Reprogrammable Bistable Metasurface for Arbitrary Electromagnetic Wave Manipulation

ABSTRACT

Mechanically reconfigurable metasurfaces have been designed to achieve continuous modulation of electromagnetic responses through the integration of deformable elements with structurally simple architectures. Although current implementations with independently addressable deformable units enable multifunctionality, their constrained phase modulation range imposes fundamental limitations on achieving fully reprogrammable metasurfaces. Here, we report for the first time a 1‐bit phase‐coding concept of a deformable unit based on the controllable interference of two three‐dimensional (3D) bistable antennas, while maintaining superior broadband performance. By employing a hollow hyper‐elastic substrate, we create a reliable platform for 3D buckling and shape switching of antennas, where out‐of‐plane loadings applied to each unit allow programming of the desired phase patterns. A reprogrammable metasurface prototype is meticulously designed and fabricated, demonstrating reliable, repeatable, and arbitrary functionality‐switching capabilities. This concept establishes a robust foundation for mechanically reprogrammable metasurfaces and opens broader possibilities for applications in adaptive imaging, mechanical sensing, cloaking, information processing, and beyond.

In this study, a mechanically reprogrammable electromagnetic metasurface is developed by leveraging 1‐bit phase‐coding capability of two bistable 3D buckled antennas in the unit. Besides the programmable functionalities, the metasurface is exhibited with simplified structures, mechanical flexibility and full‐space manipulations of incident waves.

1. Introduction

As modern radio‐frequency domains such as satellite remote communication, low‐altitude aviation, and wearable electromagnetic (EM) devices evolve toward greater intelligence, the demand for flexible EM modulation components with high integration and multifunctionality has become imminent. Reconfigurable metasurfaces, as representative compact devices, have emerged as transformative solutions due to their unparalleled capability for dynamic EM wave manipulation. They have already enabled applications in adaptive cloaking [1, 2], camera imaging [3, 4], unmanned aerial vehicle communication [5], etc.

The operating principle of reconfigurable metasurface lies in units integrated with active components such as two‐dimensional materials [6, 7, 8], phase‐change materials [9, 10, 11], and PIN diodes and varactors [12]. By altering EM properties of the units via external stimuli, these metasurfaces achieve dynamic multifunctionality in spectral responses [13, 14, 15], wavefront modulation [16, 17], and beam scanning [18, 19]. Furtherly, reprogrammable/coding metasurfaces that incorporate control circuits and field‐programmable gate arrays facilitate independent modulation capability at the unit level [20, 21, 22]. Such metasurfaces have been widely investigated in wireless information and energy transfer [23, 24, 25], intelligent transportation systems [26, 27], in‐home monitoring [28], and the Internet of Things [29]. However, despite their high modulation speed and multifunctionality, these reconfigurable metasurfaces typically depend on intricate architecture and auxiliary external control systems.

Mechanical reconfiguration strategies have emerged as an alternative approach, directly modulating EM responses by altering unit morphology under mechanical stimuli. Such metasurfaces generally consist of resonant structures integrated with deformable substrates, forming dynamic functional platforms. Compared to the above electrical method, the mechanical modulations are with low responsive speed but simplified structural composition. Nowadays, the mechanically reconfigurable functionalities are still confined in the several scopes of strain sensing [30], adaptive focusing [4], biological spectroscopy characterization [31], etc. Existing approaches include in‐plane stretching [32, 33], origami [34, 35, 36], kirigami [31, 37, 38], channel expansion [39], and three‐dimensional (3D) buckling [40, 41]. In particular, origami and kirigami leverage deformation principles to tune resonant unit morphologies in 2D or 3D space. Combined with phase‐gradient design, these metasurfaces can dynamically perform beam steering [42], focusing [43, 44], and holography [45]. The 3D buckling approach, meanwhile, exploits stress release from pre‐stretched substrates to transform planar structures into 3D morphologies, but its modulation capabilities are largely confined to spectral responses.

