Fig. 1. Overview of the multidimensional manipulation of wave fields based on artificial microstructures.

Fig. 2. (a) Schematic of the C-shaped antenna used to control the phase and amplitude of linearly polarized light simultaneously (upper panel) and simulated transmission amplitude and phase of an antenna array for different orientation angle θ (lower panel). (b) Simulated amplitude and phase of the transmitted y-polarized light for different antennas with different orientation angle θ and geometrical parameters under x-polarized normal incidence. (c) Upper panel: simulated amplitude of the converted CP light for different nanorods with different lengths. Inset shows the schematic of the gold nanorod. Lower panels: simulated electric field distributions of the Airy beams with simplified amplitude modulation (left) and without amplitude modulation (right). (d) Simulated and measured cross-polarized transmission for X-shaped structures with different intersection angles (upper panel) and schematic of the designed hologram (lower panel). (e) Upper panels: amplitude and phase profiles of the designed hologram. Lower panels: simulated and measured holographic images at proper image planes. (f) Left panel: schematic of the bilayer metasurface that can generate complex amplitude holograms. Right panels: phase (upper) and amplitude (lower) profiles of the designed hologram. (g) Upper panel: schematic of the structures used to independently and completely control the transmitted phase and amplitude. Lower panels: simulated phase and amplitude for structures with different lengths and rotation angles. (h) Measured holographic images at different observation angles. The upper two images correspond to the metasurface with a phase gradient. The lower two images correspond to the metasurface with same intensity distributions as the upper metasurface but without phase gradient. (i) Left panels: schematic of the energy tailorable multifunctional metasurface (upper) and measured light distributions of three vortex beams with order of 3, 1, 0, respectively (lower). Right panels: the designed (red), calculated (blue) and measured (green) energies of each functionality for different samples (upper) and measured image of 1951 USAF resolution test target realized by a metasurface (lower). Figure reproduced from: (a-b) ref.⁵³, Wiley-VCH; (c) ref.⁵⁸, Wiley-VCH; (d-e) ref.⁶⁰, Royal Society of Chemistry; (f) ref.⁶¹, Nature Publishing Group; (g-h) ref.⁶², Nature Publishing Group; (i) ref.⁶³, Wiley-VCH.

Fig. 3. (a) Schematic of the reflective polarization generators based on phase gradient metasurfaces. (b) The simulated polarization conversion efficiency for each polarization. (c) Left: schematic of the bilayer nano-aperture structure used to control the polarization and phase simultaneously. Middle: schematics of the polarization and phase realized by nano-aperture pairs with various dimensions and orientations. Right: measured far-field intensity distributions of the generated radially polarized beam without and with a linear polarizer (oriented at angle θ) intercepted before the camera. (d) Left: schematic of the metasurface that can generate and focus the radially and azimuthally polarized light for different LP incident beams. Middle: simulated and measured intensity distributions of the vector beams. Right: optical (bottom) and scanning electron (top) microscope images of the metasurface. (e) Schematic of the diatomic metasurface for vectorial holography. (f) Upper panels: schematic of the metasurface that can implement two independent and arbitrary phase profiles on any pair of orthogonal polarization states by combining both propagation phase and PB phase. Lower panels: measured images of the chiral holograms for different CP incident light. (g) Schematic of the arbitrary SOC (left) and the typical J-plate design (right). Figure reproduced from: (a-b) ref.⁷⁹, American Chemical Society; (c) ref.⁸³, Wiley-VCH; (d) ref.⁸⁵, Nature Publishing Group; (e) ref.⁸⁷, American Chemical Society; (f) ref.⁹⁵, American Physical Society; (g) ref.¹⁰⁰, American Association for the Advancement of Science.

