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OPTO−ELECTRONICS REVIEW 20(3), 247–254 DOI: 10.2478/s11772−012−0030−1 Influence of the Brownian movement on the motion of nanoand micro-particles in the inhomogeneous optical field C.Yu. ZENKOVA*, M.P. GORSKY, I.V. SOLTYS, and P.O. ANGELSKY Chernivtsi National University, 2 Kotsubinsky Str., 58−012 Chernivtsi, Ukraine The motion of light scattering particles of the Mie and Rayleigh micro− and nano−range type in the inhomogeneously−pola− rized optical field, with allowance made for the Brownian movement, is analysed in the paper. The spatial modulation of po− larization in the observation plane determines the spatial modulation of the volume energy density. That is why the velocity and the resulting optical force, which cause the motion of the testing particles, change according to the degree of coherence of the interacting fields. The influence of the forces which arise in the viscous medium and cause the Brownian movement upon the mechanisms of manipulating and trapping testing particles by the optical field is studied. Keywords: polarization, Poynting vector, scattering objects, degree of coherence. 1. Introduction One of the most actual tasks of the present day biomedicine is to control micro−particles and nano−particles of different nature with help of laser radiation. A controlled object can be a colloid particle, a molecule, an atom or a cell, including a bio−object, e.g., a DNA molecule, an organelle cell. One can say, that the technology of particle controlling is a po− werful tool for scientists working with micro−objects of dif− ferent nature. The process of trapping and controlling parti− cles depends on characteristics of the laser beam. At pre− sent, the possibilities to use beams of various nature, such as Gaussian beams [1,2], bottle beams [3], zero−order Bessel beams [4], self−focused laser beams [5] and even evanescent fields [6,7] are investigated. One of the principal prerequi− sites for an effective particle manipulation with help of these laser beams is their complete coherence. However, in actual practice, any laser fields are always only partially coherent [8]. Moreover, the possibility for highly accurate focusing and, then, for producing a force component capable to change the motion direction of an object is determined by the degree of corresponding beams coherence [9,10]. The performed analysis of controlling Rayleigh dielectric sphe− res [11] in the field of partially coherent radiation shows that all optical forces are greatly affected by light coherence. As coherence decreases, the magnitude of the optical forces on a dielectric sphere near the focus point greatly decreases, as well. For the light beam with good coherence optical force may be used to trap a particle and for the light beam with intermediate coherence optical force may be used to guide and accelerate a particle. *e−mail: [email protected] Opto−Electron. Rev., 20, no. 3, 2012 The aim of the paper is to investigate the peculiarities of a particle motion in a spatial periodically−modulated pola− rized field and to study the possibilities of using the pola− rization mechanisms for controlling the motion of micro− and nano−objects. The results of these investigations can find their practi− cal use in applied biomedicine [12] as well as in various directions of singular polarization optics [13–15]. The offered paper is a continuation of investigations [16,17] of the influence of spatial modulations of the aver− aged Poynting vector values on nano−size particles where the action of corresponding optical flow is not connected to a certain component of the optical force. Various compo− nents of the optical force and their e ffect on the tested parti− cles of nano− and micro−sizes are analysed in this paper. The proposed paper also investigates the influence of a coherence degree of superposing mutually orthogonal line− arly−polarized waves on the peculiarities of particle motion in a field of resulting distribution. In order to obtain more general pattern of particle motion in the viscous medium which is caused by the resulting optical field we shall ana− lyse the influence of forces determining the Brownian motion upon particle motion velocity. Thus, the aim of the given paper is to establish a connec− tion between interacting optical fields and motion velocity of tested particles positioned in energy inhomogeneous optical field. 