## 5 Conclusions  
In summary, a novel method is proposed, based on the superposition of non-diffracting phase profiles and holograms, with two linearly polarized components generating a circularly polarized quasi-non-diffractive vortex wave carrying the orbital angular momentum. Our proposed method is similar to the combination of an equivalent axion-based method and waveguide-fed-based holography; the former is adopted to analytically express the object wave while the latter is applied to realize the radiation. Only by changing the on/off states of unit cells that couple to the continuous guide-mode magnetic components, can the interferogram with different features be created and an expected object wave can subsequently be generated. This method can be viewed as one of the digital phase-keying holographic methods, and this is a notable feature compared with other kinds of holographic metasurfaces.  
Based on this method, a holographic metasurface integrated with a surface feeding source is simulated and analyzed, which produces an LHCP quasi-non-diffractive vortex wave with \(l=-1\) mode in the normal direction. The simulation results demonstrate the effective diffraction suppression and a concentrative energy distribution within \(9\lambda\) distance away from the metasurface, compared with a pure vortex wave. Furthermore, to compare the divergence trend out of the maximum non-diffractive range, results of the normalized E-field amplitude and spiral phase distributions from \(10\lambda\) to \(30\lambda\), are simulated. The numerical simulations demonstrate that the LHCP quasi-non-diffractive vortex wave possesses an almost constant divergence radius and electric field strength in the 30 times wavelength range compared with a conventional vortex wave. By this calculation, OAM purity and the transmission efficiency of the generated quasi-non-diffractive wave are analyzed in detail. As for the fabrication and experiment considerations, four factors including the processing technology, machining accuracy, impedance matching and near-field measurement are discussed comprehensively in this paper.  
The proposed designing method is equivalent to a linear superposition of two scalar impedance modulation surfaces, which provide a more flexible manipulation and lower design complexity than a method of tensor impedance modulation. It paves a new way for generating and controlling the CP quasi-non-diffractive vortex wave in short- or medium-distance, which holds great potential for miniaturization devices applied in wireless energy transmission, high-resolution imaging and intelligent detection. Moreover, this phase-keying holographic method facilitates designing dynamically reconfigurable metasurfaces and intelligent devices in future.  
Conceptualization, C.Z.; methodology, C.Z.; software, C.Z. and L.W.; validation, C.Z.; formal analysis, C.Z.; investigation, C.Z.; resources, C.Z.; data curation, C.Z.; writing--original draft preparation, C.Z.; writing--review and editing, C.Z.; visualization, C.Z.; supervision, L.D., X.C. and S.L.; project administration, L.D. and S.L.; funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by 111 project (NO. B17007), National Natural Science Foundation of China (NO. 61427801 and NO. 61601040), Beijing Science and Technology Plan Project (No. Z191100002019015).  
Not applicable.  
The authors declare no conflict of interest.