## 4 Discussion  
Through observing the E-field amplitude distributions and spiral phase patterns on the x-y planes, the OAM mode of the vortex wave is verified. To evaluate the purity of desired topological mode further, the normalized OAM spectrum from the x-y plane at the height of 9\(\lambda\) is calculated by using the Fourier transform method [37], as shown in Figure 9a. It is shown that the spectrum with \(l=-1\) mode accounts for a major part of the wave and other OAM spectrum components are below 0.1, demonstrating that the generated quasi-non-diffractive vortex wave possesses a high mode purity. The transmission efficiencies of the quasi-non-diffractive and conventional OAM waves are computed and depicted in Figure 9b, respectively. Here, the transmission efficiency is defined as the ratio of the power flow through an observational plane in the simulated environment to the counterpart on the metasurface. As evident from Figure 9b, the transmission efficiency of a conventional OAM wave exhibits a rapidly declining trend as the propagation distance increases, while the declining rate of a quasi-non-diffractive case is slower than the former and almost remains at a constant value. In addition, the farther the propagation distance, the more obvious the difference of the efficiency.  
Figure 8: Simulated distributions of the E-field amplitude on the x–z planes for (**a**) the quasi-non-diffractive vortex wave and (**b**) conventional vortex wave, respectively. (**c**) A magnified view of the non-diffractive range.  
Figure 9: The (**a**) normalized OAM spectrum of the vortex wave carrying \(l=-1\) mode OAM and (**b**) transmission efficiency of the quasi-non-diffractive and conventional OAM waves.  
As for the fabrication and the experimental setting, some factors also need to be considered. Firstly, using our proposed method, the desired metasurface can be fabricated by the printed circuit board (PCB) or 3D printing processing technology; the advantages of easy fabrication and low cost will facilitate it to be widely applied in many fields. Secondly, the machining accuracy of the slot units on the fabricated metasurface is of importance; if the machining accuracy of the edge length is too low, it will lead to a serious deviation of the central resonant frequency. For the case of extremely small side length, researchers should use high-precision micromachining technology to ensure the radiation performance of the designed metasurface. Thirdly, because a monopole, as the feed, is integrated on to the holographic metasurface, the impedance matching of the port needs to be considered. If a monopole is directly placed on the top of a conductor layer of the metasurface to excite the units, the interaction between the surface wave around the coaxial inner conductor and the surrounding metal will worsen the port matching. Therefore, it is necessary to dig an annular gap around the inner conductor, which is equivalent to a capacitive matching ring to improve matching of the port. Here, we set a ring with an outer diameter of 3.72 mm to achieve a good impedance matching.  
Lastly, in the simulation, we set observation planes at different heights above the metasurface to achieve the E-field amplitude distribution. However, for the actual measurement, a set of near-field scanning equipment is needed to test the E-field distribution on different cross sections. Generally, a near-field probe is controlled to scan on the required cross sections and sample the E-field data at constant interval. The smaller the sampling interval, the more time and resources it takes, and the researcher should find a balance.