## 4 Discussion  
In the present article, we first investigate the theoretical differences between the OSM and DM, showing that the OSM is easier to function in space-limited situations due to the unique properties of its individual microstructure when the full-model size is equal. Then, the streamlined structure has greater sampling efficiency than the discrete structure, thus the vortex light forms a more concentrated focus spot after passing through the metasurface, which is beneficial to improve the mode resolution ability. When DM arranges the modes of the OAMs, there is a large space in the left part of the focusing plane that cannot generate the focusing spot, reducing the maximum detection range and maximum detection value. The area in the left part of the focal plane where focal spots cannot be generated is related to the single unit structure in DM and the \(l_{0}\) designed in the full model, as shown in Equation (12). When the \(l_{0}\) of the full model is constant, the period \(p\) of the unit structure is smaller, and the \(\phi_{\max}^{\prime}\) is larger. However, this problem does not exist in the OSM, which can effectively use the space in the focal plane and form the focused spot throughout the circumference, as shown in Figure 4b. The above advantages make the OSM significantly increase the detection range and maximum detection value of the OAMs' modes and do not reduce the mode resolution when multiple superimposed OAMs. It cannot resolve two superimposed vortices with a mode interval smaller than \(\Delta l=5\), and it is consistent with the described spin-decoupled metasurface [37]. Still, its designed \(l_{0}\) is only 40, and the OAMs' modes resolution range  
Figure 4: Resolution efficiency of the OSM of wavelength 633 nm. (**a**). Focusing mode of two superimposed OAMs’ modes with different mode intervals simulated by FDTD. The OAMs interval increases from \(\Delta l=4\) to \(\Delta l=7\), and the left figure shows the intensity mode of the two topological charge focusing spots, and the right figure shows the intensity curve of the corresponding dashed white line. (**b**). FDTD simulation results of PMT with 124 superimposed OAM modes and mode interval \(\Delta l=10\). (**c**). Normalized intensity curve along the white dotted round line in b.  
is within \(\pm 100\) topology charge, which is far below the maximum mode detection range in this paper. Due to the characteristics of the catenary metasurface, it can only regulate LCP (or RCP) at the same time. The OSM is designed for incident vortex for LCP and is not suitable for the vortex of RCP in this paper. In addition, there are some limitations on the resolution of adjacent OAM, and strict alignment is also required during detection. Then, we demonstrated a resolving power of \(\Delta l=1\) when only a single isolated OAM mode is received at a time, there was no cross-talk between adjacent modes. However, when multiple overlapping vortices are received simultaneously, the intensity overlap between them leads to reduced resolution power. As shown in Figure 4a, FDTD simulation results show that they cannot resolve two superimposed vortices with a mode interval smaller than \(\Delta l=5\), which means that at most 180 superimposed vortices can be simultaneously detected. Similar mode overlaps and resolution limitations have been observed in the angular lens-based OAM sorting methods [35]. Since the perimeter of the ring in which the focus spot is located in the focal plane is fixed, as is the size of the focus spot, the resolution can be further improved by decreasing the focus spot (adding a super-oscillatory phase) or enlarging the perimeter of the ring (designing it into a spiral arrangement pattern). In addition, a modified azimuthal-quadratic phase mask can also effectively improve the mode resolution power, which is expressed as \(\phi_{l}^{\prime}=-\frac{n^{2}l}{l_{0}}\)[37] and indicates that the azimuth difference of adjacent OAM modes becomes \(n^{2}\) times the original one.