2.1.

Design of the Reprogrammable Metasurface

To empower the metasurface with well-controlled programmability, 400 commercial stepping motors are utilized to respectively control the $20\times 20$ 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 deg, corresponding to 64 steps per turn. More details about the stepping motor can be found in Supplementary Material 1. The rotation step number (clockwise or counterclockwise) of each motor is controlled by wireless signals from a host computer with full addressability. As shown in Fig. 1(b), 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 layers; and the bottom layer consists of 16 gears connecting with the PB meta-atoms one by one. The modules of all gears are 0.5. The yellow-green gear has 30 teeth, the light-blue gear has 30 and 16 teeth in the bottom and top layers, respectively, and the pink gear has 14 teeth. In this condition, when the stepping motor rotates a turn, it drives the PB meta-atoms to rotate 8/7 turns. Accordingly, the rotation of each meta-atom consists of 56 steps per turn. For reference, Supplemental Video S1 (MP4, 30 MB [URL: https://doi.org/10.1117/1.AP.4.1.016002.1]) is provided to show the controllable rotations. The photos of the metasurface template and more details about each component can be found in Supplementary Material 2.

Different from traditional static metasurfaces, the meta-atoms of the proposed reprogrammable metasurface are discretely arranged to avoid possible obstructions during their rotation. With the overall performance taken into consideration, a circular-shaped metal–insulator–metal structure, as schematically shown in Fig. 2(a), is chosen as the meta-atom to manipulate the PB phase in reflection at an operating frequency of 7 GHz (see Supplementary Material 3 for simulation details). 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-$\mu \mathrm{m}$ 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 $R=4.8\mathrm{mm}$ and the center distance between adjacent meta-atoms along the $x$ 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. Two important features characterize the chosen PB meta-atom in its interaction with the incident light: it provides strong anisotropy to achieve efficient polarization conversion, and it can strongly confine the resonance fields inside the meta-atom to minimize near-field coupling between neighboring meta-atoms (see Supplementary Material 3 for details). By carefully optimizing the meta-atom dimensions, such meta-atoms could efficiently convert the incident right- and left-handed circular polarizations (RCP and LCP) to reflected RCP and LCP, respectively. In principle, when this meta-atom is rotated by an angle $\theta$, the phases of reflected $R_{rr}$ and $R_{ll}$ (the subscripts $r$ and $l$ stand for RCP and LCP) are expected to follow a phase gradient of $2\theta$ and $-2\theta$, respectively, where the sign depends on the spin direction of incident polarization. Such geometric-dependent phase behavior is also known as the PB phase response.^7,8,62,63

Fig. 2

PB phase response. (a) The top portion of the PB meta-atom is a pair of Archimedean spirals with the same geometric parameters: inner radius (1.9 mm), outer radius (4.3 mm), height (0.035 mm), width (0.4 mm), and number of turns (two turns). The pink and sky-blue dials schematically depict the PB phase control resolution and variation gradients for $R_{rr}$ and $R_{ll}$, respectively. (b), (c) Measured amplitudes of $R_{rr}$ and $R_{ll}$, respectively. (d), (e) Measured PB phase response of $R_{rr}$ and $R_{ll}$, respectively, versus different rotation angles.

2.2.

Experimental Verification of PB Phase Controllability

Since the PB meta-atom can be rotated by 56 steps per turn, our metasurface enables quasicontinuous PB phase control over 28 levels. As schematically shown by the pink and sky-blue dials in Fig. 2(a), the reflectance $R_{rr}$ and $R_{ll}$ have a phase control resolution of $\pi /14$ 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 Appendix). Figures 2(b) and 2(c) show the normalized amplitude of measured $R_{rr}$ and $R_{ll}$, respectively, where the amplitude peak around the target working frequency of 7 GHz can be obtained in both spectra. $|R_{rr}|$ has a maximum amplitude of 0.91 at 6.925 GHz and $|R_{ll}|$ has a maximum amplitude of 0.7 at 6.55 GHz. Notably, when light impinges onto a chiral meta-atom that lacks mirror-symmetry, photons of different CPs will undergo different absorption, an effect known as circular dichroism or circular conversion dichroism.²⁴ The chosen PB meta-atom shows a chiral response, thus we expect a difference between $R_{rr}$ and $R_{ll}$, as shown in Fig. 2. For different applications, one can either design a PB meta-atom with in-plane mirror-symmetry to eliminate circular conversion dichroism⁷ or design chiral PB meta-atoms with stronger symmetry breaking to enhance circular conversion dichroism.⁶⁴ The red and blue circles in Figs. 2(d) and 2(e) illustrate the measured phase response of $R_{rr}$ and $R_{ll}$, respectively, at 7 GHz, as we simultaneously rotate all meta-atoms from 0 to $\pi$. Clearly, the phase variation of $R_{rr}$ and $R_{ll}$ has a positive and negative gradient versus the rotation angle, respectively. The solid lines in Figs. 2(d) and 2(e) show the linearly fitted results, where the fitting gradient of $R_{rr}$ and $R_{ll}$ is 1.9624 and $-2.0665$, respectively, which agree well with the theoretical value. In addition, Fig. S4 in the Supplementary Material shows the measured phase responses at 6, 6.7, and 7.4 GHz, which also comply well with the PB phase response. These results experimentally verify the PB phase controllability of the proposed metasurface platform in a broad band.

