Fig. 1. Typical holograms and corresponding holographic reconstructions. (a) The grayscale amplitude-only hologram can be thought of as a 2D data matrix where each pixel is represented as a specific discrete brightness value^[64]. The reconstruction of the grayscale amplitude-only hologram displays the letters “TI.” (b) The kinoform is a phase-only hologram obtained through analytic calculations. It is capable of forming a reconstructed target without any unwanted diffraction orders. In the case of the presented kinoform, its reconstruction displays the letter “DOE.”

Fig. 2. Generalized reflection/refraction laws and Huygens’ metasurfaces. (a) SEM image showcases a V-shaped antenna array meticulously patterned on a silicon wafer. Within its unit cells, eight distinct V-antennas elegantly illustrate the principles of reflection and refraction. Consequently, this design forms a consistent phase gradient across the metasurface, enabling precise control over the propagation of reflected or transmitted light^[73]. (b) Image of a crafted H-shaped antenna reflect-array positioned on a metallic backplane. This metasurface effectively introduces an interfacial phase gradient, skillfully compensating for the momentum mismatch between the propagating wave and surface wave. Consequently, this design enables nearly flawless conversion from plane waves to surface waves at virtually any incidence angle exceeding a critical threshold^[74]. (c) Illustration of a reflect-array metasurface design, featuring gold nanorods separated from a gold backplane by a ${\mathrm{MgF}}_2$ spacer. This arrangement capitalizes on the generation of robust magnetic fields when both the upper and lower gold layers are illuminated by incident light polarized along the gold rod, thanks to the near-field coupling. The efficient manipulation of radiation phase delay can be achieved by adjusting the antenna length, yielding highly effective anomalous reflection at normal incidence^[75]. (d) The surface equivalence principle is utilized to create imaginary electric and magnetic surface currents, aligning with the boundary conditions. On the right side, the depiction illustrates the magnetic field (Hz) when a y-polarized wave impinges normally upon the engineered Huygens’ metasurface, with a close-up view of its individual unit cell. The Huygens metasurface exhibits the remarkable capability to redirect an incident beam with nearly perfect efficiency, achieving close to 100% refraction into a new beam^[76]. (e) Illustration of a Huygens metasurface comprising an array of nanodisks, designed to generate both electric and magnetic polarization currents. This metasurface achieves full coverage of transmission phases spanning 360°, and it exhibits nearly perfect transmission, nearing unity^[77].

Fig. 3. PB phase and propagation phase metasurfaces. (a) SEM image of a linear arrangement of nanorods with positioned angle altering along the x-axis. Incident CPL with opposite handedness will be deflected into two directions. When the structure symmetry is circular, OSHE will occur in a PB phase metasurface due to the spin–orbit interaction^[80]. (b) Schematic of a refract dipole array metasurface. Normal refraction occurs when the metasurface is shed by RCP light, while anomalous refraction occurs with LCP light. On the right, SEM image of a metasurface generates an optical vortex beam in different wavelengths^[81]. (c) Binocular metalens uses nanopillars with different sizes to modulate the propagation phase^[85].

Fig. 4. Subwavelength gratings. (a) Subwavelength dielectric grating^[93]. It exhibits varying refractive indices along two orthogonal directions: one parallel to the grating and the other perpendicular to it. This disparity in refractive indices leads to the manifestation of a birefringence effect. Here, comparison of the birefringence dispersion of the subwavelength grating using the theory of electromagnetic Bloch waves (black square symbol) and finite element method (red circular symbol) is provided. (b) Subwavelength all-metal grating^[95]. The TE wave undergoes reflection when interacting with the subwavelength grating. Meanwhile, the TM wave transmits through the grating, yielding its own unique electric vector distributions. These distributions provide valuable insights into the behavior of the incident waves when encountering the subwavelength grating.

Fig. 5. Polarization multiplexed metasurfaces. (a) Conceptual schematic of a polarization multiplexed metasurface that combines both the propagation phase and geometric phase. Precise control of diverse orthogonal polarizations can be realized^[106]. (b) Malus metasurface-based one-to-two mapping and one-to-four mapping. Every nanorod has two orientation choices. According to Malus’ law, they generate identical transmitted amplitude but distinctive geometric phase delays, which is the so-called one-to-two mapping. By adding another set of nanobrick analyzers, the one-to-four mapping is constructed. As a result, grayscale patterns on the fabricated samples display various outputs upon illumination by a series of polarization orientations of LP light and the analyzer^[107].

