## 5 Conclusions  
For the OSM structure, a single streamlined line can cover \(2\pi\) phase control while multiple units are required in the DM structure. Therefore, in the limited space of the metasurface, the OSM can arrange more columns than the DM to achieve larger phase gradient regulation, thus significantly increasing the detection range and maximum detection value of the OAM. Moreover, the OSM also improves the problem of insufficient wavefront sampling of the DM, thus the detection resolution of the superimposed OAMs is improved. Then, when the detection range of a single OAM is greatly increased, a certain resolution of multiple superimposed OAMs can also be maintained. In addition, similar to the DM, the OSM can simultaneously detect wideband vortices covering the whole visible band. Then, in addition to being ultra thin and ultra light, the OSM also has an overall ultra-small size, making it highly integrated. At the same time, due to the large mode resolution ability of the OAMs, they can easily and quickly resolve high-capacity information, which makes it a potential application value in the medium application of optical quantum computers. Then, we investigated the mode resolution of a single OAM and multiple superimposed OAMs and demonstrated its huge OAM mode resolution power. Furthermore, the mode detection method of the OAMs is shown. The whole optical system is straightforward,and the mode resolution method is also straightforward and fast. To predict the topological charge of the vortex, it is only necessary to determine the location of the focusing spot formed on the focal plane after the vortex light passes through the metasurface. This simple and effective system will have high stability in the practical application, thus it can adapt to various working environments and increase its potential application value. It is worth mentioning that more structure arrays can be arranged on the circumference of the metasurface by adding the inner and outer radii of the full model, i.e., a more significant phase gradient can be controlled, and the scope of the OAMs' mode sorting can be further expanded. On the contrary, if the system needs to be integrated with limited space, the inner and outer circle radius of the metasurface can be reduced to meet the requirements of the system. Of course, part of the range of the OAMs' mode sorting will be lost. Moreover, if the demand for multiple superimposed OAMs' mode resolution is high, increasing the mode resolution power can be achieved by appropriately decreasing the coefficient \(l_{0}\). The scheme is simple, practical, convenient, and flexible and can be applied to many application scenarios, such as large-capacity OAM communication and highly integrated optical quantum systems. In summary, we showed a comparison of the OAM discrimination efficiency between the OSM and DM, proving that the OSM has higher mode discrimination efficiency than DM. Then, we have demonstrated a single geometric TiO\({}_{2}\) OSM-based OAM mode discrimination method via PMT of the azimuthal-quadratic phase metasurface, where vortex beams are converted into focusing modes rotating clockwise on the screen as topological charges increase. Finally, we showed that the proposed approach could be extended to the ordering of superimposed OAMs with a proper mode interval. The results show that the OSM can significantly increase the mode detection range of the OAMs but does not reduce the ability to rank multiple superimposed OAMs' modes. These results may have many important applications in momentum measurement of spin and angular momentum and detection of phase and polarization singularities. [PERSON] completed the optimization of the graphic structure and designed the final full model for simulation, data analysis, and processing. [PERSON] provided the initial simulation code. [PERSON]; [PERSON]; [PERSON] and [PERSON] participated in the revision of the first draft. writing--review and editing, [PERSON], [PERSON] and [PERSON].