2.3.

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. 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 Appendix). 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 Material 5 for details). Notably, due to the quasicontinuous phase controllability, our metasurface can flexibly work under various incident wavefronts, since the functionality distortion produced by a nonplanar 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 metasurface.^39,42 Once the desired phase distribution for certain target functionality is obtained, the corresponding rotation distribution can be calculated. In the following, we choose RCP as target operating polarization to demonstrate several representative functionalities, including metalensing, focused vortex beam generation, and holographic imaging.

3.1.

Metalensing

We first investigate the functionality of a metalens using the proposed metasurface. Figure 3(a) shows the required rotation profile for a metasurface focusing the impinging wave at (0, 0, 600 mm). The measured electric field intensity ($|R_{rr}{|}^2$) in the $xy$-plane at $z=600\mathrm{mm}$ is shown in Fig. 3(b), where a highly symmetric focal spot can be obtained. The horizontal cut of the focal spot is shown in Fig. 3(c) showing a full-width at half-maximum (FWHM) $\sim 42\mathrm{mm}$. Notably, the numerical aperture of the demonstrated metalens is about 0.587, corresponding to a diffraction-limited FWHM of $\sim 36.5\mathrm{mm}$ at 7 GHz. We remark that the generated focal spot is quite close to the diffraction limit, indicating the excellent performance of our quasicontinuous phase control. The programmability of our metasurface enables scanning the focus off-axis. Figures 3(d) and 3(g) show 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. 3(e), 3(h) and 3(f), 3(i), respectively, to perform very well in terms of their focusing and scanning capabilities. In addition, lensing with continuously varying focal lengths can also be achieved. For example, Fig. S6 in the Supplementary Material shows experimentally measured focusing at (0, 0, 450 mm), (0, 0, 600 mm), and (0, 0, 750 mm), respectively. These high-quality and compact focal spots experimentally verify the accuracy of the phase realization of our proposed metasurface.

Fig. 3

Realization of metalensing. (a), (d), (g) Required rotation profiles to realize different metalens operations for RCP waves. (b), (e), (h) Measured electric field intensities ($|R_{rr}{|}^2$) at 7 GHz on the focal plane. (c), (f), (i) Horizontal cuts of the metalens focal spots, with FWHMs = 42, 44, and 44 mm, respectively.

3.2.

Focused Vortex Generation

Electromagnetic fields with a phase profile $e^{il\phi }$ carry orbital angular momentum (OAM), where $\phi$ is the azimuthal coordinate in the transverse plane and $l$ is the topological charge. To corroborate the generality of the proposed metasurface, we show 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. 3(a) plus $l/2$ times the azimuthal angle. Figures 4(a), 4(e), 4(i), and 4(m) show the required rotation distribution across the surface to generate focused vortex beams of topological charges $l=\mathrm{1,}2,\mathrm{3,}4$, respectively. Figures 4(b), 4(f), 4(j), and 4(n) show the measured electric intensity $(|R_{rr}{|}^2$) distributions of the vortex beams, respectively, at the focal plane $z=600\mathrm{mm}$. As expected, these intensity distributions exhibit doughnut shapes, and the central dark area of the vortices is larger for increased topological charge. Figures 4(c), 4(g), 4(k), and 4(o) show 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 $|S_n|$ of each OAM (see Supplementary Material 7 for details). Figures 4(d), 4(h), 4(l), and 4(p) show the corresponding normalized $|S_n|$ as a function of $l$ from $-6$ to 6, respectively. Clearly, the target OAM component of each measurement is the strongest, whereas the other OAM components are quite weak, indicating the high purity of the generated vortex beams. The existence of unwanted OAM beams can be attributed to the square shape of the metasurface and the experimental errors (see Supplementary Material 8 for details). These results experimentally illustrate the large reprogrammability and at the same time high efficiency of our metasurface in tailoring the impinging fields at will.

Fig. 4

Focused vortex beam generation. (a), (e), (i), (m) Required rotation profiles to generate focused vortex beams with the topological charges of $l=\mathrm{1,}2,\mathrm{3,}4$, respectively. (b), (f), (j), (n) Measured electric intensity $(|R_{rr}{|}^2$) distributions and (c), (g), (k), (o) measured phase ($\angle R_{rr}$) distributions of different vortex beams, respectively, obtained at the focal plane. (d), (h), (l), (p) OAM amplitude $|S_n|$ extracted from the measured complex amplitudes of different vortex beams, respectively.

3.3.