Fig. 6. OAM generating metasurfaces. (a) SEM image of V-shaped antenna array patterned on a silicon wafer. The antennas are arranged to introduce phase shift emulating the conventional spiral phase plate and thereby can generate plasmonic OVs under LP incidence^[73]. (b) Schematic of a J-plate metasurface. It facilitates the conversion of orthogonal polarizations into entirely independent OAM states^[120]. (c) Schematic of a designed perovskite metasurface that utilizes quasi-BIC modes to realize ultrafast switching of vortex beam lasing^[121]. (d) Schematic of a phyllotaxis-inspired vortex generating metasurface. Each meta-atom can contribute to multiple vortex beam generations. The emergence of diverse OAM orders is intricately linked to the arrangement of nanoholes organized into various sets of spirals. The bottom part illustrates the measured free-space profiles of Fresnel diffraction intensity when illuminated with different wavelengths^[122].

Fig. 7. Color printing. (a) sRGB color space on CIE 1931 diagram (https://commons.wikimedia.org/wiki/File:SRGB_chromaticity_CIE1931.svg). (b) Schematic of a plasmonic color filter composed of Ag/Au nanodisks on the Au/Ag backreflector. By varying the dimensions (D) of the nanodisks and gaps (g) between nanodisks, the full palette of colors is revealed^[133]. (c) Schematic and SEM image of an all-dielectric ${\mathrm{TiO}}_2$ metasurface. High-reflection peaks at designed wavelengths can be generated by varying the unit sizes^[134]. (d) Schematic of a silver plasmonic shallow grating (PSG)-based metasurface. Its right side shows the cross-polarized spectra of reflection by CPL at normal incidence. The demonstrated high-resonance sharpness enables highly pure color production and holograms with low crosstalk in different colors shown below^[135].

Fig. 8. Color routers. (a) Top: traditional color image sensor vs chip integrated color splitters. Bottom: SEM image of the color sorting metalens alongside the measured focal plane intensity profile of the metalens when subjected to white light illumination^[136]. (b) GaN metasurface that exhibits full-color routing at the visible frequencies^[137]. (c) Inverse-designed 3D color splitter specifically engineered for placement atop the image sensor pixels. Incident light is adeptly concentrated onto four pixels within a focal plane, displaying distinctive polarization-dependent characteristics^[140]. (d), (e) Schematics of the pixel-level Bayer metasurfaces suitable for a CMOS imaging sensor, accommodating pixel sizes of $1\mathrm{\mu m}\times 1\mathrm{\mu m}$^[141] and $0.8\mathrm{\mu m}\times 0.8\mathrm{\mu m}$^[142], respectively.

Fig. 9. Nonlinear metasurfaces. (a) Conceptual schematic of photon diagrams for important nonlinear processes. New frequencies (downward arrows) are generated when the material system returns to the initial states (solid lines) from the virtual quantum–mechanical states (dashed lines) driven by the input fields (upward arrows). (b) SEM image of the sample supporting SHG with threefold rotational symmetry^[145]. (c) THG from a PB phase nonlinear metasurface. The metasurfaces with C2 and C4 rotational symmetries diffract RCP and LCP THG signals in different ways^[146]. (d) Left: schematic of a dielectric metasurface composed of a square lattice of GaP dimers supporting quasi-BIC modes. It exhibits continuous wave SHG in the visible range. Right: SEM image of the metasurface^[148]. (e) Si metasurface supporting high-Q quasi-BICs exhibiting remarkably high conversion efficiency for the THG and SHG^[149].

Fig. 10. Effect of calculation model on reconstruction quality. (a) Amplitude-only DOE is calculated by the analog method. In this approach, the DOE is generated using a random-phase-based algorithm. However, during the holographic reconstruction process, the diffraction efficiency within the target area is constrained and does not reach its maximum potential. (b) Amplitude-only DOE calculated by the freedoms-considered calculation model^[154]. This model places significant emphasis on the fundamental importance of both amplitude and phase freedoms. By harnessing these different degrees of freedom in the design and optimization process, it becomes feasible to attain higher diffraction efficiencies within the target area with relative ease.