Fig. 4. (a) Schematic of the metasurface that enables asymmetric transmission of CP light. Simulated (solid lines) and measured (circles) Jones matrix of the metasurface on linear (b) and logarithmic (c) scales. (d) Schematic of the optical response of the planar chiral metasurface. Measured zeroth-order transmission spectra (e), CD spectra (f) and circular birefringence spectra (g) of the planar chiral metasurface. (h) Schematic of the 3D Janus helical structures in two enantiomeric forms. (i) Measured transmission spectra and CDTF spectrum of the metasurface in form A for different CP incident light in the forward direction. (j) Measured transmission spectra and LDTB spectrum of the metasurface in form A for different LP incident light in the backward direction. (k) Measured transmission spectrum for different azimuthal angles of the LP incident light. Figure reproduced from: (a-c) ref.¹¹⁴, American Physical Society; (d-g) ref.¹⁴⁸, Nature Publishing Group; (h-k) ref.¹⁵⁴, Nature Publishing Group.

Fig. 5. (a) Schematic of the THG signals and their phases for C2 and C4 nanostructures. (b) Measured THG signals from the C2/PFO and C4/PFO metasurfaces with a phase gradient of the nonlinearity. (c) Schematic of the anomalous phase matching condition for phase gradient metasurfaces. (d) Measured (blue circles), calculated (black line) and simulated (red squares) FWM emission angle as a function of the grating periodicity. (e) Left panels: schematic of the V-shaped gold antennas (upper) and the nonlinear hologram metasurfaces that work at THG wavelength (lower). Right panel: the phase of the THG signals for V-shaped antennas with different arm lengths and intersection angles. (f) Schematic of the linear and nonlinear PB phases for a split ring resonator. (g) Schematic of the nonlinear metasurface that can generate different SHG holographic images for different CP states. (h) Schematic of the nonlinear metasurface that can simultaneously generate three focused optical vortices with different topological charges and different focal lengths. (i) Schematic of the unit cell of the nonlinear phase gradient metasurface based on quantum well structure. (j) Far field profiles of RCP and LCP second harmonic wave output from the metasurfaces with different phase gradients. Figure reproduced from: (a-b) ref.¹⁷², Nature Publishing Group; (c-d) ref.¹⁷⁵, Nature Publishing Group; (e) ref.¹⁸³, Nature Publishing Group; (f-g) ref.¹⁸⁴, Nature Publishing Group; (h) ref.¹⁸⁶, Wiley-VCH; (i-j) ref.¹⁸⁸, Optical Society of America.

Fig. 6. (a) Schematic of the folded Fabry-Pérot tube array for realizing structures with target-set absorption spectra. (b) Absorption spectra caused by Fabry-Pérot resonance, which is close to the theoretical limit in the semi-infinite frequency range. (c) The transmission phase of two coding elements. (d) Simulated far field distribution (upper) and simulated (lower left) and measured (lower right) field amplitude distributions of the transmitted waves divided into four beams when coding elements are distributed in a checkerboard pattern. (e) Schematic of generalized Snell's law realized by a series of tapered labyrinthine metamaterials (upper) and the phase changes of six types of unit cells (lower). (f) Measured anomalous refraction caused by controlling the wavefront phase with arrangement of the unit cells. (g) The decoupled effect of amplitude-phase (lower) caused by the holey structured lossy acoustic metamaterial (upper). (h) Upper panels: amplitude (left) and phase (right) profiles of the lossy acoustic metamaterial for generating the Airy beam. Lower panels: comparison of the Airy beam formed by amplitude phase modulation (APM) (left) and Phase modulation (PM) (right). Figure reproduced from: (a-b) ref.²¹⁰, Royal Society of Chemistry; (c-d) ref.²¹³, Wiley-VCH; (e-f) ref.²¹⁶, Nature Publishing Group; (g-h) ref.²²⁶, Nature Publishing Group.

