## 3 Results and Discussion  
### Assembling of Particles with Linearly Polarized Beam  
In typical optical tweezers, a high numerical aperture objective is used to focus a laser beam tightly for a three-dimensional potential well. In general, the aperture of the objective lens is much smaller than the waist of the trapping beam. The diameter of the objective aperture is 1 mm in the experiments. When the beams propagate through the objective lens, the diffraction patterns are visible at the slide-water interface. The bright diffraction fringes generate the diffraction optical traps near the surface of slide. Figure 1c shows the diffraction pattern of the linearly polarized Gaussian beam and the corresponding light intensity distribution. Colloidal particles can be trapped by the bright diffraction fringes. The particles are trapped two-dimensionally at the slide surface, and the supporting force balances against the scattering force to prevent the particles from escaping from the traps. As the number of trapped particles increases, the particles form a ring structure at the glass-water interface. The process of rings' structure formation is shown in Figure 2a-d. The laser power is 450 mW. The amount of 1 um particles in the solution is 2 \(\times\) 10\({}^{8}\) cm\({}^{-3}\). At first, the micro-particles are dispersed and walk randomly before turning on the trapping laser, as shown in Figure 2a. When initiating the optical tweezers, the particles are attracted by the optical forces and confined in a bright region of diffraction fringes, as shown in Figure 2b. With time going on, the number of confined particles gradually increases, as shown in Figure 2b-d. Finally, particles are assembled into the structure of several concentric rings, under the control of optical forces from bright diffraction fringes. We also use a circularly polarized beam to repeat the assembling experiments. The result is similar to that of the linearly polarized beam, and the particles are confined in the bright region of diffraction fringes to form a concentric ring structure. Figure 1: (**a**) optical tweezers setup. Instrument layout showing optical paths for 1064 nm trapping laser and lamp for bright imaging. L1–L2, lens; M1–M2, mirrors; MO, microscope objective; DM, dichroic mirror; SWP, s-waveplate; LP, linear polarizer; PF, polarization filter; (**b**) schematic illustration of the focal region produced inside the sample cell. \(z\) is the trapping depth; (**c**) diffraction pattern and light intensity distribution (a.u.) on the slide. Most of the optical tweezers are three-dimensional optical traps, which can manipulate the particles axially (in a \(z\)-direction) by changing the trapping depth. However, the optical traps generated by the bright diffraction fringes in this paper are two-dimensional traps, and there is not enough axial gradient force to overcome the scattering force for manipulating the particles in the \(z\)-direction. Contrast to three-dimensional optical traps, changing the the distance between the focus and the glass surface can not manipulate the particles in the \(z\)-direction, but can move the particles transversely in the \(x\)-\(y\) plane. By changing the the distance between the focus and the glass surface, the radii of the diffraction rings are changed at the slide surface. When the radii of the diffraction rings change, the radii of the particles rings are changed accordingly because the particles are driven by the diffraction rings in the \(x\)-\(y\) plane. The changes of rings radii are showed in Figure 2d-f. In Figure 2d, the particles rings are initially at the trapping depth of 1 \(\upmu\)m. When the trapping depth decreases, the radii of diffraction rings become small. The radii of the particles rings decrease with the decreasing of the radii of diffraction rings. Figure 2e shows the image of the particles rings when the trapping depth decreases to \(\sim\)0.5 \(\upmu\)m. It can be seen that the radii of particles rings become smaller compared to Figure 2d, and the aggregation is more compact.