Fig. 11. Fabrication of BOEs^[166]. (a) Two-step etching method. In the first step of the fabrication, a photoresist is coated on a substrate. A mask is placed on the coated substrate. After being illuminated, the exposed position is etched. By repeating this step, a complicated BOE can be fabricated. (b) Direct writing method. It employs a laser beam or an electron beam with variable intensity to directly expose the photoresist on the substrate. (c) Grayscale mask method. The grayscale mask has a multi-level transmittance. When it is placed on the coated substrate, a multi-level structure can be produced directly.

Fig. 12. High-efficiency metasurfaces. (a) Illustration depicting a reflective gap surface-plasmon-based metasurface designed to disperse incident orthogonal linearly polarized (LP) light into distinct focal points with remarkable efficiency, reaching up to 65%, and showcasing a polarization extinction ratio of up to 30 dB^[188]. (b) Schematic representation of a Huygens metasurface designed to efficiently refract light at normal incidence in the telecommunication^[189]. (c) A reflective dielectric metasurface composed of high-refractive-index Si cut wires can function as a half-wave plate with perfect reflectance near unity and over 98% polarization conversion efficiency across a bandwidth of 200 nm. Combining eight sections of specially designed Si cut-wires introduces a changing phase profile azimuthally, and results in highly efficient optical vortex beam creation over a wavelength range from 1500 to 1600 nm^[190]. (d) Two examples of transmissive dielectric metasurfaces with $2\pi$ phase coverage with high-efficiency transmission up to 36% for beam deflecting (left) and 45% for vortex beam conversion (right)^[191]. (e) Schematic of arbitrary complex vectorial optical fields with metasurface. The specially customized units in the metasurface can reflect a given polarization to target polarization with desired phases^[193]. (f) Topology-optimized, large-area, high-numerical-aperture silicon metasurface lens designed to achieve a focusing efficiency surpassing 90%^[195].

Fig. 13. Broadband DOEs. (a) Two-layer DOE. This DOE can excel in delivering exceptional performance across multiple wavelengths by employing two materials with distinct dispersion properties. Its utilization introduces two additional degrees of freedom, encompassing the depth and dispersion characteristics of the second layer. (b) Harmonic DOE. It can attain high diffraction efficiencies across multiple wavelengths while utilizing a single type of material. In contrast to conventional DOEs, harmonic DOEs feature significantly deeper phase levels. Moreover, it is worth noting that distinct diffraction orders yield maximum diffraction efficiencies for different wavelengths.

Fig. 14. Dispersion-engineered metasurfaces. (a) Top: illustration of a light-field depth sensing and imaging with an achromatic GaN metalens array^[213]. (b) Schematic of a dispersion-engineered metalens used as an aberration-corrected spectrometer. A conventional PB phase lens focuses along a curved surface, which results in limited bandwidth and resolution while a dispersion engineered metalens focuses along a plane such that the focal spots are tightly concentrated within a specific broad bandwidth on the flat camera plane^[214].

Fig. 15. Achromatic metasurfaces. (a) Top: achromatic focusing necessitates the synchronous arrival of transmitted wave packets from various locations at the focal point. Bottom: experimental intensity distribution of the designed achromatic metalens in the visible^[216]. (b) SEM image of a GaN achromatic metalens. From 400 to 600 nm, the measured intensity distributions of the brightest spots closely align with the designed focal spots. (white lines). As a result, clear line features can be captured after color correction by the achromatic metalens^[217]. (c) Schematic of a wideband achromatic metalens array designed for integral imaging. The meta-atoms are SiN nanopillars with either circular or square holes. The measured field intensity patterns between 430 and 780 nm show perfect achromatic focusing ability in the visible wavelength^[218]. (d) SEM image of a ${\mathrm{TiO}}_2$ achromatic metalens. Four types of nanostructures are employed as the building blocks: circular, ring, square, and bipolar concentric ring-shaped nanopillars with high aspect ratios of around 37.5^[219].

