Metasurfaces, as a two-dimensional quasi-planar structure of metamaterials, have attracted extensive attention of researchers due to their novel electromagnetic (EM) response properties that are far superior to natural materials (Yu et al., 2011; Chen et al., 2016; Cui et al., 2017; Zhang et al., 2017; Chen et al., 2019; Sun et al., 2019). The existence of metasurfaces provides a new and unprecedented style to freely and flexibly manipulate the amplitude, phase, and polarization of EM waves (Hao et al., 2007; Liu et al., 2014; Lei and Yang, 2017; Li et al., 2018). In recent years, they have become an important application prospect in many fields, such as microwave (Wang et al., 2019; Mao et al., 2020; Xu et al., 2020), terahertz (Yu and Li, 2016; Qi et al., 2020; Liu et al., 2021) and optoelectronic (Kildishev et al., 2013; Chorsi and Gedney, 2016; Fan et al., 2017; Han et al., 2020) devices, and stealth (Zhong et al., 2017; Joy et al., 2021) and antenna (Pan et al., 2016; Moreno et al., 2018) technology. Specifically, various metasurfaces have been proposed to implement fantastic phenomena and applications in microwave regions, including anomalous reflection/refraction (Xu et al., 2016; Bao et al., 2019), beam focusing (Zhang et al., 2019; Yuan et al., 2020a), hologram imaging (Xie et al., 2019), vortex beams (Yang et al., 2019; Chen et al., 2021), and polarization conversion and absorbing devices (Xu et al., 2018b; Wang et al., 2020).

Generally speaking, a metasurface consists of numerous well-designed meta-atoms by regularly arranging an array. For a reflective metasurface, the meta-atoms mainly contain three parts, metallic resonator, dielectric spacer, and metal ground plate, and the working performance of the metasurface primarily depends on the structure of the metallic resonator. Once the meta-atom with producing predesigned functionality and EM phenomenon is customized, there are two generic manners to adjust its phase responses under different incident waves, that is, propagation phase and geometric phase (Mueller et al., 2017). The propagation phase can be regulated by changing the dimensions of the element and is usually used to achieve different functionalities under two orthogonal linearly polarized wave incidences (Yu and Li, 2016; Cai et al., 2017; Mueller et al., 2017). Moreover, the propagation phase is insensitive to orthogonal circularly polarized (CP) incident waves, due to that two orthogonal CP waves can be separately decomposed into the superposition of two orthogonal linearly polarized waves with equal magnitude but a + π/2 or − π/2 phase difference, and thus the propagation phase generates duplicate amplitude and phase responses for left-handed circularly polarized (LHCP) and right-handed circularly polarized (RHCP) incident waves (Ding et al., 2019; Yuan et al., 2020a; Zhang et al., 2021). The latter geometric phase, also referred to as Pancharatnam–Berry (PB) phase, is excited by rotating meta-atoms that make up the metasurface array and can produce the phase shift of twice the rotated angle under a CP incident wave (Bouchard et al., 2014; Xu et al., 2017; Yang et al., 2019; Chen et al., 2021; Gou et al., 2021). The geometric metasurface operating in a reflection manner can generate a desired functionality for output waves with opposite helicity to the incident waves. Therefore, the PB phase shows anti-symmetrical phase responses with equal values and opposite signs under the LHCP and RHCP waves illuminating the metasurface, which is the conjugate symmetry property of the PB phase theory and limits the manipulation for two orthogonal CP incident waves. In order to break the constraint of the geometric phase, the propagation phase is introduced to decouple the conjugate responses under orthogonal CP wave illumination (Mueller et al., 2017; Ding et al., 2019; Yin et al., 2019; Zhang et al., 2019; Yuan et al., 2020a; Yuan et al., 2020b; He et al., 2021; Wang et al., 2021).

To date, some element structures have been proposed and applied to form the metasurface arrays with the phase profiles combining propagation and geometric phases, to implement the completely independent control of two orthogonal CP waves in microwave, terahertz, and optical regions (Devlin et al., 2017; Xu et al., 2018a; Yin et al., 2019; Guo et al., 2020; Wang et al., 2021; Zheng et al., 2021). In the microwave field, the independent wavefront controls under CP waves illumination were demonstrated by utilizing the dual-layered anisotropic meta-atoms with low linearly polarized cross talk and imposing both the geometric and propagation phases of metasurfaces (Xu et al., 2018a; Ding et al., 2019). Additionally, a multilayer element structure with various geometric degrees of freedom was designed to realize simultaneous and independent phase modulation of both orthogonal CP-transmitted waves with a specific CP wave illumination (Zhang et al., 2019; Yuan et al., 2020a; Yuan et al., 2020b). Nevertheless, the multilayer structures may ensure the efficiency of the metasurface and the required helicity-decoupled phase but at the same increase the profile thickness and manufacturing complexity. Guo et al. theoretically and experimentally illustrated a broadband single-layered spin-decoupled metasurface based on quasi-I-shaped meta-atom and applied it to a dual-CP reflector antenna (Guo et al., 2020). Moreover, single-layer reflective metasurfaces composed of anisotropic meta-atoms with a thickness of 3 mm were proposed and performed functions including polarization beam splitting and orbital angular momentum (OAM) multiplexing at 5.8 GHz (He et al., 2021). Therefore, with the rapid development of modern miniaturized and integrated systems, it is of great importance to explore ultrathin and multifunctional devices that are programmed by introducing polarization-decoupled phases and could independently control orthogonal CP waves.