2. Formation of optical forces affecting particles of various light scattering mechanisms The ways of optical trapping and manipulating of micro− −particles with help of a laser beam depend on light pressure r r force. Every photon carries a momentum equal to p = hk , C.Yu. Zenkova Unauthenticated Download Date | 6/16/17 1:18 AM Influence of the Brownian movement on the motion of nano− and micro−particles in the inhomogeneous optical field r r where k is the wave vector, k = k = 2p l, h is the Plank constant. The interaction of irradiation with substance results in a change of a photon momentum. The motion mechanism is described with help of the second and third Newton’s laws. Hence, light possesses a momentum and the change of the di− rection of light propagation determines the force involved in the direction change [18]. The motion value imparted to the particles follows from the Newton’s law: r r r r r dp d dv = (mv) = m × = ma = Fopt . dt dt dt For example, while passing through a transparent parti− cle light deflects. The refraction of light on a dielectric sur− face changes the direction of the light momentum (a particle acts as a micro−lens). The momentum change leads to the force arising which propels the particle either into a region of the maximum light intensity (transverse trapping) or into a beam focal region which is the maximum intensity zone, as well (longitudinal trapping). Consequently, the force which arises as a result of a direction change of light propagation makes a particle move into the direction of the greatest light intensity. The aim of the paper was to establish a link between the degree of coherence of interacting fields and the particle motion velocity. In order to do this, we chose two groups of particles arbitrarily called “nano−particles” and “micro−par− ticles”. For the first group of particles it is possible to use Rayleigh theory to describe the light scattering mechanism, while for the second group we use Mie theory, which is also known as Lorenz−Mie solution or Lorenz−Mie−Debye solu− tion or Mie scattering. To simplify matters, in the case of micro−particles the approximations of Ray optics were used [19]. Let us determine the resulting optical force affecting particles in the laser radiation field. By the term “resulting optical force” is meant a force which causes a directional particle motion. It can be divided into the following com− ponents: scattering force (Kepler light pressure force). It is pro− portional to the particle scattering surface and to the light intensity of paraxial Poynting vector−directed beams. This force arises because of the change of the electromagnetic wave r impulse with the dipole induced. The dipole moment is proportional to the vector of the d r electric field E. The proportional coefficient is taken as the polarizabilityr of the r molecule a. The dipole moment is calculated as d = aE. gradient force. This force arises in the field of inhomo− geneously distributed laser radiation intensity. The grea− test intensity is on the beam axis. In this case, the gradi− ent force will be directed towards the beam centre. It is often regarded as an optical force turning a micro−parti− cle and nano−particle into a multi−pole. The gradient force is usually called the dipole force for Rayleigh (submicron) particles. The gradient force is equal to the Lorenz force, affecting the created (induced) dipole and depends on the distribution of the laser radiation intensity. For absorbing and reflecting particles the suggested list of forces is complemented by forces which show the effect of the optical field on particles with corresponding proper− ties. In this case each component of the optical force can be counted using the averaged value of the Poynting vector. The instantaneous value of the Poynting vector sets, by definition, direction and density of the energy at the r r current r point and is determined by the relation S = E ´ H. The den− sity value of the energy current is S = EH = w × 1 mem 0 e 0 , where w is the energy of electromagnetic field; e, e 0 ( m, m 0 ) are the values of dielectric (magnetic) penetrability of medium and vacuum, correspondingly. As it is known, w = 2wE = 2wH , where r the r energy den− sity of the electric field is wE = (1 2)ee 0 ( E, E) and the r ener− r gy density of the magnetic field is wH = (1 2) mm 0 ( H, H). The averaged value of the Poynting vector is the time− −averaged distribution of instantaneous value taken over the whole period of time. Let us consider the superposition of two plane waves W1, W2 of equal amplitudes polarized in the plane of inci− dence (Fig. 1) and determine the averaged value of the elec− tric (magnetic) energy density and direction of the r the r r r resulting Let E (1) ( r1 , t )[ H (1) ( r1 , t )] and r (2 ) r wave r (2 )propagation. r E ( r2 , t )[ H ( r2 , t )] be the vectors of the electric (mag− netic) fields for the first and the second interacting waves. In this case, the vector of the resulting electric (magnetic) r rfield r in registration plane at therpoint r isrdefined as E( r ) = r (1the r r r r r r r E ) ( r ) + E (2 ) ( r ) and H ( r ) = H (1) ( r ) + H (2 ) ( r ). Correspon− dingly, the r direction r r of the Poynting r rvector of the resulting wave is S = S (1) + S (2 ) , where S (1) ( S (2 ) ) are the Poynting vectors of the interacting waves. Let us introduce the following definitions of the ana− lyzed planes: as far as the z−component of the field is actual in this interference scheme, the definition of planes is con− nected to the orientation of a z−component. Thus, an inci− dence plane and an observation plane coincide with each other and with the plane of the figure, e. g., XOZ. The regis− l l 248 Fig. 1. Superposition of plane waves of equal amplitudes linearly polarized at incidence plane with an interference angle of 90°. Perio− dical spatial modulation of polarization takes place in plane of inci− dence. Opto−Electron. Rev., 