Metasurfaces offer unprecedented degrees of freedom in the manipulation of electromagnetic waves and have great potential in the field of wavefront manipulation. By controlling the phase of the metasurface, one can control the propagation of electromagnetic waves, and many exotic phenomena arise. Examples include anomalous reflections [1–4], beam focusing [5–8], polarization conversion [9–11], orbital angular momentum (OAM) generation [12–15], and holographic imaging [16,17]. Among them, the geometric phase, also known as the PB phase, has been widely used in the design of metasurfaces due to its broadband modulation. The broadband property of the PB geometric phase has greatly contributed to the development of broadband functional devices based on metasurfaces. However, a potential dilemma remains with geometric phases obtained by rotating units. For right-handed circularly polarized (RHCP) waves and left-handed circularly polarized (LHCP) waves, a rotating unit always gives the same magnitude and opposite sign to the geometric phase. The PB geometric phase is usually spin-coupled, which prevents independent control of LHCP and RHCP waves. To overcome this limitation, a common approach is to combine the geometric phase of spin-decoupling with the propagation phase of spin-decoupling. In this way, it is possible to change the magnitude and even the sign of the geometrical phases of the LHCP and RHCP waves. Spin-decoupling [3,8,18–21] of circularly polarized waves is achieved by this method.

Improving the efficiency [22,23] of the aperture and energy transfer [24,25] of metasurfaces is very valuable research. It is also a very novel hotspot to apply in the field of optics, which also has a very wide range of application prospects in the field of engineering. Metasurfaces are important for compact wireless and optical communications, allowing multitasking or multifunctionality and significantly increasing information capacity. As the demand for high-speed, high-capacity information transmission increases in both optical and wireless communications, the independently controlled wavefront is being used to increase transmission capacity. To increase the channel capacity and improve the information transmission efficiency, it is crucial to achieve the geometric phase with spin-decoupling. In 2019 [26], Xu et al. broke spin-decoupling and realized a two-channel Bessel beam. In 2023 [27], Fu et al. achieved spin-decoupling of a monolayer metasurface to explain the phase difference in terms of the rotation of the current. By designing a dual-band double circularly polarized transmission array, Yang et al. [28] presented a shared aperture metasurface with four degrees of freedom low profiles in 2024. In 2024 [29], Zhu et al. achieved transmission-reflection-integrated spin-decoupling by combining 3D-printing technology with novel materials and introduced a phase delay line to create a propagation phase difference, facilitating device miniaturization and thinness. The dual-band, four-channel reflective metasurface solved the problem of spin-decoupling and planar near-field focusing.

To date, full-space spin-decoupled electromagnetic (EM) manipulation remains elusive and is rarely demonstrated. Achieving beam reconfigurability [30,31] for conformal structures is even more difficult and is hardly mentioned in any articles. For spin-decoupled conformal structures, phase delays due to structural changes are taken into account. To address the conformal integration design of spin-decoupled metasurfaces, this paper proposes a new method to achieve spin-decoupling on curved surfaces. The clever use of 3D printing [32,33] and PCB manufacturing technology greatly reduces the cost and difficulty of producing metasurfaces. Summarizing the above approach, the design needs to be carried out in the following steps. First, the phase delay ψ1(x,y) of the surface structure needs to be discussed, which compensates the phase of the curved surface structure into the initial plane. In the second step, the phase gradient ψ2(x,y) is constructed in the compensated plane, which allows beam deflection and beam focus generation. In the third step, phase ψ(x,y) of the combination is obtained by calculation, and the propagation phase and geometric phase are then calculated from the phases of the LHCP and RHCP waves.

Full phase and polarization control is achieved by combining the geometric phase and propagation phase. Independent wave control can be designed in any orthogonal polarization state, even in the case where two elliptical waves are contained in the optical region. This strategy provides an unprecedented degree of freedom in the modulation of the wavefront.