Fig. 16. Wide-angle micro-DOEs. (a) Through the application of zero-padding to the DOE plane, the sampling interval on the intermediate plane was reduced, consequently leading to a notable extension in the size of the Fresnel diffraction field when illuminated with a plane wave. (b) Experimental results when $\alpha =1.5$ (top) and $\alpha =1.6$ (bottom). The sizes of corresponding Fresnel diffraction fields are $38.9\mathrm{mm}\times 38.9\mathrm{mm}$ and $41.5\mathrm{mm}\times 41.5\mathrm{mm}$, respectively^[222].

Fig. 17. Wide-angle high-NA metasurfaces. (a) Design and fabrication of a high-NA Fourier metalens^[230]. (b) Design of a high-NA divergent metalens^[171].

Fig. 18. Switchable and tunable micro-DOEs. (a) Switchable micro-DOE^[232]. This element operates with two distinct fixed states. In its default state, when no voltage is applied, the element remains in a non-diffractive state. However, upon the application of a 5 V voltage, the element switches to a diffractive state. In the non-diffractive state, the resulting reconstruction consists of a single spot. Upon transitioning to the diffractive state, the reconstruction transforms into a series of spots. (b) Tunable micro-DOE^[235]. This combined DOE comprises two separate DOEs. The adjustment of the focal point positions for the combined DOE is achieved by rotating the second DOE.

Fig. 19. Reconfigurable micro-DOEs. (a) DMD^[237]. It is a type of MEMS DOE that consists of a series of periodically arranged micro-mirrors. These micro-mirrors can be addressed and controlled separately. For each micro-mirror, it has three states: on, off, and float. By controlling the state of each micro-mirror, different patterns can be obtained. (b) DM^[238]. It is a MEMS-based modulation device whose shape of the surface can be changed. By controlling the shape of the surface, different patterns can be obtained. (c) LCoS device^[239]. It has a similar design concept to DMD. Both of them are reflective elements. The state of each pixel in the LCoS device can be changed by addressing and controlling signals. The major difference between LCoS and DMD is that LCoS modulates the phase of the incident light, while DMD modulates its amplitude.

Fig. 20. Liquid-crystal-integrated metasurfaces. (a) Diagram illustrating the off and on states of a metasurface integrated with liquid crystal, which can be controlled in-plane electrically through voltage bias. The metasurface is composed of zig-zag suspended Au-SiN nanobridges as shown in the SEM image. A 110 nm ($\sim 7\%$)-spectral tuning was observed for applied voltage ranging from 1.5 to 2.7 V^[245]. (b) Top: digital metasurface device (DMSD) designed for use in light projection displays. The metasurface is composed of an $\mathrm{M}\times \mathrm{N}$ array of pixels, with each pixel containing gold nanorods arranged in a rectangular lattice. Bottom: working principle of the DMSD. Each array is encapsulated in a liquid crystal cell that is independently tailored via an addressable electrode. Hence, reflection from pixels can be programmably controlled, and the desired images can be displayed in the far field^[246]. (c) Top: illustration depicting an ETPM integrated with liquid crystals and employing all-dielectric metasurfaces. Bottom: by applying electrical modulation of different voltages, various phase abruptions can be achieved by manipulating the orientations of liquid crystal molecules, and thereby a varifocal metalens for different wavelengths is realized^[247].

Fig. 21. GST/VO2 metasurfaces. (a) Left: schematic of the writing of dynamic phase change metasurfaces and devices. Here, ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ (GST) is employed as the phase change material. Optical excitation by femtosecond pulses through the “write” channel alters the dielectric constant of the GST by transition between the amorphous–crystalline states. Using different illumination conditions, the working pattern can be cleaned through “read” channel^[252]. (b) Schematic of an electrically actuated GST-Ag metasurface. Set and reset pulses generate heat within the metasurface, leading to a reversible transformation between its amorphous and crystalline states. The on/off ratio of the reflectance modulation can be up to 4.5 at the wavelength of 755 nm^[254]. (c) Schematic of a ${\mathrm{Ge}}_2{\mathrm{Se}}_2{\mathrm{Sb}}_2\mathrm{Te}$ (GSST) metasurface demonstrating reflectance modulation of $\sim 30\%$^[255]. (d) Gold split ring resonator–vanadium dioxide (${\mathrm{VO}}_2$) metasurface. The resonance frequency decreases when the “insulator” becomes a “metal”^[257]. (e) Thermally controlled resonance of the ${\mathrm{VO}}_2$ antennas^[258]. (f) Mie-resonant dielectric metasurface based on ${\mathrm{VO}}_2$ material. Tunable extinction with temperature variation can be realized^[259].