20, no. 3, 2012 © 2012 SEP, Warsaw Unauthenticated Download Date | 6/16/17 1:18 AM tration plane is the plane that analysis the intensity dis− tribution, e. g., XOY. We define the time−averaged density of the energy cur− r rent at the point of observation as r [17] S= ee 0 mm 0 å { (1ij) ( r) + (2ij) ( r) + 2 r r In general case, the forces exerted on the particles by a laser beam depend on the properties of both beam and par− ticles. } r r r r tr[W ( r1 , r1 , 0)]tr[W ( r2 , r2 , 0)] × h ij(1,2 ) cos(a ij(1,2 ) ) × cos(d e ) i,j r r r where jij( m ) ( r ) =< Ei( m ) ( r , t ) E j*( m ) ( r , t ) > and m = 1,2; i,j = ( m ,n ) x, z, h ij determines the degree of mutual coherence of the corresponding fields (m, n = 1,2) and is defined by Eq. (2); a ij( m ,n ) is the argument of h ij( m ,n ) and determines the phase difference between i– and j– components of the field, d e is the phase difference between the beams (in this case their electrical parts) at the registration plane. The mu− r r tual coherence matrix W ( r1 , r2 , t ) describes the coherence properties of the vector optical fields and characterizes the r correlation of the fields at two different spatial points: r1 and r r r (1) r r2 [20,21]. It is defined as W ( r1 , r2 , t ) =< Ei ( r1 , t ) E (j2 )* r ( r2 , t ) >, where i, j = x, z. Within the framework of such an approach the degree of mutual coherence of the field [22] is defined as r r h ij ( r1 , r2 , t ) = (1) Rayleigh particles Let us consider the formation of the optical force affecting Rayleigh particles. Depending on the interaction mechanism of the electro− magnetic wave and Rayleigh particles of various optical properties, the optical force can be imagined as a decompo− sition of a traditional gradient, scattering, absorbing and reflecting components of the optical force [27]. The direc− tion of an optical force gradient component is stipulated by a distribution gradient of energy volume density. The direc− tion of scattering and absorbing components is set by the direction of energy flow propagation. The direction of a reflecting component is set by the orientation of a particle surface. In order to trap particles of a given class it is enough r r Wij ( r1 , r2 , t ) = r r r r tr[W ( r1 , r1 , 0)] × tr[W ( r2 , r2 , 0)] r r Wij ( r1 , r2 , t ) r r r r å Wii ( r1 , r1 , 0)Wij ( r2 , r2 , 0) (2) ij The distribution of the time−averaged density of the energy current in space according to Eq. (1) determines the current value at different points of the observation plane and is unambiguously determined by the degree of coherence of the superposing waves h ij . The direction of the resulting current is set by the direction of the Poynting vectors of these waves. When accounting the superposition of two mutually orthogonal linearly−polarized fields, the modulation of the averaged Poynting vector value, e. g., the spatial modula− tion of the energy density, is noted in the observation plane. The gradient force, expressed by the Poynting vec− tor, forms the particle distribution in this plane. Moreover, the change of the degree of coherence leads to the change of the modulation depth of the energy bulk density, which, in its turn, determines gradient force value and peculiari− ties of particle motion. This type of modulation of the ave− raged Poynting vector values is especially actual for calcu− lating optical forces affecting Rayleigh scattering particles. As it was shown in papers, changes of the depth of polarization modulation in the analyzed scheme depend on a degree of coherence of superposing waves [23–26]. Mie scattering is polarization dependent. It can be supposed that the distribution of polarization states in the observation plane determines the optical force value causing the particle motion. Opto−Electron. Rev., 20, no. 3, 2012 to take into account only a gradient component while calcu− lating the optical force in the first approximation. Then the optical force can be presented as r sn r 1 Ftr = - n m aÑE 2 + m S, 2 c r 1 where Fgrad = - n m aÑE 2 is responsible for the effect of 2 the optical force gradient component. As it is known r c S= 4p e 2r E s, m r where s is an unit vector in the direction of propagation [28]. c e 2 Or S = E . 4p m r 2pn m a 4pS m 1 T h e n E2 = a n d Fgrad = - n m aÑE 2 = c e 2 c m ÑS e Thus, the effect of the gradient force is linked with the gradient of energy volume density and, correspondingly, with the value of the coherence degree of interacting fields. Temperature effects influencing the motion of particles arranged in the optical field take place in the medium sur− rounding the particle. In certain cases, the force which is 249 C.Yu. Zenkova Unauthenticated Download Date | 6/16/17 1:18 AM Influence of the Brownian movement on the motion of nano− and micro−particles in the inhomogeneous optical field determined by temperature effects can exceed the gradient force value and hinder the capture of nano−particles. Here only a correct choice of laser radiation power allows to cre− ate such temperature conditions that make the force caused by temperature change insignificantly in comparison with the gradient force which determines the capture