Fig. 1. Conceptual illustration of the proposed space-time-coding metasurface for dynamic modulation of the state of polarization (SOP) across the high-order Poincaré sphere (HOPS) representation. The metasurface, driven by an FPGA with a modulation frequency f0, operates the incident electromagnetic wave with carrier frequency fc and polarization state |θ⟩ (preset to 45°) to generate the +1st harmonic wave at fc+f0. The SOP on HOPS is synthesized from right-hand |Rm⟩ and left-hand |Ln⟩ polarized vortex components, carrying orbital angular momentum with topology charges m and n, respectively. Examples of SOPs on various HOPS surfaces include arbitrary holography on HOPS0,0, and vector vortex beams (VVBs) on HOPS1,3 and on HOPS−1,3.

Fig. 2. Schematic diagram of the proposed meta-atom. (a) The exploded view of the meta-atom. (b) The top layer, (c) the bias layer, and (d) the bottom layer of the proposed meta-atom.

Fig. 3. Analysis of the proposed meta-atom. Surface current distributions at 5.8 GHz under x-polarized incidence for States (a) “0/0” and (b) “1/0”. Transmission amplitude and phase responses under (c) x- and (d) y-polarizations for different state combinations. (e) Example of a time-coding sequence: “001001100011”. (f) Effective +1st-order harmonic response for a periodic sequence with length L=12. (g) Magnitude and phase spectra of harmonic components for the sequences “000000111111”, “111111111100”, and “001001100011”.

Fig. 4. Design of arbitrary polarization holography represented by HOPS0,0. (a) Target images corresponding to different polarization states. (b) Calculated amplitude (Ax, Ay) and phase (ϕx, ϕy) distributions for x- and y-polarizations. (c) Illustration of time-space-coding sequences, exemplified by the complex amplitude mapping of the letter “L” under x-polarized incidence. (d) Calculated images.

Fig. 5. Analysis of vector vortex beams (VVBs) represented by HOPS1,3 and HOPS−1,3. (a), (c) Conceptual illustrations of the target vector beams. (b), (d) Calculated amplitude and phase distributions of the x- and y-polarized components. (e), (g) Calculated magnitude distributions. (f), (h) Magnitude projections onto four linear polarization bases: x, y, 45°, and −45°. (i), (k) Phase distributions of right-handed circular polarization (RCP) components. (j), (l) Phase distributions of left-handed circular polarization (LCP) components.

Fig. 6. (a) Top view and (b) bottom view of the fabricated space-time-coding metasurface prototype. Processing diagrams of (c) bias layer and (d) ground layer. (e), (f) Near-field experimental setup.

Fig. 7. (a) The measured results of arbitrary polarization holography represented by HOPS0,0. (b) The correlation coefficients of calculated images and measured images to the target. (c) The polarization purities for each image under specific polarization states. The (d) magnitude distributions and (e) phase distributions (|R⟩ and |L⟩) of VVB represented by HOPS1,3. The (f) magnitude distributions and (g) phase distributions (|R⟩ and |L⟩) of VVB represented by HOPS−1,3. The calculated and measured OAM mode purities for VVB represented by (h) HOPS1,3 and (i) HOPS−1,3.

Fig. 8. Measured transmission magnitude of the proposed metasurface under (a) x- and (b) y-polarized incidences, with all meta-atoms configured in identical states from four representative state groups. (c) Measured harmonic spectra corresponding to six distinct target functions.