A metasurface with reconfigurable spin-decoupling is presented in this paper. Decoupling of circularly polarized waves is achieved by merging the propagation and geometric phases, and phase compensation from curved to planar structures is achieved based on generalized Snell’s law. Spin-decoupling of curved structures and beam reconfigurability of metasurfaces are realized for the first time. Combining the properties of water-based metasurfaces instead of phase-change materials ultimately achieves beam reconfigurability with spin-decoupling. As shown in Fig. 1, the reflected wave from the metasurface can switch between two states (state 1, radiation at a fixed angle; state 2, radiation along orthogonal sections of the cylinder). In the modelling process, the metasurface-skin with ultra-thin and highly efficient properties was created based on 3D-printing technology and PCB manufacturing technology. The final design of the conformal metasurface is just 2.6 mm, and the fabrication method can be generalized to metasurfaces of arbitrary shapes. The metasurface proposed in this paper overcomes the problem of conformal integration design and fabrication of curved structures while having good electromagnetic wave manipulation properties.

Theoretically, for irregular and complex structures, it is very difficult to control the scattering by controlling the phase of their wavefront. This is because generalized Snell’s law states that the wave reflected from a conformal structure is related to the angle of incidence, which is often difficult to determine for conformal structures. To achieve spin-decoupling on the conformally structured metasurface, the phase change caused by the change in the angle of incidence must be resolved. Here we propose a new solution for the spin-decoupling of conformal metasurfaces by combining generalized Snell’s law with the spin-decoupling theory while satisfying the phase compensation of both. Generalized Snell’s law and spin-decoupling theory are used to design superposition phase gradients for curved metasurfaces. The exact derivation is given in Appendix B.

The structure of the unit is shown in Fig. 2 and consists of seven layers of dielectric. The first and last layers are copper with a thickness of 0.035 mm. The second and sixth layers are F4B (εr=3.0, and tand=0.001) with a thickness of 0.2 mm. The third and fifth layers consist of 0.8 mm resin (εr=3.0, and tand=0.0375). The fourth layer consists of a 0.6 mm air layer (water layer in another state) combined with a cross-structured resin. Propagation phase differences can be introduced in the X and Y directions by varying the length of the metallic cross-structure in the surface layer. At the same time, the PB phase is introduced into the operating band by rotating the cross structure. This allows LHCP and RHCP waves to be decoupled by combining two uncorrelated phases. The metal structure is attached to a 0.2 mm thick F4B dielectric plate, which is ultra-thin enough to be bent. This is the highlight of this paper and provides the basis for the study of conformal structures.

The thickness and structure of the water layer influence the electromagnetic properties of the metasurface, and the simulated S-parameters of the metasurface with different structured water layers are shown in Fig. 2(d). When the intermediate layer of the metasurface is a full layer of water, the unit reflection coefficient is about −5dB. When the water layer is optimized to structured water, the metasurface has a reflection coefficient close to −3dB, as shown in unit B. The cross-polarized reflection coefficients of the metasurfaces are switchable between 0 dB and −14dB, comparing the states with and without water. The real and imaginary parts of the permittivity are shown in Fig. 2(e). The permittivity of water is larger. By optimizing A to B, the water content is reduced, the imaginary part of the permittivity decreases, and the loss decreases, so the co-polarization reflection coefficient increases. Structure C is a combination of air and the dielectric layer, so the real part of the calculated permittivity is between air (1) and dielectric (2.7), and the imaginary part is close to 0. At this time, the dielectric layer is close to loss-free, so the coefficient of cross-polarized reflection is close to 0 dB.

Figure 2(f) calculates the refractive index, which is also equal to the speed of light c at a given wavelength in a vacuum divided by its speed v in a given material, n=c/v. The larger the refractive index of the material, the slower light propagates through the material. The loss in unit A is greater, so the refractive index is greater, and the electromagnetic wave propagates slower. So we optimize the unit structure, and the refractive index of unit B decreases and the loss decreases. The refractive index of unit C is minimized.