of Rayleigh nano−particles. r r In the first approximation we will consider that Fopt = Fgrad , which allows us to connect particle trapping velocity with energy inhomogeneity value of the optical field and a coherence degree of interacting initial fields. Mie scattering particles Models for Mie scattering particles are based on a computer simulation of optical forces caused by reflection and refrac− tion from a spherical surface neglecting diffraction effects. Using conservation of the momentum, the total force acting onto the sphere will be the summation of all the force acting onto it. The scattering force ( Fsc ) and the gradient force ( Fgrad ) can be simplified into the following equations [29] n P ïì T 2 [cos( 2q -2e ) + R cos( 2q )] ïü Fsc = m í 1 + R cos( 2q ) ý (3) c îï 1 + R 2 + 2 R cos 2e þï and Fgrad = n m P ìï T 2 [cos( 2q -2e ) + R sin( 2q )] üï í 1 + R sin( 2q ) ý, (4) c ïî ïþ 1 + R 2 + 2 R cos 2e where q is the angle of incidence, e is the angle of refraction and R and T are the Fresnel reflection and the refraction coeffi− cients, P is the power of the incident light, n m is the index of refraction of the surrounding medium. R and T are polarization dependent and, therefore, so is the optical force. The resulting force includes the effects of all internally reflected and re− fracted beams. Hence, it is exact within the corresponding ap− proximation. Absorption of laser energy power by Mie parti− cles can take place as well. The overall force exerted by a beam with a given profile is simply a vector sum of forces resulting from the ensemble of rays that comprise the beam. Thus, in this case Fopt = Fsc + Fgrad . The modulation of polarization in the observation plane, considered in the proposed interference scheme, causes the change of both optical force components ( Fsc , Fgrad ) and the redistribution of particles in motion in the analyzed field. The computer simulation of the Mie particle motion in the inhomogeneously−polarized optical field makes it possi− ble to determine the influence of the polarization modulation depth and the coherence degree of interacting linearly−pola− rized plane waves upon the velocity of particle motion and the resulting force pre−setting this motion [23–25]. 3. Simulation of mechanical forces which determine particles behaviour in viscous medium May the analyzed particles (Rayleigh or Mie ones) be situ− ated in a viscous medium. Let us assume, that the mixture 250 consists of a viscous incompressible carrier phase and sphe− rical particles whose radius is r and whose mass is m. While moving in liquid a particle experiences friction r force, which at therconstant value of the velocity v is defined r r by Stokes law as Fst = 6phrv = mgv, where g is the friction coefficient, h is the dispersive medium viscosity. In this case, it is not enough to introduce the friction force (Stokes force) to describe Brownian motion of this object. Such an approximation corresponds to an approximation of the con− tinuous medium. In order to take into account the atomic structure of the liquid, Langevin introduced a corresponding additional force FL = my(t ) into the motion equation which is a random time function. The directions of such a random force are on equal term and the averaged values of the force are equal to zero. The correlation time of the Langevin force values is equal to zero. In this case, the correlation time of L the Langevin force values t cor is much less than the relaxa− tion time of particles at the expense of the friction force L t rel = 1 g , e. g., t cor << t rel . Such random sources are d−correlated and the random process y(t) can be considered as Gauss process [30]. Thus, the random process, which is preset by the Brownian motion, is approximated with the use of the Gauss distribution. Then, the equation of particle motion, under the effect of the optical force in the viscous medium and with allowance made for the Brownian movement, is put down as r r r r dv r = Fopt + Fst + F0 + FL , m dt r where F0 is the external force, e. g., gravity force. 4. Simulation results The computer simulation was performed within the frame− work of the approach set forth in Introduction. The contribu− tion of gradient force and light scattering force to the result− ing optical force which conditions the particles motion is studied, as well. The investigation was performed in a spatial periodi− cally−polarized optical field, which was formed as a result of interference of two plane−polarized equal in intensity waves in the incidence plane [23–25]. Both lasers and partially coherent sources were used as radiators. In the offered interference scheme with inhomogeneous intensity in a registration plane, the modulation of the energy volume density is realized in the observation plane. The formed inhomogeneous optical field is able to influence particles position. The optical force influence on particles depends on coherence properties of superposing waves which form the energy inhomogeneous field. Let us consider behaviour of the tested particles in the inhomogeneous optical field, which, according to the experiment proposed in Ref. 16, are particles of hydrosol of gold of 1− and 