## 3 Results and Discussion
### Patterns Affected by Particle Size and Concentration  
In the experiments, polystyrene microspheres with a diameter of 2 \(\upmu\)m, 1 \(\upmu\)m, 0.5 \(\upmu\)m, and 0.2 \(\upmu\)m are used for the optical trapping. As shown in Section 3.1, the 1 \(\upmu\)m particles form a ring structure. However, the 2 \(\upmu\)m particles assemble to form a close-packed structure in the experiments. When the trapping laser beam irradiates at the slide, and the distance between two bright diffraction fringes are related to the aperture of the microscope objective. The distance between two bright fringes is about 2 \(\upmu\)m at a trapping depth of 1 \(\upmu\)m. Therefore, the 1 \(\upmu\)m particles are confined at the bright fringes and the rings of particles can be distinguished individually. When the size of trapped particles becomes larger, each particle bestrides two bright fringes. Then, the particles form a compact structure, and no ring structure can be observed. The 0.5 \(\upmu\)m particles can form a ring structure at a trapping depth of \(\sim\)0.5 \(\upmu\)m, as shown in Figure 4a. The laser power is 820 mW, and the particle concentration is 4 \(\times\) 10\({}^{9}\) cm\({}^{-3}\). It is found that some particles is unstable. When the diameters of particles become smaller, the optical forces from the diffraction fringes acting on the particles decrease drastically. The gradient forces of some fringes are not enough to overcome the Brownian motion, so some particles randomly leave the diffraction fringes. It is beneficial to confine more particles stably in the rings at higher laser power. At this concentration, it is similar to the phenomenon of 1 \(\upmu\)m particle. The radii of particle rings can be changed by changing the trapping depth. When the trapping depth is larger than 3 \(\upmu\)m, there is no ring pattern formed. The 0.2 \(\upmu\)m particles with a concentration of 4 \(\times\) 10\({}^{9}\) cm\({}^{-3}\) do not form a stable ring structure at the trapping depth of \(\sim\)0.5 \(\upmu\)m and even the laser power is added to 1.5 W. We believe that the gradient forces on the 0.2 \(\upmu\)m particles generated by the diffracted fringes have been overwhelmed by the thermal fluctuations; therefore, diffraction fringes can not confine the 0.2 \(\upmu\)m particles to form stable ring structures. In this paper, we also do the experiments with 0.5 \(\upmu\)m and 0.2 \(\upmu\)m particles at large concentrations. It is found that the formed patterns are different from that at the low concentration. Even the diffraction fringes can not confine the particles stably, the 0.2 \(\upmu\)m particles can form the unstable ring structure at the trapping depth of 5 \(\upmu\)m when the concentration is added to 10\({}^{11}\) cm\({}^{-3}\). There are lots of particles attracted into the bright diffraction fringes. Since the concentration of particles is so high, there are many particles around the diffraction fringes. The number of particles entering and leaving the rings are equal, so the particles can form a clear ring structure under the action of very weak gradient forces. Figure 3: Confinement capabilities of diffraction traps for 1 \(\upmu\)m particles. (**a**) the confinement capability as a function of laser power at a particle concentration of 4 \(\times\) 10\({}^{8}\) cm\({}^{-3}\); (**b**) the confinement capability as a function of particle concentration at laser power 820 mW. Furthermore, even at the position where the trapping depth reaches 15 \(\upmu\)m, the ring structure formed by the 0.5 \(\upmu\)m particle is still clearly visible at the concentration of 10\({}^{11}\) cm\({}^{-3}\). At the concentration of 10\({}^{11}\) cm\({}^{-3}\), the 0.5 \(\upmu\)m particles rings are changed with trapping depth increasing, as shown in Figure 4b-f. When the laser beam is focused on the slide, the radius of the particles ring is small. As the trapping depth increases, the higher order diffraction fringes are able to gather the particles, which gradually increase the radii of particle rings.