Fig. 1. Schematic of the cascaded metasurfaces enabling adaptive aberration corrections for focus scanning. (a) Overview of cascaded metasurfaces, consisting of two layers of mechanically rotated transparent metasurfaces (with rotation angle α₁ and α₂, respectively), is capable of dynamically scanning the focal spot on the custom-designed aberration-corrected scanning surface (purple surface) compared to the aberration-uncorrected scanning surface (blue surface). Here, r_c represents the position of focal spot, and θ_c and φ_c represent the polar angle and azimuth angle of focal spot. Insets illustrate the intuitive physical picture of the typical origin of scanning aberrations, using hyperbolic scanning lenses an example (blue panel), and how to adaptively correct these scanning aberrations with the coherent interplay between three different phase functions (purple panel). (b) Photograph of fabricated meta-device with two-layer all-silicon metasurfaces fixed in a motorized rotation stage. (c) Scanning electron microscope (SEM) image of the fabricated metasurface samples.

Fig. 2. Searching algorithm for optimal phase-profile parameters. (a) Schematic of meta-device for adaptively corrected planar scanning. (b) The theoretical working efficiency η varies with φ₀ and Δα, where the total phase profiles Φ_tot (α₁, α₂, r) for different rotation angle {α₁, α₂} are depicted as the right panel. (c) The average working efficiency $\overline{\eta }$ varies with Δα_max and φ₀, where the dashed grey line represents the optimized $\overline{\eta }$ with varying Δα_max, and the star symbol is the selected parameters (φ₀ = 15°) to balance the scanning range (Δα_max = 30°) and efficiency. (d) The longitudinal focal position z_c varies with F₀, χ₀ and Δα for fixed φ₀, where z_c~Δα dependence for different values of F₀ and χ₀ are depicted in the right panel. (e) The average scanning aberration $\overline{\delta }$ varies with F₀ and χ₀ with the star symbol denoting the optimal chosen (F₀ = 8.4λ, χ₀ = 16.3k₀, φ₀ = 15°).

Fig. 3. The experimental setup and terahertz characteristics of the meta-device for adaptively corrected planar scanning. (a) Schematics of the experimental setup, with the theoretical phase profiles and the top view SEM of each layer in the right. (b) Theoretical (dashed), simulated (solid) and experimental (dotted) results of longitudinal focal position for adaptively corrected planar scanner (blue) compared with hyperbolic scanning lenses (black). Experimental (c) and simulated (d) intensity distributions on xz-plane (top) and xy-plane (middle) corresponding to different Δα, and the intensity profiles along the diameter (bottom) at the focal plane with the full width at half maximum (FWHM) marked. Here, the grey dashed lines in (c) and (d) represent the position of the maximum intensity of focal spot.

Fig. 4. Terahertz characteristics of the adaptively corrected dual-focus scanner. (a) Design strategy of the meta-device for scanning two focal spots in different scanning surfaces, with the theoretical phase profiles and the top view SEM of each layer in the right. (b) Theoretical (dashed), simulated (solid) and experimental (dotted) results of the position for focal spot A (blue) and B (pink) of the adaptively corrected dual-focus scanner. The blue plane and pink plane are two vertical planes at the azimuthal angle 0° and 30°. (c–f) Experimental intensity distributions on two vertical planes (top) for two focal spots at the azimuthal angle 0° (dashed blue) and 30° (dashed pink) corresponding to different Δα, with two horizontal planes (bottom left) at focal plane for focal spot A (solid blue) and B (solid pink). The intensity profiles along the diameter (bottom right) at the focal plane with the FWHM marked.