A key limitation of mechanically reconfigurable metasurfaces is that constituent units often deform collectively rather than independently, hindering truly programmable functionalities. Recent developments have introduced independent amplitude coding to achieve reconfigurable scattering properties [46] and three‐fold holographic displays [47], yet programmable phase control remains elusive. This challenge originates from the unpredictable and insufficient phase shift during independent unit deformation. As a desirable example, Xu et al. [48] demonstrated mechanically coded reflective Pancharatnam–Berry phase‐based functionalities by rotating supercells integrated with micro‐motors, but such designs inevitably increase structural complexity. Therefore, new coding strategies based on mechanical reconfiguration are required to enable structurally simplified yet fully programmable phase control.

In this work, we propose a novel 1‐bit phase‐coding unit concept based on the controllable interference of two 3D bistable antennas, enabling a reprogrammable EM metasurface for arbitrary wavefront manipulation. Structurally, the 3D antenna is formed via controlled buckling of planar morphologies by releasing a pre‐stretched customized hollow substrate. This design allows flexible and cyclic switching between two stable states through out‐of‐plane loading. Based on the theoretical phase shift of the two‐fold rotational symmetric structure, two perpendicular bistable antennas are integrated within a single reprogrammable unit, yielding 1‐bit phase coding capability, a feature not previously achieved by conventional mechanical reconfiguration methods. A metasurface prototype fabricated using 3D buckling exhibits excellent morphology‐switching performance. During programming, external loading enables the metasurface to perform specific phase patterns tailored to the desired functionality. Extensive simulations and experimental characterizations confirm its ability to realize reprogrammable one‐ and two‐dimensional phase‐gradient profiles, supporting dynamic beam steering, focus sweeping, and reconfigurable holographic projection. These results not only demonstrate the practical viability of the proposed design but also establish a pathway toward a new class of mechanically tunable and programmable metasurfaces.

2. Results

2.1. Design Principle of the 3D Bistable Reprogrammable Metasurface

The design concept of a mechanically reprogrammable metasurface is inspired by the changeable EM responses of deformable units composed of bistable antennas under external mechanical loading. As input coding patterns, the applied mechanical loadings on each unit are transformed into spatial phase distributions by the metasurface platform, as shown in Figure 1a. For the bistability design, the mechanical structure is assembled through 3D buckling of a planar antenna within a biaxially pre‐stretched hollow substrate under compressive forces. As depicted in Figure 1b, the hollow silicone substrate is first pre‐stretched to a biaxial strain ε _x = ε _y = 10%, after which the terminal ends of the antenna, consisting of a copper and polyimide layer, are selectively bonded to the substrate. Notably, the geometric length of the antenna is designed as l = 6 mm to match the hole diameter of the stretched substrate. To ensure bonding reliability, the terminal‐end width and antenna width are optimized as m = 1.2 mm and w = 0.4 mm, respectively. Upon releasing the biaxial strain to its initial length, the hole diameter contracts from 6 mm to 5 mm, and the planar antenna compresses into a 3D buckled structure with upward or downward stable shapes, denoted as Shape 1 and Shape 2.

FIGURE 1.

Design concept of the 3D bistable reprogrammable metasurface. (a) Schematic of the proposed reprogrammable EM metasurface. (b) Formation process of the 3D buckled bistable antenna. A pre‐stretched patterned substrate compresses the planar line‐shaped structure into a 3D morphology while providing a platform for bistable switching under out‐of‐plane loadings. (c) Cross‐polarized transmission amplitude and phase of the bistable antenna under linearly polarized incidence. (d) Reprogrammable unit composed of two bistable antennas oriented perpendicularly. The index i represents antenna Shape 1 or 2. (e) Transmissive spectral responses of the units in different states. Two antennas with the same morphology induce destructive interference, while units composed of different antenna shapes produce equivalent amplitudes and a constant phase difference of 180°.

