Design of the reprogrammable metasurface. In order to empower the metasurface with well-controlled programmability, 400 commercial stepping motors are utilized to respectively control the 20 × 20 supercells. Each stepping motor is equipped with an addressed circuit for the power supply (terminal voltage of 5 V) and rotation control. The step angle is 5.625°, corresponding to 64 steps per turn. The maximum response frequency is ≥ 1000 pps and the maximum starting frequency is ≥ 500 pps, respectively (see Supplementary 1 for details). The rotation step number (clockwise or counterclockwise) of each motor is controlled by wireless signals from a host computer with full addressability (see Supplementary 2 for details). As shown in Fig. 1b, a three-layered gear set is utilized to transmit the torque from the motor to the PB meta-atoms: the first layer consists of the main gear attached to the output shaft of the stepping motor; the middle layer consists of four gears that connect the first and last layer; the bottom layer consists of 16 gears connecting with the PB meta-atoms one by one. The rotation ratio is 7/8, i.e., the rotation of each PB meta-atom consists of 56 steps per turn. In the experiments, considering the transmit load and accuracy of rotation angles, the rotation speed of PB meta-atoms is set to about 2 s per turn. For reference, a Supplementary Video is provided to show the controllable rotations.
Different from traditional static metasurfaces, the meta-atoms of the proposed reprogrammable metasurface are discretely arranged to avoid possible obstructions during their rotation. Thus, the resonance is designed to be strongly localized inside each PB meta-atom to suppress crosstalk. With the overall performance taken into consideration, a circle shaped metal-insulator-metal structure, as schematically shown in Fig. 2a, is chosen as the meta-atom to manipulate PB phase in reflection at an operating frequency of 7 GHz. The PB meta-atom consists of two Archimedean spirals with the same geometric parameters, which are C2 rotation-symmetric with each other along the normal axis. Both the spirals and the bottom metallic film are made from 35 µm thick copper. They are fabricated using standard printed circuit board technology over a 3 mm thick FR4 substrate, with relative permittivity of 4.2 and a loss tangent of 0.025. The radius of the meta-atom is R = 4.8 mm and the center distance between adjacent meta-atoms along x and y directions is about 10.7 mm, leaving a minimum distance of about 1.1 mm to ensure smooth rotation of each meta-atom. By carefully optimizing the meta-atom dimensions, such meta-atom could efficiently convert the incident right- and left-handed circular polarization (RCP and LCP) to reflected RCP and LCP, respectively56. In principle, when this meta-atom is rotated by an angle θ, the phase of reflectances Rrr and Rll are expected to follow a phase gradient of 2θ and −2θ, respectively, where the subscript r and l stands for RCP and LCP. Such geometric dependent phase behavior is also known as the PB phase response2,19,20.
Experimental verification of PB phase controllability. Since the PB meta-atom can be rotated by 56 steps per turn, our metasurface enables quasi-continuous PB phase control over 28 levels. As schematically shown by the pink and sky-blue dials in Fig. 2a, the reflectance Rrr and Rll have a phase control resolution of π/14 and opposite phase gradients. To experimentally characterize the metasurface, an experimental setup is established by a vector network analyzer (VNA, Agilent N5230C) and two broadband horn antennas (see Methods). Figures 2b and 2c illustrate the normalized amplitude of measured Rrr and Rll, respectively, where the amplitude peak around the target working frequency of 7 GHz can be obtained in both spectra. |Rrr| has a maximum amplitude of 0.91 at 6.925 GHz and |Rll| has a maximum amplitude of 0.7 at 6.55 GHz. Notably, the spectra are quite different from each other, and such phenomena can be attributed to the broken mirror-symmetry induced by the chiral geometry of the meta-atom, at the basis of the PB phase response. The red and blue circles in Figs. 2d and 2e illustrate the measured phase response of Rrr and Rll, respectively, as we simultaneously rotate all meta-atoms from 0 to π. Clearly, the phase variation of Rrr and Rll has respectively a positive and negative gradient versus the rotation angle. The solid lines in Figs. 2d and 2e show the linearly fitted results, where the fitting gradient of Rrr and Rll is 1.9624 and − 2.0665, respectively, which agree well with the theoretical value. These results experimentally verify the PB phase controllability of the proposed metasurface platform.