Fig. 22. Chemical reaction metasurfaces. (a) Top: working principle of a hydrogen-responsive plasmonic metasurface. The colors in the metasurface can be eliminated under exposure of ${\mathrm{H}}_2$, and restored in ${\mathrm{O}}_2$. Bottom: evolution of color erasing and restoring for an optical image during hydrogenation and dehydrogenation^[260]. (b) Top: schematic of an electrochemically controlled plasmonic metasurface based on voltage-responsive PANI. Bottom: integrating two addressable metasurfaces enables the electrochemically switchable holography display^[263].

Fig. 23. Nanomechanical metasurfaces. (a) Thermally tunable metasurface consisting of reconfigurable and nonreconfigurable nanobridges, where the reconfigurable part is steered by a differential thermal response in Au and SiN. A relative transmission change of up to $\pm 50\%$ was demonstrated^[271]. (b) Schematic of current carrying zig-zag-shaped nanostrips that are driven by the Lorentz force. A large reciprocal magneto–electro–optical effect was observed^[272]. (c) All-dielectric reconfigurable metasurface electro-optic modulator. It can modulate the transmission spectra, which results in a giant electrostriction^[173]. (d) Electromechanically reconfigurable chiral metasurface. It comprises alternating conductive and isolated nanobeams that are all perforated with alternating large and small semicircular notches. Such design was chosen to form a simplified (2D) spiral-like hole, which can be deformed into a 3D helix-like geometry by their mutual out-of-plane displacement actuated by the electrostatic force between the metasurface and another ITO-coated back-plane. As a result, giant eletrogyration that is six orders of magnitude stronger than that in natural materials such as quartz was observed^[176]. (e) Light-induced giant optical nonlinearity in a plasmonic reconfigurable metasurface. Differential optical forces by a pump-laser illumination exerted on metasurface arrays cause nanoscale reversible mutual displacements of neighboring narrow and wide nanowires. This process can significantly modulate the transmission of another probe beam. The modulation strongly relies on the intensity of the pump beam^[273]. (f) 6G meta-device driven by piezoelectricity realizing 3D varifocal. The 3D printing method is used for the THz meta-device fabrication. Metasurfaces are rotated accurately in real time to realize ultrafast dynamic control of the focal spots^[274].

Fig. 24. Metasurfaces integrated with 2D materials. (a) hBN hyperbolic metasurface supporting strongly volume-confined phonon polaritons^[276]. (b) $\mathrm{Au}\text{-}{\mathrm{WS}}_2$ metasurface with tunable nonlinear valley-locked chiral emissions^[278]. (c) Metasurface consisting of a monolayer ${\mathrm{MoS}}_2$ on subwavelength asymmetric gratings that can spatially separate opposite valley excitons^[279]. (d) Patterned WS₂ zone plate supporting excitons that enhance and modulate the focusing efficiency by 33% by the electrical gating^[280]. (e) Twisted $\alpha \text{-}\mathrm{MoO}3$ bilayer structure that can realize topological transitions in dispersion engineering when the relative orientation between the layers is rotated to a magic angle^[281]. (f) Tunable unidirectional nonlinear emission from a ${\mathrm{MoS}}_2$ truncated cone metasurface^[283].

Fig. 25. Diffractive imaging lenses. (a) Imaging system using two concatenated millimeter-scale flat lenses^[285]. The numerical aperture and physical dimensions of this diffractive lens can be readily enhanced through improvements in the fabrication process. In comparison to metalenses and conventional refractive lenses, its manufacturing process is notably simpler. (b) Diffractive lens that integrates functions of multiple conventional elements^[286]. This diffractive lens excels at correcting chromatic aberrations across an exceptionally wide bandwidth. Even when operating at a high numerical aperture ($\mathrm{NA}=0.81$), the achromatic functionality of the designed diffractive lens remains highly effective. It is worth noting that the two diffractive lenses share identical structures, with the only variation being the support substrate—glass for visible and NIR wavelengths, and silicon for other wavelengths.