Fig. 7. (a) Schematic of the topological Chern insulators (upper) and the projected band diagram of the sonic crystal (lower). The red and blue lines represent the edge states distributed on different edges. (b) Upper panel: schematic of the transmission of the acoustic quantum spin hall effect. Lower panel: calculated projected band diagram of the topological phononic crystal. The red and blue lines represent two pairs of interface states with opposite propagation directions distributed on different interfaces. (c) Upper panels: schematic of the two dimensional acoustic phononic crystal (left) and the valley states (right). Lower panels: the band diagram (left) and the band transition diagram (right). (d) Schematic of the phononic crystal of type-I Weyl points (left) and the distribution of type-I Weyl points in Brillouin zone (middle). Fourier transforms of the surface wave fields on the XZ plane that show the Fermi arc of type-I Weyl points(right). (e) Schematic of the phononic crystal of type- II Weyl points (left) and the distribution of type- II Weyl points in Brillouin zone (middle). Fourier transforms of the surface wave fields on the XZ1 plane that show the Fermi arc of type-II Weyl points (right). (f) Upper panels: schematic of the quantized quadrupole (left), the corresponding tight bound model (middle) and the corresponding structural unit (right). Middle panels: diagram of experimental equipment (left) and the corresponding distribution of the bulk, edge and corner response at an arbitrary frequency (72.0 kHz) (right). Lower panel: the frequency regions of bulk, edge and corner states. Figure reproduced from: (a) ref.²³⁰, Institute of Physics; (b) ref.²³³, Nature Publishing Group; (c) ref.²³⁴, Nature Publishing Group; (d) ref.²³⁸, Nature Publishing Group; (e) ref.²³⁹, American Physical Society; (f) ref.²⁴⁸, Nature Publishing Group.

Fig. 8. (a) Left panel: schematic of the metasurface based on multi-dielectric stacked layer structures that can realize ultrahigh saturation structural colors. Right panel: the simulated CIE 1931 chromaticity coordinates for the samples with different periods and gaps. (b) Schematic of the multiplexed hologram metasurface that can realize direct polarization measurement. (c) Schematic of the angle-multiplexed all-dielectric metasurface (upper) and the reflection spectra of the metasurface for different incident angles (lower). (d) Normalized reflection spectra of the metasurface before (upper) and after (middle) coating a polymethyl methacrylate (PMMA) layer. Lower panel: absorption spectrum obtained from the measured reflection spectra (black line) and absorption spectrum of a PMMA layer on a gold surface obtained from standard infrared reflection absorption spectroscopy measurement (orange dashed line). (e) Design approach (upper left) anld experimental characterization (upper right and lower panels) of an OAM-multiplexing hologram metasurface that can encode different holographic images into different OAM channels. Figure reproduced from: (a) ref.²⁶⁵, American Chemical Society; (b) ref.²⁸⁴, Optical Society of America; (c-d) ref.³⁰⁴, American Association for the Advancement of Science.; (e) ref.³¹³, Nature Publishing Group.

Fig. 9. (a) Schematic of the process of acoustic hologram imaging. Left panels: target image and phase distribution of target image. Middle panel: the metamaterial corresponding to the phase distribution. Right panels: workflow for acoustic metamaterial reconstructing target acoustic images. (b) Scheme of a metasurface carpet cloak. The black arrows are the incident waves; the blue arrows and red arrows are the reflected waves with and without metasurface carpet cloak. (c) A typical unit cell of the metasurface carpet cloak and its corresponding S11 parameters. (d) Left panels: Schematic of the unit cell of flat acoustic superlens and the flat acoustic superlens. Reft panels: experimental demonstration of subwavelength focusing (upper) and imaging (lower) using a flat acoustic superlens. (e) Upper panels: schematic of the Weyl phononic crystal and its unit cell. Lower panel: the experimental observation of topological negative refraction. (f) Upper panels: schematic of the sonic crystal based on Kekulé lattice (left) and the k-space analysis on the outcoupling of armchair termination at f = 5.6 kHz (middle) and zigzag terminations at f = 5.8 kHz (right). Lower panels: the measurements (upper) and simulations (lower) of three types of topological acoustic antennas corresponding to zigzag domain walls and armchair terminations (left and middle), the armchair domain wall and the zigzag termination (right). Figure reproduced from: (a) ref.³²⁷, Nature Publishing Group; (b-c) ref.³²⁸, Nature Publishing Group; (d) ref.³³³, Nature Publishing Group; (e) ref.³³⁵, Nature Publishing Group; (f) ref.³³⁶, American Physical Society.