Figure 3 shows the eight units of the metasurface, the exact dimensions of which are given in the figure. Unit V (VI/VII/VIII) has the same dimensions as unit I (II/III/IV) but is rotated by 90°. As a result, they have the same reflection amplitude, but the phase shift values differ by 180° due to the PB phase.

Figure 4 shows the simulation parameters of the metasurface unit. Since the X and Y directions of the metasurface are symmetrical, we use the X direction to analyze the reflection coefficients and phases. Figure 4(a) shows the parameter diagram of the metasurface unit in the absence of water. When Lx is varied from 2 mm to 9.8 mm, the amplitude at 14 GHz is always close to 0 dB, and the phase difference is close to 360° coverage, which can satisfy the requirements of the spin-decoupled propagation phase. Figure 4(b) shows that under the incidence of the linearly polarized wave, the X polarized reflection phase covers 360°, and the Y polarized reflection phase remains almost constant as Lx is varied from 2 mm to 9.8 mm. Thus, this metasurface can be used to achieve spin-decoupling. When the circularly polarized electromagnetic wave is incident, the S-parameters of the eight metasurface units are shown in Figs. 4(c) and 4(d). The amplitude values are all close to 0 dB at 14 GHz, and their reflection phases cover 360°. Figure 5(a) shows the variation of the phase of metasurface (MS) I with the angle of rotation for the LHCP and RHCP waves. The RHCP shows an opposite trend to the LHCP, and the absolute value of the phase shift is twice the angle of rotation.

Figure 5(b) shows the diagram of the unit parameters in the state of water addition. As shown in the figure, when a water layer of 0.6 mm thickness is added, which changes with the change of Lx, the phase gradient of the unit structure is destroyed after the addition of water, and the reflection coefficient of the unit decreases. Both its amplitude and phase do not satisfy the theoretically calculated values, and the spin-decoupling is destroyed. Theoretically, the beam deflection can be controlled by controlling the presence or absence of water in the unit structure.

Once the spatial target phase distribution of the reflected wave is determined, the linearly polarized reflection phase ψx(x,y) and the rotation angle θ(x,y) at the corresponding position metasurface are obtained. In this paper, the target phase in the range of 0°–360° is discretized into four states using 2-bit coding. With 90° steps, the numbers “00,” “01,” “10,” and “11” describe the reflection phases at 0°, 90°, 180°, and 270°, respectively. Decoupled independent modulation of orthogonal circularly polarized electromagnetic waves using a single metasurface requires the independent coding of two circularly polarized incident waves on a single unit. Therefore, by combining the four phase states of LHCP waves and the four phase states of RHCP waves, a total of 16 metasurface units with different structural parameters are required. The geometric dimensions and orientation angles of the metasurface units corresponding to different circularly polarized phase states at the incidence of LHCP and RHCP electromagnetic waves are given in Table 1.Table 1.

2-Bit Reflection Phase Corresponding to the Size and Geometric Orientation of the Metasurface Unit under the Circularly Polarized Wave

The design flow from the planar surface to the curved surface is shown in Fig. 6. In this design, to achieve spin-decoupling on a curved surface, the phase compensation ψ1(x,y) from the curved surface to the planar surface is first calculated by Eq. (B6), and then the phase ψ2(x,y) required for beam deflection can be calculated by Eq. (1), as shown in Fig. 7. The deflection angles of this design are 35° and −20° at the incidence of RHCP and LHCP waves, respectively. The total phase ψtotal(x,y) is obtained by superposition, as shown in Fig. 8. Then the lengths and rotation angles of Lx and Ly at each point are obtained from Table 1, ψ(x,y)=2πλxsinα.(1)