Fig. 26. Sensing metasurfaces. (a) Comparison between linear and nonlinear plasmonic sensing. A refractive index change in the surrounding material of the metasurface causes shifts in the resonance frequency. The resultant feedback signal is much larger for a nonlinear process (i.e., third harmonic generation) than that for a linear process (i.e., transmittance) because of the narrowing of the third harmonic resonance^[296]. (b) Plasmonic metasurface-integrated wearable SERS sensing system. It consists of a sweat extraction component and a SERS sensing component. The SERS sensing component is built on a plasmonic metasurface composed of silver nanocubes. The analytes from human sweat are drawn to the electromagnetic hotspots between nanocubes, which can be analyzed by SERS. The device can simultaneously detect different drugs and their concentrations contained in the human sweat samples^[298]. (c) Ultrasensitive displacement metrology using a superoscillatory metasurface. Based on the superoscillation effect and PB phase design, a displacement detecting capability better than 1 nm ($\sim \lambda /800$) in experiment and $\sim \lambda /4000$ in theory was demonstrated^[300].

Fig. 27. Chiral metasurfaces. (a) Multilayer chiral metasurface with each layer consisting of the same nanorod arrays but in different orientation angles^[304]. (b) Pneumatically actuated terahertz chiral metasurface. By controlling the air pressure above and beneath the metasurface, its spiral components can be deformed upwards and downwards to form a 3D helix with opposite handedness^[266]. (c) A giant optical activity can be observed in a nano-kirigami metasurface fabricated using focused ion beam milling technology^[308]. (d) Strong intrinsic chirality can be realized in a dielectric metasurface consisting of ${\mathrm{TiO}}_2$ gammadions^[309]. (e) Chiral metasurface with maximum chirality at BIC modes. Shaping the symmetry of an array of dielectric bars can transform the resonance mode from BICs to quasi-BICs, which results in the maximum chirality with an extremely high quality factor^[310]. (f) Slant-perturbation metasurface to realize intrinsic chiral-BICs^[311].

Fig. 28. Information transmission with DOEs. (a) Diffractive coupler with high efficiency^[314]. The coupler was intentionally designed to exhibit strong directionality by incorporating a silicon overlay prior to defining the grating. Experimental results demonstrated an impressive coupling efficiency of 55%, while theoretical calculations projected an even higher efficiency of 80%, all at a wavelength of 1.53 µm. (b) Multilevel DOE for WDM^[316]. When employed, this coupler facilitates the straightforward multiplexing of wavelengths, allowing for spectral separations between channels to be reduced to just 8 nm, all while maintaining a low crosstalk level of $-18\mathrm{dB}$.

Fig. 29. Photonic spin Hall metasurfaces. (a) A giant photonic spin Hall effect (PSHE) is observed even at normal incidence in a plasmonic metasurface with rapid phase gradient^[322]. (b) PSHE in a polarization selective SPP plane-wave coupler metasurface. Unidirectional launching of SPPs locked with the incident spin state was demonstrated^[323]. (c) Schematic of a photonic spin Hall lens. Incident light with two circular polarizations produces a split focusing path, which can further be applied to OAM-mode angular sorting^[328]. (d) On-chip photonic spin Hall metasurface composed of two gratings with different spatial arrangements. It can be used to simultaneously detect the polarization and geometric center of the incident cylindrical vortex vector beam^[329].

Fig. 30. Optical communication metasurfaces. (a) Dammann optical vortex grating (DOVG) for the multiplexing and de-multiplexing of multiple OAM signals^[330]. (b) Inverse-designed broadband multiplexed OAM emitter. Coaxial OAM beam emission covering the entire telecommunication range was demonstrated^[331]. (c) CVB sorting by optical geometric transformation using a PB phase metasurface. Different spin components of a CVB can be unwrapped from a donut shape to two straight lines but along opposite directions. Following the phase correction process, the CVB is ultimately focused onto a solitary light spot, and the degree of lateral displacement is directly proportional to the input CVB orders^[332]. (d) Left: schematic of a CVB-generating metasurface consisting of Au nanorods on a ${\mathrm{SiO}}_2$ thin film above an Au mirror plane. Right: LCP and RCP illuminations generate CVBs with different orders in different directions^[333]. (e) Integrating a plasmonic metasurface on the ends of fibers can coherently modulate light with light and are capable of executing signal processing functions that mimic input/output relationships similar to XOR, AND, and NOT operations^[175]. (f) Metasurface-patterned dielectric waveguides can be employed as linear- and circular-polarization (de)multiplexers, respectively shown in the top and bottom^[334]. (g) Arbitrary Stokes vector detection using a PB phase metagrating^[335].