Rotation distribution design for reprogrammable optical functionality. Since each supercell can be individually controlled, the metasurface yields a variety of optical functionalities by designing the rotation distribution over the surface. We define the metasurface as the xy-plane and its center the origin of our coordinate system. In order to experimentally characterize the performance, a broadband antenna is coaxially mounted at (0, 0, 2100 mm) as a feeding source, and a waveguide probe is used to scan the electric filed distribution (see Method). Since the wave emitted by the antenna is not a plane wave as it reaches the metasurface, we should compensate its phase to make it collimated (see Supplementary 3 for details). Notably, thanks to the quasi-continuous phase controllability, our metasurface can flexibly work under various incident wavefronts, since the functionality distortion produced by a non-planar incident wavefront can be easily compensated. Such flexibility is quite important in practical applications, especially in scenarios in which the feeding antenna can hardly be placed in the Fraunhofer region of the metasurface43,47. Once the desired phase distribution for certain target functionality is obtained, the corresponding rotation distribution can be calculated by dividing by 2 or −2, according to the target polarization handedness. In the following, we choose RCP as target operating polarization to demonstrate several representative functionalities, including metalensing, focused vortex beam generation and holographic imaging.
Metalensing. We first investigate the functionality of a metalens using the proposed metasurface. Figure 3a illustrates the required rotation profile for a metasurface focusing the impinging wave at (0, 0, 600 mm) at an operating frequency of 7 GHz. The measured electric field intensity (|Rrr|2) in the xy-plane at z = 600 mm is shown in Fig. 3b, where a highly symmetric focal spot can be obtained. The horizontal cut of the focal spot is shown in Fig. 3c showing a full-width at half-maximum (FWHM) ~ 42 mm. Notably, the numerical aperture of the demonstrated metalen is about 0.587, corresponding to a diffraction-limited FWHM of ~ 36.5 mm at 7 GHz. We remark that the generated focal spot is quite close to the diffraction limit, indicating the excellent performance of our quasi-continuous phase control. The programmability of our surface enables scanning the focus off-axis. Figures 3d and 3g present the desired rotation profiles for focusing at (-80, 0, 600 mm) and (120, 0, 600 mm), respectively. The measured electric field intensities and the horizontal cuts of the focal spots are shown in Figs. 3e,h and 3f,i, respectively, shown to perform very well in terms of their focusing and scanning capabilities. These high-quality and compact focal spots experimentally verify the accuracy of the phase realization of our proposed metasurface.
Focused vortex generation. Electromagnetic fields with a phase profile eilφ carry orbital angular momentum (OAM), where φ is the azimuthal coordinate in the transverse plane and l is the topological charge. To corroborate the generality of the proposed metasurface, we demonstrate reprogrammable focused vortex generations in Fig. 4. These vortices are designed to coaxially focus at (0, 0, 600 mm), thus their target rotation angle distribution is the one in Fig. 3a plus l/2 times the azimuthal angle. Figures 4a,e,i,m show the required rotation distribution across the surface to generate focused vortex beams of topological charges l = 1,2,3,4, respectively. Figures 4b,f,j,n illustrate the measured electric intensity (|Err|2) distributions of the vortex beams, respectively, at the focal plane z = 600 mm. As expected, these intensity distributions exhibit doughnut shapes, and the central dark area of the vortices is larger for increased topological charge. Figures 4c,g,k,o illustrate the corresponding measured phase distributions, where the azimuthal angle dependence clearly reveals the vortex nature of the focused beams. To quantitatively analyze the quality of the vortex beams, we extracted and integrated the complex amplitudes to get the amplitude |Sn| of each OAM (see Supplementary 4 for details). Figures 4d,h,l,p respectively illustrate the corresponding normalized |Sn| as a function of l from − 6 to 6. Clearly, the target OAM component of each measurement is the strongest, while the other OAM components are quite weak, indicating the high purity of the generated vortex beams. These results experimentally illustrate the large reprogrammability and at the same time high efficiency of our metasurface in tailoring the impinging fields at will.
Holographic imaging. Metasurface holography has become a well-established approach to address inverse engineering problems for electromagnetic waves. In order to further explore the wavefront control capability of our programmable metasurface, we apply it to construct computer-generated holographic images in Fig. 5. In our demonstration, the Chinese sentences “天津大学” (Tianjin University) and “大同云冈” (Datong Yungang) were generated in the image plane at z = 600 mm. The required rotation profile for each word, as shown in Figs. 5a-d and 5i-l, is calculated by a modified Gerchberg-Saxton algorithm56,57 (see Supplementary 5 for details). To confirm the functionality, we calculated the holography imaging by considering the meta-atoms as point sources with ideally designated hologram phase profiles. The calculated results are shown in Supplementary 5, which comply well with the target sentences. To experimentally demonstrate these holographic images, we rotate the meta-atoms according to the required rotation profile and measured the corresponding electric intensity (|Err|2) distribution. Although the holograms have only 20 × 20 pixelated phase points, the generated holographic images, as shown in Figs. 5e-h and 5m-p, are of very high-quality and in good agreement with calculations, indicating the excellent wavefront control capability of the proposed reprogrammable metasurface platform.