The bistable antenna can reversibly switch between Shapes 1 and 2 under out‐of‐plane loading without experiencing plastic deformation. Essentially, it can be modeled as a fixed‐end beam, and its theoretical cross‐sectional profiles are consistent with finite element analysis (FEA) results (see Section S1). Although Shapes 1 and 2 are symmetric, their stress distributions differ slightly owing to the dual‐layer copper/polyimide composition; further comparisons are provided in Section S2. To explore the EM modulation capability of the bistable deformation, 3D antenna Shapes 1 and 2 were modeled as individual unit cells to calculate spectral responses at the microwave band using CST software. As shown in Figure 1c, a linearly polarized wave with a 45° azimuth angle excites the 3D antennas, and the orthogonally polarized component is recorded on the transmission side. In this cross‐polarized transmission channel, the maximum amplitudes of both antennas are close to 0.5, attributed to the consistent geometry along the incident and transmitted polarization directions. The spectral peak of Shape 2 is blue‐shifted relative to Shape 1, while their phase profiles nearly overlap across the operating band.

After understanding the spectral responses of individual 3D bistable antennas, two such antennas were arranged orthogonally to form a deformable unit capable of efficiently modulating complex amplitudes through reconfiguration. This modulation originates from constructive or destructive interference of EM waves propagating through the perpendicularly oriented antennas. As shown in the insert of Figure 1d, the two axes parallel and orthogonal to the incidence polarization direction are selected as v‐ and u‐axis, respectively, and the transmissive electric field of a single horizontal antenna can be expressed as

$$\left(\begin{array}{c}{E}_u\\ E_v\end{array}\right)=\left(\begin{array}{cc}{t}_{uu}^{0^{\circ }}& t_{uv}^{0^{\circ }}\\ t_{vu}^{0^{\circ }}& t_{vv}^{0^{\circ }}\end{array}\right)\left(\begin{array}{c}0\\ E_{in}\end{array}\right),$$ (1)

where $t_{ij}^{0^{\circ }}$ represents the complex transmittance of the antenna at the orientation α = 0° and the subscript i (j) represents the transmissive (incident) polarization state. When the antenna is located at the orientation ⍺, the transmissive matrix T ^α becomes

$$T_{\alpha }=R\left(-\alpha \right)\left(\begin{array}{cc}{t}_{uu}^{0^{\circ }}& t_{uv}^{0^{\circ }}\\ t_{vu}^{0^{\circ }}& t_{vv}^{0^{\circ }}\end{array}\right)R\left(\alpha \right),$$ (2)

where R is a 2 × 2 coordinate rotation matrix $(\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array})$. Herein, the v‐to‐u cross‐polarized transmittance component is

$$t_{uv}^{\alpha }=\left({\cos }^2\alpha -{\sin }^2\alpha \right)t_{uv}^{0^{\circ }}.$$ (3)

For a specific orientation α = 90°, the above transmittance is expressed as $t_{uv}^{{90}^{\circ }}=-t_{uv}^{0^{\circ }}$, in other words, the phase difference is 180° between antenna orientations α = 0° and α = 90°. The complex amplitude of a 3D antenna can be expressed as $A_i{e}^{j{\phi }_i}$ at α = 0° and $A_i{e}^{j({\phi }_i+{180}^{\circ })}$ at α = 90°, where the subscript i represents the shape 1 or 2. By assembling two bistable antennas with an orientation difference 90°, a unit with periodicity P = 16 mm is constructed to perform four states. As the two antennas are both in upward or downward shapes (labeled as unit state 2), its transmissive complex‐amplitude $A_i{e}^{j{\phi }_i}+A_i{e}^{j({\phi }_i+{180}^{\circ })}$ is zero owing to the phase difference induced destructive superposition. For the opposite shapes (labeled as unit state 0/1), the surface current together with the antenna is rotated with the clockwise or counterclockwise angle 90° when the unit state is switched to the other one (see Figure S3a). Therefore, the constant phase difference ± 180° of each sub‐unit is produced to superpose in a unit and achieve the 1‐bit phase coding. The surface current at two frequencies performs with the same characteristics but various intensity, meanwhile the phase difference 180° is still available along the propagation direction in Figure S3b. Actually, the frequency parameter is not involved in the above derivation process, thus the constant phase difference is independent of the broadband frequencies.

