## 3 Results and Discussion
### Forming Steady Patterns of Particles in a Salt Solution  
The particles form a ring structure in deionized water because they are confined by the gradient forces generated by the diffraction spot. It is the same as the previous studies, and the particles are trapped against the surface and can not escape from the traps [15; 21; 25]. However, the aggregation is unstable without the laser confinement. When the laser is off, the particles are free to move and the formed patterns of particles will be destroyed. Forming steady patterns of micro-particles is of great interest. The interaction between the dispersed particles can be described with Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Our above experiments are carried out in deionized water, and the particle structures are destroyed when the laser is off. In order to form steady patterns of micro-particles, there must be chemical conditions such that the particles have strong interactions. If the particles are in a salt solution, the ionic concentration will change the interaction of the particles, and eventually change the particle structures [31; 32; 33]. Previous research has demonstrated that the interaction of the particles can be adjusted by using different concentrations of NaCl in polystyrene solution, and found that 0.5 mol/L NaCl is very appropriate for forming steady patterns [34]. Under this NaCl concentration, the particles are mostly single and do not gather quickly, which makes pattern formation easy. In the experiment, the 0.5 um particles are washed and dispersed in 0.5 mol/L NaCl solution. The particle concentration is 4\(\times\)10\({}^{9}\) cm\({}^{-3}\). In the experiment, the particles are attracted into the diffraction traps at a trapping depth of \(\sim\)0.5 um. When the particles are attracted into the diffraction rings, the particles do not walk randomly but adhere to the slide surface firmly. The ring pattern is steady, and the structure is clear in view. The steady pattern formed by the diffraction traps remains even when the laser is off. This method can be used to print the particle patterns on the surface of the slide. The process of duplication is shown in Figure 6. When a particle pattern is completed, then the pattern is moved to the left by the sample stage. After 50 s, the particles form a new particle pattern by the diffraction fringes. The method for assembling particles in this paper is limited with the particle size. According to experiment results, the method can not assemble the particles with a diameter larger than 2 um into a ring structure because the large particles are closely assembled. Furthermore, this method also fails to assemble the particles with a diameter smaller than 500 nm into a ring structure. When the particle diameter becomes smaller, the gradient forces generated by the diffraction fringes are insufficient to overcome the Brownian motion. The diffraction traps demonstrated in the paper can only assemble transparent colloidal particles but can not be used to assemble metal particles and absorbing particles. For metal particles, the forces exerted by the diffraction fringes repel them to leave the traps. For the absorbing particles, the laser \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Polarization** & **Main Peak** & **1 st Peak** & **2 nd Peak** \\ \hline Linear & 1 & 0.54 & 0.31 \\ Radial & 1 & 0.33 & 0.12 \\ Azimuthal & 1 & 0.93 & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Intensity of the diffraction peaks. heating of particles results in a strong thermal gradient that drives the particles to leave the diffraction fringes [35; 36; 37]. Plasmonic tweezers may be a suitable method to assemble the metal or absorbing particles [38; 39; 40; 41]. The size of the ring structure formed by particle assembly is limited. The action range of the diffraction fringes are limited, so the particles can only be assembled within the action range and it is difficult to assemble the particles in a large scale.