In this paper, single-layer ultrathin reflective metasurfaces are proposed to demonstrate multiple functionalities via the polarization-decoupled phase for dual orthogonal CP incident waves. They consist of anisotropic meta-atoms, which can realize well the independent control of orthogonal linearly polarized EM waves by using the propagation phase. The reflection matrix of a metasurface under the illumination of orthogonal CP waves is analyzed, and then the polarization-decoupling phase can be obtained by adjusting the geometric dimensions and rotating meta-atoms at specific angles, imposing the propagation phase and geometric phase simultaneously. On the basis of this concept, the designed metasurfaces can impose distinct phase profiles and respond differently to dual orthogonal CP waves, implementing independent manipulation for incident EM waves with left circular polarization (LCP) and right circular polarization (RCP) states. For proof of concept, we design three kinds of bifunctional metasurfaces operating in a reflection manner for three representative applications in the microwave domain. To be more specific, one of them achieves beam focusing with distinct focal lengths under the illumination of two orthogonal CP waves. Another one acts as an OAM multiplexor, which generates vortex waves with different topological charges when LHCP and RHCP waves separately illuminate the metasurface. Moreover, the third one is a beam deflector that can deflect two orthogonal CP incident waves by different reflection angles according to the generalized Snell’s reflection laws. The verification experiments are performed, and the results coincide well with the simulated ones.

The EM waves with orthogonal circular polarization states can be represented as the superposition of EM waves with two orthogonal linear polarization bases and expressed as follows: | λ + 〉 = | λ x + 〉 | λ y + 〉 = 1 i (1a) | λ − 〉 = | λ x − 〉 | λ y − 〉 = 1 − i (1b) where “ + ” and “ − ” represent a pair of orthogonal circular polarization states, namely, LCP and RCP waves in this paper, and the subscripts “x” and “y” are the coordinate components at the Cartesian coordinate system. When the EM waves are incident on the designed meta-atom structure, the reflected output wave polarization states are complex conjugates with respect to each input polarization state {|λ ⁺⟩, |λ ⁻⟩}; mathematically, { | ( λ + ) * 〉 , | ( λ − ) * 〉 } , where * denotes the complex conjugate (Mueller et al., 2017). To independently control the orthogonal polarization states λ + and λ − , the designed metasurface needs to impose desired and distinct phase profiles ϕ ⁺(x, y) and ϕ ⁻(x, y) on λ + and λ − . That is, the Jones matrix of the anisotropic metasurface element at each point should simultaneously satisfy: J ( x , y ) ⋅ | λ + 〉 = e i ϕ + ( x , y ) ⋅ | ( λ + ) ∗ 〉 (2a) J ( x , y ) ⋅ | λ − 〉 = e i ϕ − ( x , y ) ⋅ | ( λ − ) ∗ 〉 (2b)

The above two expressions can be deduced and recast to obtain the Jones matrix, as follows: J ( x , y ) = e i ϕ + ( x , y ) ⋅ | ( λ x + ) ∗ 〉 e i ϕ − ( x , y ) ⋅ | ( λ x − ) ∗ 〉 e i ϕ + ( x , y ) ⋅ | ( λ y + ) ∗ 〉 e i ϕ − ( x , y ) ⋅ | ( λ y − ) ∗ 〉 | λ x + 〉 | λ x − 〉 | λ y + 〉 | λ y − 〉 − 1 (3)

Further, for two orthogonal CP incident waves, the Jones matrix of the element at coordinate (x, y) can be obtained by substituting Eq. 1; Eq. 2; Eq. 3: J ( x , y ) = e i ϕ + ( x , y ) e i ϕ − ( x , y ) − i ⋅ e i ϕ + ( x , y ) i ⋅ e i ϕ − ( x , y ) 1 1 i − i − 1 = 1 2 e i ϕ + ( x , y ) + e i ϕ − ( x , y ) − i ⋅ e i ϕ + ( x , y ) + i ⋅ e i ϕ − ( x , y ) − i ⋅ e i ϕ + ( x , y ) + i ⋅ e i ϕ − ( x , y ) − e i ϕ + ( x , y ) − e i ϕ − ( x , y ) (4)