To validate the proposed design, the transmissive amplitudes and phases of all unit states were calculated (Figure 1e, lower subplots). For unit States 0 and 1, the amplitude profiles are identical, and the phase difference consistently remains −180° across broadband frequencies. In contrast, units with identical antenna shapes exhibit negligible amplitudes and only minor variations in phase profiles. The deformation level of the unit can enhance the transmissive amplitude (see Section S4), although switching highly deformed or stressed antennas requires overcoming significant mechanical resilience. From the perspective of a linearly polarized incident wave, the 45° azimuth angle was optimized to maximize transmission efficiency (see Section S5). These results align well with the theoretical design and confirm the broadband 1‐bit phase‐coding characteristics of the proposed reprogrammable unit.

2.2. Fabrication of the 3D Bistable Reprogrammable Metasurface

Following the establishment of the design principle for mechanically reprogrammable units, a metasurface composed of 25 × 25 units was fabricated using the buckling‐induced formation strategy illustrated in Figure 1b. The fabrication process primarily involved femtosecond laser patterning and selective bonding of the unit array onto a prestrained substrate. As shown in Figure 2a, a dual‐layer copper/polyimide film was attached to a thermally releasing tape (TRT) to maintain array periodicity. A femtosecond laser (pulse power: 160 mJ, scanning speed: 0.4 mm/s, 13 passes) was used to cut the film into designed patterns while preserving the TRT backing. After peeling away the residual film, only the patterned units remained adhered to the TRT layer. In parallel, a CO₂ laser (power: 210 W, speed: 70 mm/min, wavelength: 1064 nm) was employed to ablate a hole array in a silicone film, forming the elastic substrate. The film was then biaxially stretched and fixed in a mechanical fixture. A polyethylene terephthalate (PET) mask was aligned with the antenna terminals to define bonding regions. Silicone adhesive was selectively deposited through the mask, and the PET layer was quickly removed to prevent premature solidification. The patterned unit array with the TRT backing was laminated onto the pre‐stretched substrate and aligned with the hole array. After curing, the TRT was heated to ${300}^{\circ }\mathrm{C}$ for 30 s and peeled off to transfer the units. Finally, the biaxial strain was gradually released, transforming the planar antennas into bistable 3D shapes oriented upward or downward.

FIGURE 2.

Fabrication of the 3D bistable reprogrammable metasurface. (a) Fabrication flow diagram of the reprogrammable metasurface. (b) Photograph of the metasurface sample before and after release of substrate strain. c) Photographs of a single unit in different bistable states.

Figure 2b shows the fabricated metasurface sample and its morphologies before and after strain release. The overall dimensions of the planar and buckled samples are 44 × 44 cm² and 40 × 40 cm², respectively. At the macroscopic level, the metasurface exhibits good periodicity, ensuring consistent amplitude and phase responses across units. In the buckled state, upward‐ and downward‐oriented antennas are distributed arbitrarily, demonstrating the practical feasibility of the bistable design. The right subplot of Figure 2b displays the top views of 3 × 3 units, with an enlarged image of a planar antenna terminal. At the microscale, the antenna structures remain continuous, with only minor thermal effects near the edges. To experimentally evaluate bistability, a representative unit was subjected to cyclic out‐of‐plane loading. As shown in Figure 2c, the unit maintained a stable state over multiple switching cycles, with rapid and repeatable shape transformations. Furthermore, all shapes fully recovered to their initial states after repeated loading, underscoring the reliability of the bistable design. These results confirm the feasibility and repeatability of the bistability concept, establishing a robust foundation for mechanically reprogrammable metasurfaces.

2.3. Controllable Beam Steering

To validate the EM modulation capability of the bistability‐inspired metasurface, controllable beam‐steering functionality was investigated by programming one‐dimensional phase patterns. Figure 3a illustrates beam steering in the yz‐plane, achieved by applying gradient‐phase distributions along the y‐axis. A dual symmetric beam is generated along the z‐axis with deflection angle θ. Full‐wave simulations were performed to calculate far‐field scattering patterns of the metasurface under various coding sequences. In the model, 25 units were arranged along the y‐direction, with periodic boundary conditions applied along x and open conditions along y.

FIGURE 3.

Controllable beam steering with the 3D bistable reprogrammable metasurface. (a) Schematic illustration of beam steering achieved by unit state coding. (b) Simulated and measured far‐field scattering properties of the metasurface under various coding patterns. (c) Comparison of simulated and measured deflection angles. (d) Reflective amplitude and phase difference of the unit at States 0 and 1.

