Figure 2 (a1) shows the working principle of particle trapping by using a single TOF. When a laser light is injected into the TOF, the beam is highly focused near the end of the TOF, yielding an optical gradient force Fg and scattering force Fs. Fg draws particles towards the light-intensity region of the light, while Fs pushes particles away from the stronger light intensity region. Particles beside the optical axis of the TOF can be trapped and confined to the axis by the transverse gradient force Fg. When the particle is located in the trapping region, the gradient force Fg dominates the motion of particles and the particle can be trapped to the tip. When the particle is situated in the driving region, the scattering force Fs dominates the motion of particles and the particle can be driven away in the propagation direction of the beam. Optical force can be obtained by integrating the time-independent Maxwell stress tensor < TM>along the enclosing surface of the particle. <TM> is described by18
<TM > = DE*+ HB*-1/2(D·E*+H·B* )I (1)
Where D is the electric displacement, H is the magnetic field, E is the electric field, B is the magnetic flux field, and༩is the isotropic tensor. The optical force Fo `can be acquired by
$${\mathbf{F}}_{\mathbf{o}}={\oint }_{\mathbf{s}}^{}(<{\mathbf{T}}_{\mathbf{m}}>\bullet n)\text{d}\text{s}$$
2
Which include two orthogonal components, i,e. the gradient force Fg and the scattering force Fs.19
To study the trapping ability of the TOF, the suspension was firstly kept stationary (i,e. the fluid velocity was 0 µm/s. Figure 2 (b1) and (b2) show optical microscope images of trapping of particles by the TOF in the trapping rengion, where the gradient force is dominated. Once the 980-nm laser light at an optical power of 30 mW was launched into the TOF, particle A and B with a diameter of 3 µmwere captured to the TOF tip in turn by the optical gradient force Fg. As the time goes by, there are only two particles were trapped at the end of the TOF, other particles confined to the axis were pushed away along the propagation direction of the light by the scattering force. To expand the range of optical manipulation, a fluidic flow was introduced, the direction of which is opposite to the laser beam, as schematized in Fig. 2 (a2). Particle C would suffer from the opposite viscous drag force Fd induced by the flow, which can be calculated using the Stokes Law:
Fd = 6πrηv (3)
where r is the radius of SiO2 particles, ηis the dynamic viscosity of water solution at room temperature, and v is the flow velocity of particle solution.
Figure 2 (b3) shows the microscope image of a single particle trapping in the driving region, in which the red and black arrows indicate the laser and flow direction, respectively. When the particle C was pushed away from the TOF by the scattering force Fs, it was subjected to the opposite viscous drag force Fd. Therefore, the particle C can be stably trapped to the optical axis, where the optical scattering force and viscous drag force achieved a stable equilibrium. The position of the particle can be controlled by adjusting the laser power or the fluid velocity. By further observation it can be seen, when particle D was transported towards the TOF along the optical axis by the fluid flow, it was bound closely to the particle C. With more SiO2 particles trapped one after another, a particle chain was organized along the optical axis of the TOF. Figure 2 (b4) shows a formed chain of 4 particles by the cooperation of scattering force Fs, viscous drag force Fd and binding force (axial gradient force Fg). Unlike traditional optical trapping, there are no predefined three-dimensional stable positions before a particle is introduced into the field in the driving region of the TOF. The presence of the particle modifies the field distribution. When the SiO2 particle with a low absorption is irradiated by a 980-nm laser light, it acts as a microlens, focusing and/or diverging the light, exerting an axial gradient force (binding force) on the adjacent particle, which would be bound to the preceding particle,18 as schematically shown in Figure (a3). D indicated the distance between the TOF tip trapped two particles and the particle chain. Figure 2 (b5) and (b6) show the formed particle chains with numbers of N = 7 and N = 12. It was found that, with increasing the number of the bound particles, the position of the particle chain is fixed (D = 10 µm)。
Figure 3 shows four sequential images taken by the CCD at an optical power of 30 mW, and the interval is 1 s. The flow velocity was set to be 20 µm/s, the direction of which is opposite to the light propagation. It can be seen that, at t = 0 s, a six particle chain was formed in front of the TOF tip trapped two particles with a distance of 10 µm. Particle A was delivered to the formed particle chain along the axis of the TOF with a average velocity of 20 µm/s by the flow, and bound tightly to the former particle by the cooperation of viscous drag force Fd, gradient force Fg, and scattering force Fs. It should be pointed out that, particle B was not trapped by the binding force but moved with the fluidic flow with a velocity of 20 µm/s.
After a chain of 8 particles was organized, the position of which can be shifted by adjusting the laser power. The flow velocity was fixed at v = 20 µm/s, and D denotes the distance between the TOF trapped two particles and the particle chain. Figure 4 (a) shows the dependence of measured distance D on injected optical power. The results show that, with an increase of the optical power, the particle chain was gradually pushed away from the TOF tip with the increase of D. On the contrary, the particle chain was delivered toward the TOF tip by decreasing the optical power. This is because the optical scattering force is proportional to optical power. Figure 4 (b) shows that, when the optical power launched into the TOF was set to be 60 mW, due to the viscous drag force is proportional to the flow velocity, the distance D can also be alerted by changing the velocity of flow. The formed chain was propelled toward the TOF tip by increasing the flow velocity, and driven away from the TOF tip with reducing the flow velocity. Therefore, controllable and position designated manipulation of particle chain with different numbers from 1 to 13 can be achieved. By further experiment, it was found that, when the number of particle chain exceed 14, it is difficult to form a stable particle chain due to the fluid perturbation.