Holographic Imaging

Metasurface holography has become a well-established approach to address inverse engineering problems for electromagnetic waves. 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 characters “天津大学” (Tianjin University) and “大�?�云冈” (Datong Yungang) were generated in the image plane at $z=600\mathrm{mm}$. The required rotation profile for each word, as shown in Figs. 5(a)–5(d) and 5(i)–5(l), was calculated by a modified Gerchberg–Saxton algorithm,^64,65 in which the conventionally used Fresnel diffraction formula is replaced by the Rayleigh–Sommerfeld diffraction formula (see Supplementary Material 9 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 Fig. S9 in the Supplementary Materials, which comply well with the target characters. To experimentally demonstrate these holographic images, we rotated the meta-atoms according to the required rotation profile and measured the corresponding electric intensity ($|R_{rr}{|}^2$) distribution. Although the holograms have only $20\times 20$ pixelated phase points, the generated holographic images, as shown in Figs. 5(e)–5(h) and 5(m)–5(p), are of very high-quality and in good agreement with calculations, indicating the excellent wavefront control capability of the proposed reprogrammable metasurface platform.

Fig. 5

Holographic imaging. (a)–(d), (i)–(l) Required rotation profiles to generate holographic images of Chinese characters “天津大学” (Tianjin University) and “大�?�云冈” (Datong Yungang), respectively. (e)–(h), (m)–(p) Corresponding measured electric field intensities ($|R_{rr}{|}^2$) of holographic images obtained at $z=600\mathrm{mm}$.

3.4.

Polarization-Sensitivity Manipulation

Polarization sensitivity is an important feature of metasurfaces. Since the proposed metasurface is based on the PB phase concept, once all the meta-atoms are arranged to achieve the desired phase profile $\mathrm{\Phi }$ for specific functionality under LCP (RCP) incidence, the corresponding phase profile under RCP (LCP) incidence turns to ${\mathrm{\Phi }}^{\prime }=-\mathrm{\Phi }$. In most cases, the phase profile of ${\mathrm{\Phi }}^{\prime }$ cannot maintain the same functionality as that of $\mathrm{\Phi }$. For instance, Fig. S10 in the Supplementary Material shows the measurements in the case of the metasurface are designated to generate a holographic image of the word “PB” under an LCP incidence, where the measured $|R_{ll}{|}^2$ successfully forms the holographic image while the measured $|R_{rr}{|}^2$ is very noisy. Similarly, the demonstrated functionalities shown in Figs. 3Fig. 4–5 are also polarization-sensitive and limited to work for RCP. Inspired by a recent work that utilized binary geometric phase control to achieve polarization-insensitive metalensing in the visible range,⁶⁶ we find that the proposed metasurface can also maintain the same functionality for multipolarizations. For instance, Fig. S11 in the Supplementary Material shows the rotation profile of meta-atoms to achieve metalensing at (0, 0, 600 mm), where the orientation angles are binarily arranged with $-\pi /4$ and $\pi /4$. In this condition, the reflected intensity profiles of $|R_{rr}{|}^2,|R_{ll}{|}^2,|R_{xy}{|}^2$, and $|R_{yx}{|}^2$ can focus at the same spot, as shown in Fig. S11f-I in the Supplementary Material.

In addition, the polarization-dependence and wavelength-independence of PB phase control can be further exploited to achieve polarization and frequency multiplexed functionalities.⁶⁷ For achieving functionality under RCP for wavelength ${\lambda }_1$, the desired phase distribution can be calculated as ${\mathrm{\Phi }}_{R,1}$. Similarly, for achieving other functionality under LCP for wavelength ${\lambda }_2$, the desired phase distribution can be calculated as ${\mathrm{\Phi }}_{L,2}$. To multiplex these phase distributions into one set of meta-atoms, one can arrange the rotation profile as $\theta =\arg [\exp (i{\mathrm{\Phi }}_{R,1})+\exp (-i{\mathrm{\Phi }}_{L,2})]/2$. In this condition, under RCP incidence the metasurface will perform the phase profiles of ${\mathrm{\Phi }}_{R,1}$ and $-{\mathrm{\Phi }}_{L,2}$, and similarly under LCP incidence the metasurface will perform the phase profiles of $-{\mathrm{\Phi }}_{R,1}$ and ${\mathrm{\Phi }}_{L,2}$. If the target functionalities are metalensings, their corresponding negative phase distributions ($-{\mathrm{\Phi }}_{L,2}$ and $-{\mathrm{\Phi }}_{R,1}$) correspond to divergences and thus have slight influences on the focusing spots achieved by positive phase distributions (${\mathrm{\Phi }}_{R,1}$ and ${\mathrm{\Phi }}_{L,2}$). For instance, Fig. S12 in the Supplementary Material experimentally shows that the proposed metasurface can focus the $|R_{rr}{|}^2$ of 6.3 GHz and $|R_{ll}{|}^2$ of 7 GHz at different positions. For multiplexing further complicated functionalities, the crosstalk from unwanted parts becomes serious. If only the intensity profile of the target functionality is important (such as metalensing and holography), the phase profiles of ${\mathrm{\Phi }}_{R,1}$ and ${\mathrm{\Phi }}_{L,2}$ can be carefully optimized to reduce the crosstalk.⁶⁷ Nevertheless, to delink the multiplexed functionalities for RCP and LCP channels, due consideration must be paid into the spin-independent design freedom, such as propagation phase (see Supplementary Material 13 for details).