For beam‐modulation, the metasurface was implemented with five coding sequence periods: ‘10’, ‘110’, ‘1100’, ‘11100’, and ‘111000’. Due to the 1‐bit phase coding design, the deflected beams were symmetrically distributed along the z‐axis. Figure 3b presents the simulated and measured angular distributions of the transmitted beams within the range from −90° to 90°. As expected, the deflection angle decreases with increasing coding period. Minor discrepancies between simulation and experiment are attributed to manual alignment errors. For the coding period ‘10’, the maximum simulated and measured deflection angles were 56.5° and 55°, respectively. For the sequence ‘111000’, the deflected beam peaks at 17° (simulation) and 16° (measurement), with other coding deflection angles shown in Figure 3c. Additionally, the deflected beams become narrower as the coding period increases. The simulated (measured) full width at half maximum (FWHM) of the deflected beam was 9.5° (12.5°) for the coding period ‘10’ and 5° (6°) for ‘111000’. Notably, the maximum transmittance of 0.0464 was achieved for the period ‘111000’, which could be further improved by enhancing the transmissive amplitude of the reprogrammable unit.

Although Figure 1e only shows the transmissive characteristics of the designed unit, the constant phase difference of 180° and the identical amplitude response are also preserved in reflection mode (see Figure 3d). The simulated deflection results in the reflective space are presented in Figure S6b, showing deflection angles identical to those in transmission. Notably, the maximum transmissive amplitude reaches around 0.2 at 11.2 GHz, while the reflective amplitude is 0.137 at the same frequency. Thus, the transmissive mode exhibits superior deflection efficiency compared to the reflective mode. Together, these simulated and experimental results confirm the one‐dimensional coding capability of the mechanically reprogrammable metasurface and demonstrate its potential for multifunctional beam steering.

2.4. 3D Spatial Modulation of Focus

After validating the one‐dimensional phase‐coding capability, the reprogrammable metasurface was further coded with two‐dimensional phase patterns to realize the dynamic focus in 3D space. As shown in Figure 4a, by assigning unit states (0/1) through applied loading, the phase of transmitted waves from all units can be independently manipulated to generate constructive superposition at a desired focal point. For a focal spot located at (x ₀, y ₀) on plane z, the required phase distribution φ(x, y) on the metasurface plane is given by

$$\phi \left(x,y\right)=\frac{2\pi }{\lambda }\left(\sqrt{{(x-x_0)}^2+{(y-y_0)}^2+f^2}-f\right),$$ (4)

where (x, y) is the unit coordinate, λ is the operating wavelength, and f is the focal length. In this study, the operating frequency was set to 11.2 GHz. Owing to the 1‐bit coding nature of the metasurface, the calculated phase values were binarized as 0°/180° to achieve the focusing effect. The focusing performance in 3D space was characterized in terms of in‐plane off‐axis scanning and variable focal length.

FIGURE 4.

3D spatial focusing with the 3D bistable reprogrammable metasurface. (a) Schematic of 3D modulation. (b) Off‐axis focus movement on the z = 300 mm plane, sequentially through (0,0), (0,60), (60,60) and (60,0). Longitudinal focus tuning at planes (c) f = 200 mm, (d) f = 300 mm, and (e)f = 400 mm. The electric fields along the path y = 0 on the focusing planes are extracted to characterize the beam width.

As depicted in the left panel of Figure 4b, a focal spot was sequentially moved across four target points: F₁(0, 0), F₂(0,60), F₃(60,60), and F₄(60,0) on the z = 300 mm plane. The metasurface phases were coded according to the patterns shown in the first row of Figure S7. Full‐wave simulations at 11.2 GHz (see Methods) were used to monitor the normalized electric field on the target plane, as plotted in Figure 4b. Distinct focusing spots were observed at all four states, with coordinates consistent with the design. The normalized |E| values for the four spots were 0.964, 0.962, 1, and 0.962, showing minimal variation across states. For measurements, the electric field on the target plane was scanned in a microwave chamber with a spatial step size of 6.25 mm (see Methods). The right panel of Figure 4b shows that the measured focusing effect matched the simulations, albeit with slightly enlarged spot sizes. The corresponding measured |E| values were 0.874, 1, 0.953, and 1, and the spot positions agreed well with the design. These results demonstrate the 2D gradient‐phase coding capability of the metasurface in producing movable focal spots on a given plane.