The results of CST full wave simulation are shown in Fig. 9. The electric field at 14 GHz is analyzed for different incidences of circularly polarized electromagnetic waves. Figures 9(a) and 9(b) show the electric field distributions at the incidence of RHCP wave and LHCP wave, with the electromagnetic waves reflected at angles of 35° and −20°. By definition [34,35], the deflection efficiency is the ratio of the power of the reflected electromagnetic wave to the power of the incident electromagnetic wave on the metasurface. The deflection efficiencies are calculated to be 40.77% and 77.22% at RHCP wave incidence and LHCP wave incidence, respectively. The simulation results of the electric field show that the metasurface achieves spin-decoupling for the incidence of circularly polarized electromagnetic waves. To verify the reconfigurability of the curved metasurface, we simulated and compared the electric field distribution in the state of adding water, as shown in Figs. 9(c) and 9(d). In the water addition state, the outgoing electric field is almost perpendicular to the tangent of the curved surface. There is no effect of beam deflection and spin-decoupling. It is proved by comparative analysis that the metasurface with or without a water layer can control the switching of spin-decoupling. The function of spin-decoupling on the reconfigurable metasurface proposed in this paper is verified.

Far-field scattering was simulated and tested, in which the electromagnetic wave was reflected at a certain angle, as shown in Figs. 10(a) and 10(b). The simulation results were consistent with the test results, and the good performance of the metasurface was verified.

Spin-decoupled metasurfaces are widely used in wireless communications, power transmission, and beam shaping. With the variety of changes in communication environments, planar structures are no longer sufficient for use in complex environments. To the best of our knowledge, there are almost no articles on spin-decoupling of conformal structures. In the previous section, we have modulated the beam at the incidence of different circularly polarized waves. In this section, the realization of surface focusing on a conformal metasurface is discussed to demonstrate the applicability of surface spin-decoupling, ψF(x,y)=2πλ(x2+y2+F2−F).(2)

Figure 11 shows the curved surface compensated phase and the focus compensated phase. For RHCP and LHCP waves, the focal points F are set to 100 mm and 150 mm, respectively. The compensated phases ψR1(x,y) and ψL1(x,y) of the planar structure are calculated from Eq. (1). The total phase is obtained by superimposing the focused phase ψF1(x,y) [ψF2(x,y)] and the compensated phase ψR1(x,y) [ψL1(x,y)], and then the values of Lx, Ly, and θ are obtained by Eq. (B12). Specific phase values and parameters as well are given in Fig. 12.

Figure 13(a) shows the electric field distribution in the X–Y section when the LHCP electromagnetic wave propagates along the −Z direction and the electric field is focused in the center of the section, which is in accordance with the physical law of beam focusing. Figure 13(b) shows the electric field distribution in the X–Z section, where the electric field is concentrated around 100 mm, which corresponds to the set focal distance. Since the phase compensation of the unit provides a certain degree of freedom, the focus is spread over 95–105 mm. Figures 13(c) and 13(d) show the electric field distributions of different cross-sections at the incidence of the RHCP wave. To verify the correctness of the application of Snell’s law and spin-decoupling theory to metasurfaces, we compare and analyze the focusing properties of the conformal metasurface with the planar structure. The planar focusing electric field distribution is shown in Fig. 14. The electric field distributions in the corresponding X–Y and X–Z cross-sections are almost identical to the curved surface. The focal points are both 100 mm and 150 mm. Focusing efficiency is defined as the ratio of the energy in the focal spot region to the total energy incident on the focusing system. According to Refs. [36,37], the focusing efficiency was calculated to be 50.896% for RHCP wave incidence and 48.94% for LHCP wave incidence. Comparison of full wave simulation results shows that the present structure has good wavefront manipulation properties and can achieve spin-decoupling of arbitrary circularly polarized waves. The application of generalized Snell’s law in the surface structure solves the difficult problem of wavefront manipulation of the conformal shape, which provides a solution idea for the multifunctional wavefront manipulation problem of the complex structure.

In the presence of water, the simulation compares the electric field distribution of the LHCP and RHCP wave, as shown in Fig. 15. Figures 15(a)–15(d) show the electric field distributions for different cross-sections. In comparison with Fig. 13, it is clear that the focal point disappears after addition of water and the electromagnetic wave spreads in a cylindrical shape. The electric field at the corresponding focal position is also changed. The simulation results confirm that the water-based metasurface proposed in this paper has the property of being tunable in multiple focal positions.

