## 2 Design Principle and Procedure  
### Design Principle  
In this research, a monopole-integrated holographic metasurface generating a circularly polarized quasi-non-diffractive vortex wave carrying the desired OAM mode, is proposed. The proposed metasurface consists of a back-grounded substrate covered by inhomogeneous slot units and a monopole as the surface feeding source. The upper conductor layer and the bottom grounded layer form a parallel-plate waveguide, supporting the surface wave produced from the feeding source, propagated as a cylindrical wave in the cavity. When the surface wave, viewed as the reference wave, interacts with the slot units arranged according to the interferogram, an expected object wave can be recovered and radiated into the air, as depicted in Figure 1.  
As an important part of the holography, the analytical forms of the object wave first need to be decided. Herein, a quasi-non-diffractive vortex wave is the object wave, which has the character of adjustably converging radii and a controllable depth-of-field. Owing to the non-diffracting and self-healing properties [28], the Bessel beam is deeply investigated and used to alleviate the problem of diffraction. As a special solution of the Helmholtz homogenous wave equation in the cylindrical system, the intensity transverse profile of a Bessel beam is independent of distance and fits to the Bessel function [29]. The idea that a Bessel beam carrying the infinite energy is produced by an inf  
Figure 1: Scheme of a monopole-integrated holographic metasurface generating a quasi-non-diffractive vortex wave carrying the desired OAM mode. impractical and cannot be realized. In practice, we only can use the aperture with a finite size to generate a Bessel beam characterized by quasi-non-diffraction within the specialized range. Introducing the non-diffractive feature of the zeroth-order Bessel beam into the vortex wave will create a high-order quasi-Bessel vortex wave. Currently, there are mainly two methods to achieve the quasi-Bessel beam: one method is to steer the wavefront of the incident wave by using lens-like devices [17; 30; 31; 32]; the second method is dependent on the inward cylindrical travelling wave aperture [21; 33; 34; 35]. Herein, our proposed method is similar to a combination of the two methods; an equivalent axion-based method is adopted to analytically express the object wave while waveguide-fed-based holography is applied to realize the radiation. By superposing the phase profile of the Bessel beam and the vortex wave, a quasi-non-diffractive vortex wave in the controllable propagation direction of (\(\theta\), \(\varphi\)) can be generated and its phase profile \(\Phi(x,y)\) can be expressed as follows:  
\[\Phi(x,y)=lphi-k[\sin\beta\sqrt{x^{2}+y^{2}}+(xsin\theta\cos\varphi+ysin\theta sin \varphi)], \tag{1}\]  
where \(l\) is the topological charge, \(phi\) is the azimuth angle, and \(k\) denotes the wavenumber in the air space. The \(\beta\) is the base angle of the equivalent axicon and its value should not be less than the minimum allowed in the non-diffracting condition. The \((x,y)\) and (\(\theta\), \(\varphi\)) represent the surface coordinate positions of each cell and the radiation angle, respectively. Due to the fact that an interferogram is the interference result of a reference wave and an object wave, its pattern is closely related to the polarization, amplitude and wavefront of two waves. For the generation of a circularly polarized wave, we proposed a method [36] by superposing x- and y-polarized holograms independently. Combining this method and the phase profile of the quasi-non-diffractive vortex wave obtained from Equation (1), the analytical expression of a required object wave \(\mathbf{P}_{CPBOAM}\) can be expressed as follows:  
\[\mathbf{P}_{CPBOAM}=\mathbf{P}_{objx}+\mathbf{P}_{objy}=A_{0}e^{i\varphi(x,y) }(\hat{x}+j\hat{y}), \tag{2}\]  
where \(A_{0}\) denotes the amplitude of the wave and is set as the value of 1 here.