## 3 Modeling, Simulation and Analysis
### Modelling and Simulation of the Metasurface
For illustrating the quasi-non-diffractive feature of the vortex wave generated from the proposed metasurface, the normalized electric-field (E-field) amplitude and spiral phase distributions of the LHCP components on the different x-y cross-sections, located at the height range \(3\lambda\) to \(9\lambda\), are calculated and depicted in Figure 6(a1-g2) due to the maximum non-diffracting distance of \(Z_{\text{max}}=146.95\) mm (i.e., \(9.8\lambda\)). The normalized E-field amplitude distribution of a quasi-non-diffractive vortex wave is still a doughnut-shaped zone, and a null zone is located in the center of the energy distribution. In Figure 6(a1-g1), the divergence radius of the null zone of the vortex wave is about \(5\) mm (\(0.33\lambda\)), \(2\) mm (\(0.13\lambda\)), \(3\) mm (\(0.2\lambda\)), \(3.35\) mm (\(0.22\lambda\)), \(4\) mm (\(0.27\lambda\)) and \(4.3\) mm (\(0.29\lambda\)), respectively, which almost remains stable within the \(9\lambda\) range. Due to the formation of a non-diffractive wave which is superposed by forward and backward waves, the non-diffracting feature becomes constant from the \(Z_{\text{max}}/2\), which results in the divergence radius of \(3\lambda\), slightly larger than the other values. In addition, the outer radius of the E-field amplitude distribution enlarges slowly and does not cover the x-y cross-section, with a radius of \(60\) mm, until the vortex wave propagates at a distance of \(9\lambda\) away from the metasurface. During this progress, most of the energy is highly concentrated around the propagating axis. Figure 5: The simulated model of the proposed metasurface and its simulation results of radiation characteristics. (**a**) Top view of the proposed metasurface; (**b**) 3D radiation pattern; (**c**) reflection coefficient \(|S11|\); (**d**) and normalized power levels at planes of \(\varphi=0^{\circ}\) and \(\varphi=90^{\circ}\), respectively. In order to demonstrate the effect of diffraction suppression clearly, a holographic metasurface generating a conventional vortex wave carrying the same topological charge is designed as a reference of comparison. The normalized E-field amplitudes and the spiral phase distributions are presented in Figure 6(h1-n2). As shown in these figures, the divergence radius of the null zone of the vortex wave is close to 2.5 mm (0.17\(\lambda\)), 3.1 mm (0.21\(\lambda\)), 5 mm (0.33\(\lambda\)), 10 mm (0.67\(\lambda\)), 14 mm (0.93\(\lambda\)) and 17 mm (1.13\(\lambda\)), respectively, which shows a more obvious trend of divergence than a non-diffractive case in the specified range. In addition, the intensity of the energy around the center is more divergent than the vortex wave characterized with the non-diffraction feature. The spiral phase patterns of two kinds of vortex waves are also illustrated in Figure 6(a2-g2) and (h2-n2), respectively. The variation of the phase within one cycle is 360\({}^{\circ}\) clockwise, which demonstrates the spirally topological mode is \(-1\). Moreover, the intrinsic properties of a vortex wave are not influenced by the introduction of the diffraction feature. Furthermore, to compare the divergence trend out of the maximum non-diffractive range, simulated results of the normalized E-field amplitude and spiral phase distributions from 10\(\lambda\) to 30\(\lambda\) are also illustrated in Figure 7. As for the quasi-non-diffractive vortex wave, the divergence radii of the null zone (approximately 11 mm, 17 mm, 20 mm, 22 mm and 36 mm, respectively) enlarge slowly and maintain a relatively concentrated energy envelope. In contrast, the divergence radii of the null zone of the vortex wave are approximately 10 mm, 17 mm, 23 mm, 30 mm and 51 mm, respectively, which shows a more serious trend of divergence than a non-diffractive case in the specified range. The simulated results are consistent with the hypothesis that, although located at the area outside of the non-diffracting distance, the divergence trend of the quasi-non-diffractive vortex wave is always weaker than the conventional vortex wave [17].