## 3 Modeling, Simulation and Analysis
### Modelling and Simulation of the Metasurface  
Once the size of slot units and characteristic parameters of the object wave are determined, a metasurface generating a circularly polarized quasi-non-diffractive vortex wave can be created. Herein, we construct a metasurface radiating a left-handed circularly polarized (LHCP) quasi-non-diffracting vortex wave carrying \(l=-1\) mode OAM in 20 GHz. The base angle (\(\beta\)) of the equivalent axicon is specified as 15\({}^{\circ}\) and the aperture (\(D\)) of the metasurface is 78.75 mm as a result, which codetermines the largest non-diffractive distance, i.e., \(Z_{\text{max}}=D/(2 tan\beta)\) = 146.95 mm. Each row of the proposed metasurface with square size contains 21 slot units, the period of which is set as \(p\) = 3.75 mm. The scheme of the calculation process of the final slot-type distribution pattern is illustrated in Figure 3. Following the design procedure, substituting the related parameters into the Equations (1)-(3), the phase profiles of two linearly polarized object waves (\(\textbf{P}_{objy}\textbf{P}_{objx}\)) and reference waves (\(\textbf{H}_{refx}\), \(\textbf{H}_{refy}\)) can first be computed. Afterward, based on the holographic interference principle, two interference phase profiles (\(phase_{y-pol}\), \(phase_{x-pol}\)), calculated by linearly polarized waves, can be obtained by using Equation (4). By applying the binary judging method with a fixed threshold to two interference phase profiles, respectively, their corresponding single slot-type distribution patterns are achieved. The y-polarized slot-type pattern contains two kinds of states including the no-slot and the horizontal slot, which denote \"00\" and \"01\" in binary way, respectively. Similarly, the x-polarized slot-type pattern also has two states referring to the no-slot and the vertical slot, which denote \"00\" and \"10\", respectively. Finally, by superposing each binary value of the two linearly polarized slot-type distribution patterns (\(S_{y}\), \(S_{x}\)) directly, a final slot-type distribution pattern (\(S\)) can be conveniently achieved. This pattern contains four kinds of values ranging from 0 to 3, which denotes no-slot, horizontal, vertical and cross-type slot units, respectively. Figure 2: The model and simulation results. **(a)** The simulation model of a slot unit; **(b)** 3D radiation pattern of the unit model. **(c)** Scattering parameters (\(|S11|\), \(|S21|\)) of the model; **(d)** The simulated far-field radiation patterns of the unit cell on the planes of \(\varphi\) = 0\({}^{\circ}\) and \(\varphi\) = 90\({}^{\circ}\), respectively. Herein, the threshold is preliminary determined by the numerical optimization with the help of Matlab and its calculation process (refer to Figure 4). Firstly, the holographic computation is performed by using the objective wave and reference wave, and the interference phase distribution on the metasurface is obtained. Secondly, the interference phase distribution is compared with the initial threshold by binary algorithm to obtain the slot distribution. Afterward, combined with the phase distribution and binary slot distribution of the metasurface, the radiation characteristics of the metasurface can be computed, including gain, wavefront phase and OAM spectrum. Next, the three calculated results are compared with the desired target values (Gain_ set, Phase_ set and OAM_ Spectrum_set). If the requirements are not met, the original threshold is adjusted and recalculate from the second step. If the requirements are satisfied, the process is complete and the current threshold is determined as the final value. Since computation causes a lack of consideration of coupling between the units, it is essential to conduct the joint computation and simulation between the Matlab and ANSYS software. By using the simulated E-field data to revise the threshold further, a suitable threshold can be decided.