm (d). 1.2.4. The influence of the beam waist W 0 on the total intensity distribution a b c d Figure 1.8. Total intensity distribution with different values of waist radius W 0 side: 2 µm (a), 1.5 µm (b), 1 µm (c) and 0.5 µm (d). 1.2.5. Optical forces on dielectric particles Scattering force: ( ) ( ) ( ) 2 2 , , , , , , , , , scat pr l pr r n n F z t d z C I z t d z C I z t d c c ρ ρ ρ = −    (1.21) The force with gradient radial coordinates: ( ) ( ) ( ) ( ) ( ) , 2 2 2 0 0 2 0 0 2 , , , 2 , , , , , , W 1 4 W 1 4 l r grad I z t d I z t d F z t d cn z d cn z d ρ σ ρ ρ σ ρ ρ ρ ρ ρ ε ε = − −     + + + −            ɶ ɶ ɶ ɶ ɶ ɶ (1.22) 7 The force follow the propagation axis: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 4 2 0 0 , 2 2 2 2 2 2 0 0 2 2 2 4 2 0 0 2 2 2 2 2 0 0 2 1 4 2 W 2 , , , W W 1 4 2 1 4 2 W 2 , , , W W 1 4 l grad z r z d z d z d k I z t d kt F z n ck c c z d z d z d z d k I z t d kt z n ck c c z d ρ σ ρ ε τ τ ρ σ ρ ε τ τ   + + + − +   = − − +     + +     − + − − −   + − +   + −     ɶ ɶ ɶ ɶ ɶ ɶ  ɶ  ɶ ɶ ɶ ɶ ɶ ɶ ɶ ɶ ɶ  ɶ ɶ ɶ ɶ (1.23) 1.2.6. Influence of waist radius W 0 on the vertical optical force distribution If particle is located between two trap boundary regions, it will oscillate freely (thermal motion), meaning that the optical force components have no role in trapping dielectric particles. Under the rising direction of the beam waist radius, the magnitude of the trap region will increases gradually, but the maximum value of the optical power decreases with the results 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 µm (a); 1 µm (b); 1.5 µm (c) and 2 µm (d). 1.2.7. Effect of pulse width τ ττ τ on the distribution of vertical optical force 8 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 µm (a), d = 10 µm (b), d = 15 µm (c), d = 20 µm (d). 1.2.9. Influence of waist radius W 0 to the transverse optical force [...]... MST, No.5, 02-2010, pp.54-60 5 H Q Quy, H D Hai, The simulation of the stabilizing process of glass nanoparticle in optical tweezer using series of laser pulses, Commun In Phys., Vol.22, 2012, pp 175-181 6 H Q Quy, H D Hai, V T Hoai, Dynamics of the dielctric nanoparticle in temporal-incoherent optical tweezer, Adv In Opt Phot Spectr & Appl.(Hội nghị quang học quang phổ 2012) VII, ISSN 1859-4271, 2012,... also create good stable region 4.6 The impact of pulse delay on the stable area In fact when making optical trap using two Gaussian pulses in the opposite direction can’t usually eliminate all objectivity incorrect such as: The selection of the optical system, the optical path of two Gaussian pulse beams to the target etc , leading to the phase difference between two pulses (delay between two pulses) Therefore,... the time delay between the two pulses (δT< 2τ) 25 PUBLICATIONS RELATED TO THESIS 1 H Q Quy, M V Luu and H D Hai, Influence of Energy and Duration of Laser Pulses on Stability of Dielectric Nanoparticles in Optical Trap, Comm in Phys., Vol.20, No.1, 2010, pp.37-43 2 H Q Quy, M V Luu, Hoang Dinh Hai and Donan Zhuang, The Simulation of the Stabilizing Process of Dielectric Nanoparticle in Optical Trap... Beams, Chinese Optic Letters, Vol 8, No 3 / March 10, 2010, pp.332-334 3 H Q Quy, H D Hai, M V Luu, The Influence of Parameters on Stabe-time “Pillar” in Optical Tweezer using Counter-propagating Pulsed Laser Beams, Computational methods for Science and Technology, Special Isue (2)(Ba lan), 2010, pp 61-66 4 H Q Quy, H D Hai, The simulated influence of optical parameters on stable space-time pillar of nano-particle... diameter’s dependence on the beam waist radius 19 4.4 Effect of pulse width on the stable area Figure 4.7 The dependence of the Figure 4.8 The dependence of the stability time on the Gaussian pulse stability diameter on the Gaussian width pulse width 4.5 Effect of pulse repetition frequency on stable area Figure 4.9 Stability of the particles depends on pulse repetition frequency f = 1 6.τ Figure 4.11... and particle radius a (assume that particles have microspheric shape) Geometry regime is applied for a >> λ , Rayleigh regime a 0,1 µJ and beam waist radius W0 . counter-propagating Gaussian pulse beams. 1.2.1. Optical configuration of two counter-propagating Gaussian pulse beams. Diagram of the optical tweezers’ principle using two Gaussian beams in. 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. 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.