Beyond horizontal focus shifting, the metasurface was also employed to tune the focal length. Three focal lengths, 200, 300, and 400 mm, were designed, with the corresponding binarized phase patterns shown in the second row of Figure S7. Simulated electric fields in the x‐z plane are shown in Figure 4c–e (upper panels), where focal spots are highlighted at 184 mm, 282 mm, and 376 mm, respectively. Due to the 1‐bit coding limitation, the maximum phase deviation from the ideal design can reach nearly 90°, affecting focusing accuracy. The marked black curves in the x‐z plane represent the electric field amplitude along x = 0, indicating that the focal spot length increases with the focusing distance. Under constant input power, the focusing intensity decreases as the spot area enlarges, with maximum electric field amplitudes of 1, 0.86, and 0.80 for three focal spots, respectively.

To compare simulations and measurements, the electric fields on various x‐y focal planes were extracted and plotted in the middle subplots of Figure 4c–e. Both simulated and measured results show clear intensity contrast between focal and non‐focal planes, although the measured fields exhibit higher background levels. Furthermore, the electric fields along y = 0 mm were extracted and are shown in the lower subplots of Figure 4c–e. The measured beam widths are slightly larger than those predicted in the simulation. As representative parameters, the simulated FWHM values were 24 mm, 30 mm, and 38 mm for the three focal spots. In general, the demonstrated tunable off‐axis focal movement and variable focusing length confirm the effectiveness of the reprogrammable metasurface for 3D spatial modulation of focus.

2.5. Reprogrammable Holographic Displaying

To further demonstrate functional versatility, the reprogrammable metasurface was coded with 2D gradient‐phase distributions to realize dynamic holographic displays. As schematically illustrated in Figure 5a, the metasurface, coded with a two‐level phase pattern φ₁, was employed to display various holographic images A ₀ on an imaging plane. Given the limitations of two‐level phase distributions, a modified Gerchberg‐Saxton (GS) algorithm was developed to optimize holographic reconstruction. In the conventional GS method, the input amplitude A ₂ on the imaging plane is treated as the amplitude matrix A ₀ of the target image and used to perform an inverse Rayleigh‐Sommerfeld (RS⁻¹) diffraction calculation. However, even with sufficient iterations, the retrieved phase profile often converges to a local optimum, leading to compromised reconstruction quality under 1‐bit phase constraints (see the first row of Figure S9b). To address this issue, the input amplitude A ₂ on the metasurface was iteratively updated by combining the RS diffraction amplitude A ₁ with the target amplitude A ₀. Specifically, each element $a_2^n(i,j)$ of the normalized amplitude matrix norm(A ₂) was updated as

$$\left\{\begin{array}{c}{a}_2^n\left(i,j\right)=a_2^{n-1}\left(i,j\right)+k\mathrm{while}\left|a_1^{n-1}\left(i,j\right)-a_0\left(i,j\right)\right|\ge \delta \\ a_2^n\left(i,j\right)=a_2^{n-1}\left(i,j\right)\mathrm{while}\left|a_1^{n-1}\left(i,j\right)-a_0\left(i,j\right)\right|<\delta \end{array}\right.,$$ (5)

where the superscript n represents the iteration number, and a ₀(i,j) and $a_1^{n-1}(i,j)$ are elements of the target and iterative amplitude matrices A ₀ and A ₁, respectively. In this study, the parameters δ and k were set to 0.1 and 0.05, respectively. The above correction was only applied to the target regions (marked as ‘1’ in Figure 5a), and more calculation details were provided in Section S8. Based on this modified GS algorithm, holographic images of numbers ‘1’ to ‘6’ were designed on the plane z = 240 mm at 11.2 GHz, and the corresponding two‐level phase patterns were plotted in Figure 5b. As shown in Figure S9b, the modified algorithm significantly improves intensity uniformity in the target regions and yields markedly better imaging quality compared with the conventional method.