100−nm size and are located at room tem− perature. Opto−Electron. Rev., 20, no. 3, 2012 © 2012 SEP, Warsaw Unauthenticated Download Date | 6/16/17 1:18 AM We analyze the motion of Mie and Rayleigh particles in the resulting optical field which is formed by the interaction of two waves of different values of the coherence degree. On a viscous medium side, a place of particle localization, a complex force is affecting particles. It essentially changes the resulting force. Thus, when changing randomly the loca− tion of particles by the force Brownian component, time dis− tribution of the optical force changes, as well. In the process of simulating forces which pre−set the Brownian motion the order of force values is chosen commensurable with the order of the resulting force value. Let us analyse Mie particles motion Time dependence of the resulting optical force which con− sists of gradient and scattering forces is presented in Fig. 2. In this case, the Brownian force component can influence the optical force distribution. The coherence degree of interacting waves influences the optical force value. The change of the coherence degree leads to the change of depth of a spatial modulation of pola− rization and, correspondingly, to the change of depth of a spatial modulation of the averaged Poynting vector value which essentially influences the gradient component of the resulting optical force. If we neglect the influence of the medium on a particle motion, we obtain the maximum re− sulting optical force provided that the optical field is formed by a coherent interaction of the initial waves (an optical force gradient component is at its maximum and a scattering component of the optical force is present). When the inter− action of the initial waves is incoherent, only the scattering component of the resulting optical force will take part in the formation of the resulting optical force. The Brownian particle motion influences time distribu− tion of the resulting optical force. Thus, the fluctuations of the optical force are explained by random chaotic particle motion, connected to chaotic influence of the Brownian force (Fig. 2, curves 2 and 3). The optical force gradient Fig. 2. Time dependence of resulting optical force, affecting Mie particle, with allowance made for random fluctuations in motion caused by influence of the Brownian forces. Opto−Electron. Rev., 20, no. 3, 2012 component moves the particle into a region of the maximum energy density, correspondingly the Brownian component of the force randomly removes the particle from the maxi− mum. The result of changing the particle position will be the optical force change which will again return it to the region of the maximum. Let the optical field be formed by an inco− herent interaction of superposing fields with the absence of the optical force gradient component (Fig. 2, curve 1). Then, the random particle motion, caused by the Brownian force effect in the homogeneous optical field does not influence any optical force and the force remains constant. The resulting force is changed equally by random force components, arising from the side of the liquid during the particles motion and from the resulting optical force. Only under the effect of the optical force, particles redistribute in the optical field and concentrate in the region of the energy density maximum value, continuing their directional motion. Mechanical forces, induced by the medium and sur− rounding particles, try to push them out of their location into which the gradient optical force directs them. We shall compare the particle motion velocity when the Brownian motion is not taken into consideration in the resulting force (Fig. 3) and the velocity of particle motion when the Brownian force is taken into consideration in the resulting force (Fig. 4). The plots which describe time dependence of the parti− cle motion velocity and are presented in Fig. 3 show, that the increase of the coherence degree leads to the particle motion velocity increase in the regions of the maximum energy density value. The energy density maximum gradi− ent in the case of absolutely coherent waves determines the particle motion maximum velocity. Figure 4 shows the motion velocity change of Mie parti− cles which are localized in the viscous medium. The forces which cause the motion velocity change possess a compo− Fig. 3. Motion velocity of Mie particles under change of coherence degree of interacting waves (h (1, 2 ) ):1 - h (1, 2 ) = 1; 2 - h (1, 2 ) = 0.5; 3 - h (1, 2 ) = 0. The normalized value of velocity motion relative to the value, obtained in the optical field with two interacting abso− lutely−coherent linearly−polarized plane waves. 