# Centrosymmetric Optical Vortex
## 4 Results and Discussion
The first row of Figure 4 shows the experimental intensity patterns of the CSOV, and the second row displays the numerical simulation intensity patterns. For our experimental results, the number of the light petals increased with the increasing PRF, which is consistent with the numerical simulation intensity. The bottom row of Figure 4 depicts the OAM distribution with 4 \(\times\) magnification of the areas in the white dashed frames in the second row of Figure 4, respectively. Furthermore, the whole OAM distributions of the CSOVs are shown in the subset of Figure 4a3-d3. With the increasing PRF, the magnitude of the local OAM of the areas in the white dashed frames are increased first and finally decreased. The reason is that the increasing PRF leads to the increase of the OAM's magnitude. Meanwhile, as the interference area increases, the positive and negative local OAM cancel each other out [26]. Moreover, the increasing gradient force of the black circle dashed frames in Figure 4a3-d3 indicates that the CSOV can provide stronger trapping force with a larger PRF. Figure 4: Distributions of the intensity and OAM density of the CSOVs with the PRF = 4, 6, 8, 10, respectively. (**a1–d1**) are experimental intensity, (**a2–d2**) are numerical simulation intensity, and (**a3–d3**) are OAM density distribution. To study the properties of the CSOV, the center profiles of the CSOV's intensity and OAM rings in Figure 4 are plotted in Figure 5. For the intensity distributions, two peaks form at \(\theta\)= \(\pm\)\(\pi\)/2 due to the generation of petals in the interference area, which ensures a larger gradient force to form an optical trap. Meanwhile, the OAM decreases to zero at the intensity peak positions. For the local OAM distribution profiles located in the non-interference area, the magnitude of the OAM increases with the increasing PRF, which reflects that the local OAM maintains the properties of the spiral phases used in the initial field. To enhance the regulatory flexibility of the CSOV, the cone angle of the axicon is used as an adjustable parameter to modulate the radius. The intensity and OAM distributions of the CSOVs (PRF = 4) with different cone angles \(\alpha\) are shown in Figure 6. One can find that the radius of the CSOV increases with the cone angle increasing. To quantitatively represent the relationship between the radius and the cone angle, we fitted the experimental dates, as shown in Figure 6a1. Their relationship is accord with the linear equation, \(r\) = 0.0985 + 1.36\(\alpha\), and the correlation coefficient is 0.99977. Furthermore, the magnitude of the OAM density decreases due to the constant total OAM. Owing to the optical trap formed in the interference areas demonstrated in the above, the regulation property of the cone angle \(\alpha\) indicates the potential significance in the separating cells. Figure 5: (**a–c**) are the center profiles of the CSOV’s experimental intensity, numerical simulation intensity and OAM rings of Figure 4, respectively. For instance, the positions of the date ring and the three points 0, \(-\pi\) and \(\pi\) are shown in Figure 4a1.