For curved structures, not only the effect of structural changes on metasurface properties should be considered, but also the manufacturing process of curved structures. It is still a difficult point in current research how to achieve the common integrated design of curved structures. This structure incorporates 3D-printing technology to achieve ultra-precise design of curved structures using resin. Arbitrary curvature can be achieved using 3D-printing technology. Combined with PCB manufacturing technology, the ultra-thin F4B was produced as shown in Fig. 16(c), and its ultra-thin characteristic also provided a good basis for the design of the conformal structure.

By injecting a layer of water into the center of the dielectric plate, it is possible to modulate the scattering characteristics of circularly polarized waves. Metasurfaces have tunable scattering properties, whose scattering characteristics can be switched between two states. By controlling the beam deflection to a fixed angle, the scattering characteristics of the triangle or the ground can be camouflaged. This metasurface can be used for cloaking and camouflage of conformal structures. Combined with spin-decoupled dual channels, it can achieve controllable multi-focus focusing and can be used in power transmission, multi-channel communications, and other areas. Figure 17 shows the process of 3D-printing the medium and a diagram of the metasurface-skin structure. The experiments were carried out in the microwave chamber. Figure 16(d) shows the experimental test environment diagram and the metasurface with the water test diagram. The experimental results are in agreement with the simulation results, and the experimental results are well verified.

The use of water-based metasurfaces in this paper has great application value. Water-based materials instead of phase-change materials can reduce the cost. Water-based materials can switch between two states at any time, whereas phase-change materials must switch into two states under specific conditions. Therefore, water-based metasurfaces are much more controllable. In addition, the combination of 3D-printing technology allows the design of metasurfaces with arbitrary curvature. The use of phase-change materials is difficult to realize in conformal structures, and the properties of curved phase-change materials need to be discussed. The use of water-based metasurfaces is a perfect solution to these problems. Moreover, it is possible to realize the design of the metasurface in any structure. There are, of course, limitations to the development of water-based metasurfaces. Water injection takes longer and requires a pump to pressurize the water to improve efficiency. Different structural water must be designed for different working frequency bands of the metasurface, and the design process is more complicated. These are questions that need to be addressed in the further research.

To compare the performance advantages of the metasurface proposed in this paper, the present structure is compared with spin-decoupled metasurfaces reported in recent years. It can be seen from Table 2 that this work has some advantages in terms of tunability, thickness, and fabrication of conformal structures. It is worth noting that this work is the first, to our knowledge, to achieve spin-decoupling in curved structures. Meanwhile, the method proposed in this paper can be widely applied to the phase design of other conformal structures, including triangles and metasurfaces with different curvatures. The manufacturing method of 3D-printing technology combined with PCB technology proposed in this structure is applicable to the manufacturing of other multi-layer structures and can effectively improve the manufacturing accuracy. Since the propagation phase is resonance induced, it has the limitation of a narrow bandwidth, so it is very interesting work to increase the bandwidth next.Table 2.

Performance Comparison of the Spin-Decoupled Metasurface

Here, curved spin-decoupled multifunctional metasurfaces are demonstrated, which provide efficient control of circularly polarized waves in space. In contrast to all previous literature, including unlocked double spin and chiral selective metasurfaces, we use 3D printing to generate conformal reconfigurable spin-decoupled metasurfaces. The metasurface solves the difficult problem of wavefront manipulation of conformal structures and achieves conformal integration combined with good electromagnetic manipulation performance. Reconfigurable multifunctional electromagnetic metasurfaces are realized in combination with water-based metasurfaces. Through experimental results, we have shown that our unique approach is not only of unprecedented value in terms of channel enhancement (6G communications), but also paves the way for areas such as conformal cloaking and holographic imaging.