FIGURE 5.

Holographic displaying with the 3D bistable reprogrammable metasurface. (a) Modified GS algorithm for two‐level phase holograms. (b) Calculated phase distributions corresponding to target holographic digits ‘1’ to ‘6’. (c) Full‐wave simulated and (d) measured holographic images at the designed imaging plane. All electric‐field distributions are normalized to the maximum value. (e) Calculated PSNR values of the images, quantifying reconstruction quality. (f) Calculated holographic efficiency of the metasurface for different images.

To experimentally demonstrate the reprogrammable holographic functionality, 1‐bit units were spatially coded according to the patterns in Figure 5b, and full‐wave simulations were performed to compute the electric field on the plane z = 240 mm. As shown in Figure 5c, all target images were clearly reconstructed, although non‐uniform amplitudes appeared due to internal unit field variations and interference between adjacent units (see Section S10). The experimental results were presented in Figure 5d. Compared to simulations, the measured images exhibited greater non‐uniformity in the electric‐field distribution, but the target profiles remained observable. The reduced image quality was attributed to the fact that the incident wave in the measurement setup cannot be considered a perfectly planar wave. Although this study demonstrates only six‐channel holography, the reprogrammable capability of the metasurface is, in principle, unlimited, providing a flexible route toward reconfigurable holographic displays with broad applicability.

For a quantitative assessment of imaging quality, the peak signal‐to‐noise ratio (PSNR) was calculated as $10{\log }_{10}(\frac{\mathrm{Ma}{\mathrm{x}}^2}{\mathrm{MSE}})$, where Max denotes the maximum gray‐scale value of pixels in the image, and MSE represents mean square error between the reconstructed electric‐field distribution and the target image. The MSE is given by $\mathrm{MSE}=\frac{1}{mn}{\sum }_{i=1}^m{\sum }_{j=1}^n{(E_{ij}-A_{ij})}^2$, where E_ij and A_ij are the simulated or measured electric field and the target amplitude, respectively. As shown in Figure 5e, the PSNR values of the simulated images are consistently higher than those of measured ones, in agreement with the visual quality of the images in Figure 5c,d. The maximum and minimum PSNR values are 15.96 dB (simulated) and 15.08 dB (measured) for digit ‘1’, and 11.85 dB (simulated) and 11.01 dB(measured) for digit ‘6’, respectively. As another representative property, the holographic efficiency was defined as the ratio of energy on the imaging plane to that of the incident beam over an area of 400 × 400 mm² (see Section S11 for more details). The calculated efficiency remains nearly constant at 5% across all images in Figure 5f and could be further improved by enhancing the cross‐polarized transmissive amplitude of the reprogrammable unit.

These phase‐coding functionalities demonstrate the effectiveness of the proposed bistable reconfiguration concept successfully, meanwhile highlight the repeatability of the fabricated device. In terms of device reliability, the antenna structures are still flexibly controllable even after all the measurements (see Video S1), and the antenna resistance is unchanged during the shape‐switching process (see Video S2). Such copper/polyimide composition design in the 3D assembly technique has been extensively adopted to develop pressure sensors that are operational with thousands of loading cycles [49, 50]. However, there are some metrics that should be enhanced for further applicability. The device efficiency can be improved by designing a Fabry–Pérot cavity via implementing metal‐grating layer as a reflective layer, and the transmissive amplitude of the new unit reaches 0.81 at 10.4 GHz (see Section S12), which is comparable to the amplitude level of the published work [51]. Besides the phase‐only functionalities, the simultaneous amplitude‐ and phase‐coding capability [52, 53], is also feasible to code the complex‐amplitude for the Airy beam generation (see Section S13). Furtherly, by arranging four antennas inside a unit, a 2‐bit phase coding paradigm is also achievable while only available at a single frequency point (see Section S14). For the future prospect, such bistability‐based phase‐coding concept can be with automatic actuating instead of manual loading method by integrating the light‐sensitive polymer films [54] onto the selective regions of the antenna, then the antennas can be independently actuated to deform and code the expected phase by controlling an external light source array.