251 C.Yu. Zenkova Unauthenticated Download Date | 6/16/17 1:18 AM Influence of the Brownian movement on the motion of nano− and micro−particles in the inhomogeneous optical field Fig. 4. Change of Mie particle motion velocity under the effect of forces arising from optical field and viscous medium, including forces caused by the Brownian movement. Fig. 5. Change of resulting optical force, affecting Rayleigh parti− cles in viscous medium with allowance made for the Brownian forces. nent induced by the optical force action and the action of force on the liquid side. In this case, the Brownian compo− nent of the resulting force determines random changes of the velocity which is supported by the results of a computer simulation and is shown in Fig.4. Irrespective of the cohe− rence peculiarities of initial superposing waves, the optical field influence on the velocity motion will be the same. The gradient component of the optical force determines the place of particle trapping. The force, acting on the mini− mum side, e. g., the Brownian motion force, is responsible for the position of particles in the place of trapping (Fig. 5, curves 2 and 3). Let us analyse the velocity change of Rayleigh particles, positioned in the optical field, when the Brownian motion is taken into account (Fig. 6) and when the Brownian motion is not taken into account (Fig. 7). In the case of an incoherent interaction of fields (Fig. 6, curve 3) zero value of the optical force is responsible for the absence of any influence upon the particle motion. Any coherent interaction of optical fields causes the cre− ation of such a resulting optical field which is able to change the particles motion dynamics in this field (Fig. 6, curves 1 Let us analyze the motion of Rayleigh particles The size of Rayleigh particles in our computer simulation was 1000 times smaller than the size of Mie particles and the mass of Rayleigh particles is 100 times smaller than the mass of Mie particles. Figure 5 shows the change of the resulting optical force affecting Rayleigh particles in the viscous medium. The scattering component of the optical force is much smaller than the gradient force. That is why we can neglect the scat− tering component for Rayleigh particles. If the optical field is formed by incoherent interaction of the initial waves, the resulting optical force practically zeroes. It is caused by the absence of energy gradient density (Fig. 5, curve 1). The increase of the coherence degree of the superposing waves stipulates the increase of modulation depth of the energy volume density distribution. This, in its turn, causes a significant increase of the optical force gradient compo− nent. The random change of the optical force value is explained by the fact that the random effect of the Brownian forces try to bring the particle out of the position into which it is directed by the optical force gradient component. In order to return the particle into its initial position, the optical force must compensate for the Brownian force action. This results in random changes of the optical force which is shown in Fig. 5, curves 2 and 3. When the gradient force does not arise and the gradient energy volume density is absent, the Brownian forces random effects on the resulting optical force are not significant (Fig. 5, curve 1). 252 Fig. 6. Change of motion velocity of Rayleigh particles with time and with change of coherence degree of interacting waves (h (1, 2 ) ): 1 - h (1, 2 ) = 1; 2 - h (1, 2 ) = 0.5; 3 - h (1, 2 ) = 0. Normalized value of velocity motion relative to value, obtained in optical field with two interacting absolutely−coherent linearly−polarized plane waves, is plotted along the ordinate. Opto−Electron. Rev., 20, no. 3, 2012 © 2012 SEP, Warsaw Unauthenticated Download Date | 6/16/17 1:18 AM References Fig. 7. Dependence of motion velocity of Rayleigh particles with forces affecting particles from optical field and from viscous me− dium, including forces causing the Brownian motion. and 2). While comparing curves 1, 2 and Fig. 6, it is possible to say, that the coherence degree of superposing optical fields essentially influences the particles motion velocity. The coherence degree is also set by the time during which the particle changes its position and localizes in the maxi− mum energy regions of the inhomogeneous optical field. While analysing the time dependence of Rayleigh parti− cle motion velocity (Fig. 7), we can see that the influence of the optical field on the motion velocity is essential at the ini− tial moments when particles redistribute in the inhomoge− neous optical field under the effect of the resulting optical force. In this case, the gradient force effect is sufficient for changing the velocity. With time, when the particle is trapped by the optical field and the motion velocity is zero (Fig. 6), the availability of Brownian forces affects ran− domly not only the particles location, but also the velocity of their motion. Matching between the particle motion velocity and the degree of coherence of superposing waves forming the optical field for particle location disappears with time as well. General time necessary for a redistribution of particles in the optical field is much shorter for Rayleigh particles than for Mie particles. 5. Conclusions When examining particles characterized by different light scattering mechanisms, we analysed the resulting force which causes the particle motion and consists of the optical force and the forces arising on the liquid side. It includes the force causing the Brownian motion of the particles under investigation, as well. 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