Terahertz waves refer to electromagnetic waves between microwave and infrared wave, which can be applied in different fields such as communication, sensing, radar, and imaging. Terahertz coding metasurface, as an important device for modulating terahertz waves, has the advantages of simple structure, small size, low cost, low loss, and high efficiency. The coding metasurface units are arranged according to a certain coding sequence, and by changing the phase difference between the units, the flexible modulation of terahertz waves can be achieved to generate various forms of beams. However, when the design of a general terahertz coding metasurface is completed, the function and operating frequency are relatively single. In order to fully utilize the coding metasurface, an anisotropic metasurface is proposed, which can regulate the incident orthogonal polarized waves separately. And a frequency independent coding metasurface has been proposed, which can separately regulate the incidence waves at different frequency points to generate different forms of beams. In addition, the phase change materials such as vanadium dioxide (VO₂) were used to achieve the switching of transmission and reflection modes of terahertz waves, thereby achieving the goal of full spatial modulation of electromagnetic waves. The above methods improve the ability of the coding metasurface to regulate terahertz waves, but the integration level still needs to be improved. Therefore, we integrate these technologies to achieve multi-frequency and multi-beam tunable terahertz coding metasurface in full space, greatly improving its ability to regulate terahertz waves.

In this paper, a coding metasurface which can regulate the circular polarized waves and orthogonal polarized waves separately is proposed by combining the principle of PB geometrical phase as well as the frequency independence and anisotropy of double crosses. In addition, introducing the phase change material VO₂, flexible switching of terahertz waves between transmission and reflection is achieved by changing its phase change state. The details are as follows. When VO₂ is in an insulating state, the designed coding metasurface is a single-frequency-point 3-bit PB geometrical phase transmitting coding metasurface, which generates transmission-type vortex waves with topological charge number of 1. When VO₂ is in a metallic state, the designed coding metasurface is a dual-frequency-point independently adjustable 1-bit anisotropic reflective coding metasurface, which generates four symmetric beams, of which two symmetric beams on the xoz plane with RCS reduction and two symmetric beams are on the yoz plane, respectively.

The designed coding metasurface units (Fig. 1) with identical metallic split-ring structures in the third, fifth, and seventh layers are rotated from 0° to 157.5° in a step of 22.5° to obtain a total of eight coding metasurface units (Fig. 2). When VO₂ is in an insulating state and a circularly polarized wave with f₁=0.6 THz is incident, the units maintain a high transmission amplitude and strictly satisfy a phase difference of 45°. The design conditions for a 3-bit transmission type coding metasurface unit are met. Arranging them according to a certain coding sequence [Fig.4(b)] can produce transmission-type vortex waves with topological charge number of 1 (Fig.5). When VO₂ is in a metallic state and the orthogonal polarized waves of f₂=0.5 THz and f₃=0.85 THz are incident, a dual-frequency and anisotropic 1-bit reflective-type coding metasurface unit (Fig. 3) is designed by using the two cross structures. After arranging them according to a certain coding sequence [Figs. 4 (c)-(f)], the perpendicular incidence of y-polarized wave with f₂=0.5 THz on the xoz plane produces two symmetric beams [Figs. 6(a) and 6(b)]. When a y-polarized wave with f₃=0.85 THz is incident vertically, two symmetric beams are generated on the yoz plane [Figs. 6(c) and 6(d)]. When a x-polarized wave with f₂=0.5 THz is incident vertically, four symmetrical beams are generated [Figs. 7(a) and 7(b)]. When a x-polarized wave with f₃=0.85 THz is incident vertically, a diffuse scattering beam can be generated [Figs. 8(a) and 8(b)], realizing RCS reduction. The results show that with the rational design of the coding metasurface combined with the phase transition state of VO₂, the frequency of the incident wave source, and the polarization state, the full space regulation of terahertz wave's reflection and transmission can be realized and five beam forms on the same coding metasurface can be obtained.

In this paper, a coding metasurface with full space multi-frequency and multi-beam tunability is designed by changing the phase transition state of VO₂, combining the principle of PB geometrical phase and the cross unit structure with dual-frequency anisotropy. A 3-bit transmission coding metasurface with an operating frequency of f₁=0.6 THz is designed to produce a transmitted vortex beam. And a dual-frequency 1-bit anisotropic reflective coding metasurface with operating frequencies of f₂=0.5 THz and f₃=0.85 THz is designed to produce various forms of symmetric and scattered beams. This coding metasurface, which introduces phase change material and realizes full space multi-frequency multi-beam regulation by transmission and reflection, is important for designing multifunctional terahertz beam modulation devices.