3. Conclusion

We have presented a mechanically reprogrammable EM metasurface that leverages interference between two orthogonally arranged, bistable 3D buckled antennas. By employing a pre‐stretched hyperelastic substrate with a hole array, we induce controlled 3D buckling while enabling stable, reversible bistable switching. The resulting 1‐bit coding unit provides broadband phase control in both transmission and reflection modes. Fabricated using a thermal release transfer process, the metasurface demonstrates versatile EM wave manipulations—including arbitrary beam deflection, 3D focal scanning, and multifunctional holographic displays—achieved through simple out‐of‐plane actuation. Looking ahead, expanding the coding states beyond 1‐bit could enable advanced functionalities such as vortex beam generation and vectorial holography. This bistability‐driven approach establishes a new paradigm for programmable metasurfaces, with broad potential in applications such as cloaking, augmented reality, and 3D imaging.

4. Methods

4.1. FEA Simulation for Structure Buckling

The deformed morphologies of the 3D bistable units were analyzed and optimized using FEA in Abaqus. The simulation consisted of two steps: biaxial pre‐stretching and strain releasing. The hyperelastic properties of the patterned silicone substrate were modeled using the Mooney‐Rivlin model (C ₁₀ = −0.1152 MPa,C ₀₁ = −0.8989 MPa, D ₁ = 0) fitted from tensile measurement data. The elastic moduli of copper and polyimide were set to E _Cu = 119 GPa and E _PI = 2.5 GPa, respectively, with a Poisson's ratio of 0.34 for both materials. First, the patterned substrate was modeled and stretched by 10% biaxial strain to match the hole diameter with the planar resonator length (6 mm). In the releasing step, the stretched substrate was imported as the initial state, and the terminal regions of the planar structures were bonded to the substrate. Displacement loading was then applied to release the strain, transforming the planar structures into 3D morphologies. Various initial geometric imperfections were introduced to control the bistable states. Finally, the deformed meshes were converted into solid models, which were imported into the EM simulations.

4.2. EM Simulation for Unit and Metasurface

The deformed structures were imported into CST Microwave Studio to simulate their EM responses. For the spectral responses of individual unit, unit cell boundaries were applied in the in‐plane dimensions of the Frequency‐Domain Solver, while open boundaries were applied along the propagation direction. Two fixed reference planes were used in all simulations to ensure equivalent propagation distances. One‐dimensional phase‐gradient metasurfaces were modeled using the Time‐Domain Solver to simulate beam‐steering effects under plane‐wave excitation. A far‐field monitor at 11.2 GHz was employed to calculate scattering patterns. Periodic boundaries were applied along the single‐unit direction, with open boundaries along the others. For full metasurface simulations, open boundaries were applied in all directions, and electric‐field monitors were introduced to characterize focusing or holography. To reduce memory usage, the calculated cross‐sectional profiles from Figure S1 were used to generate the unit models, which were then arrayed to form the complete metasurface.

4.3. Metasurface Measurement

The reprogrammable metasurface was characterized in a microwave anechoic chamber and the antenna morphologies were manually manipulated by a tweezer before the measurement (see Video S1). During all measurements, the sample was placed at 45° relative to the horizontal plane, and the antennas were oriented along either the horizontal or vertical direction to match the electric‐field polarization. For the beam‐steering measurements (see Figure S14a), both the sample and excitation antenna were mounted on a rotation platform, while the receiving antenna was fixed in the far field. The far‐field transmissive scattering properties were then obtained by rotating the platform. For the focusing and holography measurements (see Figure S14b), a waveguide probe mounted on a robotic arm was used to scan the electric‐field amplitudes and phases on the designed imaging plane. To ensure accuracy, the excitation antenna was precisely aligned with the center of the metasurface sample and the scanning region. In both setups, the polarizations of the receiving probe/antenna and the excitation antenna were orthogonal to capture the cross‐polarized response.

Funding

National Natural Science Foundation of China (Grant No. 52175115).

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File 1: adma73968‐sup‐0001‐SuppMat.pdf.

Supporting File 2: adma73968‐sup‐0002‐VideoS1.mp4.

Supporting File 3: adma73968‐sup‐0003‐VideoS2.mp4.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.