In particular, the Jones matrix is unitary and symmetric, so it can be recast as its canonical form: J ( x , y ) = Q A Q − 1 = c o s θ ( x , y ) − s i n θ ( x , y ) s i n θ ( x , y ) c o s θ ( x , y ) e i φ x ( x , y ) 0 0 e i φ y ( x , y ) c o s θ ( x , y ) − s i n θ ( x , y ) s i n θ ( x , y ) c o s θ ( x , y ) − 1 (5)

Then, the unknown quantities in Eq. 5 can be obtained through simple mathematical derivation with combining Eq. 4, as follows (Mueller et al., 2017; Xu et al., 2018a; Yuan et al., 2020b): φ x ( x , y ) = 1 2 ( ϕ + ( x , y ) + ϕ − ( x , y ) ) (6a) φ y ( x , y ) = 1 2 ( ϕ + ( x , y ) + ϕ − ( x , y ) ) − π (6b) θ ( x , y ) = 1 4 ( ϕ + ( x , y ) − ϕ − ( x , y ) ) (6c) where the Jones matrix is framed based on the linear polarization coordinate base, and A is a diagonal matrix, whose elements are the eigenvalues of J, and Q is an orthogonal matrix, whose columns are the eigenvectors of J. The eigenvalues in matrix A impose the phase shifts φ _x and φ _y along the x- and y-polarized directions, while the eigenvectors impose the angular orientation θ of the meta-atoms relative to the reference coordinate system. Specially, the phase shifts φ _x and φ _y can be introduced using the propagation phase and attained by varying the dimensions of the anisotropic element along the x- and y-directions, and the angular orientation θ can be introduced using the geometric phase and attained by rotating the meta-atom in an anticlockwise direction. The above derived result can be understood as an integration of the propagation phase and geometric phase in a single meta-atom.

In general, on the basis of Eq. 6 and assigned spatial phase distributions ϕ ⁺(x, y) and ϕ ⁻(x, y) for the specific functionalities under LHCP and RHCP incident waves, the φ _x , φ _y , and θ of a meta-atom located at a concrete coordinate (x, y) can be calculated. Then, the metasurface array can be established using the eligible meta-atoms and applied to implement the independent manipulation for dual orthogonal CP incident waves.

The photographs of the three fabricated metasurface samples and the experimental environments are shown in Figure 7. The prototypes of the metasurfaces are fabricated using the printed circuit board (PCB) technique, as shown in Figure 7A, where the insets show zoomed parts for a clear illustration. Moreover, metasurface1 is applied to realize the function of beam focusing with different focal lengths under dual orthogonal CP incident waves; metasurface2 can separately generate converged vortex waves with the OAM modes of −2 and 3 under the waves with LCP and RCP states illuminating, while metasurface3 reflects the two normal incident plane waves with orthogonal CP states to two directions with different deflected angles. The near-field planar scanning system is exhibited in Figure 7B, which is mainly composed of a fixed platform, feeding antenna, position-controllable field probe, and vector network analyzer (VNA). During the measurement, the metasurface prototypes are illuminated with a dual CP horn antenna placed about 1.5 m away from the samples to ensure the incident wave to be a quasi-plane wave as used in simulations. The rectangular waveguide testing probe moves along the x and y directions to measure the intensity and phase wavefront distributions of the reflected wave. Moreover, the scanning planar area of 340 mm × 340 mm is perpendicular to the radiation beams. The near-field distributions of the beam focusing metasurface and the OAM multiplexed metasurface are performed by using the testing method. It should be noted that the distance between probe and metasurface should be adjusted to the focal lengths in the near-field experiments. The far-field measurement environment is presented in Figure 7C, where the samples and a dual CP horn antenna are placed on a board 1.5 m away from each other, and the board is fixed on a rotary stage and can freely rotate 360° in the horizontal plane. Here, the antenna is connected to a VNA and acts as a feeding antenna, whereas another CP horn antenna is placed far away from the rotating platform as a receiver to record far-field scattering patterns. The 2D-normalized far-field scattering patterns of the OAM-multiplexed metasurface and the beam deflection metasurface are performed at the measurement system.

In conclusion, the theoretical method of the combining geometric phase and propagation phase has been utilized to design ultrathin spin-decoupled meta-devices. A single layer and ultrathin meta-atom operating at 14 GHz are proposed based on a cross-shaped resonator. Guided by the theoretical method, three distinct ultrathin bifunctional metasurfaces have been designed, simulated, and measured, which separately realize the functions of focusing with distinct focal lengths, vortex beams generation with different OAM modes, and beam deflection with different deflection angles and deflection directions, as the dual orthogonal CP waves illuminate the metasurfaces. Moreover, the simulated results have been validated by the microwave experiments, and good agreements are achieved between simulated and measured results, verifying the effectiveness of the theoretical method and the performance of the metasurfaces. The research results in this paper provide a new idea to design low-profile and multifunctional meta-devices and may be expected to significantly improve the capacity of the metasurface in future.