Fig. 31. Programmable metasurfaces. (a) A coding comprises elements of either 0 or $\pi$ phase response in reflection. Using biased diodes as elements and a field-programmable gate array (FPGA), the coding metasurface can perform functions of a programmable metasurface dictated by a coding sequence^[337]. (b) Schematic of a space–time-coding digital metasurface. The coding elements were loaded with positive–intrinsic–negative (PIN) diodes so that the reflection can be sequentially switched under applied control voltage^[339]. (c) GeTe-based multiple-functions-in-one coding metasurface for controlling terahertz beam, including beam splitting, tilting, and focusing. Each coding element can be phase changed selectively by laser activation^[340].

Fig. 32. Micro-DOEs for space-variant interconnections. (a) Space-variant optical module of the shuffle-exchange interconnection^[362]. Within this network configuration, a lens situated in the first off-axis lenslet array serves to collimate and guide the light emitted from the light source. This directed light is then further manipulated by one or more lenses placed in the second off-axis lenslet array. Each of these lenses in the second array focuses and concentrates the light onto its respective detectors. This optical setup enables controlled signal routing and interconnections within the system. (b) Space-variant optical interconnection network structured by a multifaceted CGH^[364]. The compact interconnect distance between the array planes and the CGH resulted in a system with compact physical volume. (c) Multilayer feed-forward neural networks based on the interconnection architectures^[365]. Despite the relatively small overall system volume, the limited-fan-out architecture had the capacity to accommodate a significantly larger number of input and output nodes. This efficiency in node management was achieved by carefully optimizing the interconnection design, allowing for a compact yet highly scalable optical computing system.

Fig. 33. A terahertz diffractive deep neural network (${\mathrm{D}}^2\mathrm{NN}$)^[372]. The DOEs within this network were fabricated through the innovative technique of 3D printing. This physical ${\mathrm{D}}^2\mathrm{NN}$ exhibits the remarkable capability to execute myriad functions at the speed of light, a velocity vastly surpassing that of electronic neural networks. Notably, with the exception of the energy required for illumination, this physical ${\mathrm{D}}^2\mathrm{NN}$ can carry out a wide range of functions without consuming additional energy.

Fig. 34. Holographic display based on optical hologram. (a) Recording and reconstruction of an optical hologram^[12]. When a coherent beam interacts with a target object, it undergoes a phenomenon known as diffuse reflection, which is primarily due to the irregular and uneven nature of the object’s surface. The information about the target object is effectively encoded into the coherent beam during its interaction with the object. Subsequently, another coherent beam, characterized by the same wavelength and polarization properties as the original beam, is introduced to interact with the object beam at a specific location called the holographic plane. This interaction results in the creation of interference patterns. By employing a photographic film, the interference fringes can be readily recorded. When the same reference beam illuminates the recorded interference fringes again, the 3D object can be reconstructed via diffraction. (b) Optical-hologram-based refreshable holographic display^[375]. It can be erased by uniform illumination at the writing wavelength.

Fig. 35. Learning-based holographic method^[387]. This system boasts memory efficiency and operates smoothly at a 60 Hz refresh rate while handling a resolution of $1920\times 1080$ pixels, all on a single consumer-grade GPU.

Fig. 36. Metasurfaces for quantum technologies and topological photonics. (a) Quantum entanglement between SAM and OAM in a dielectric metasurface^[423]. (b) Combination of an array of specially designed metalenses with a nonlinear crystal makes a multiphoton quantum source^[424]. (c) Topological metasurface comprising silicon nanopillars organized into hexagon lattices supports strong THG^[430]. (d) Metasurface supporting topological phase around the exceptional point (EP), which is referred to as the exceptional topological (ET) phase. Combining the ET phase with PB phase was further designed to realize an ET + PB metasurface. Scattering from the EP is polarization-dependent, introducing topological properties into the domain of industrial applications at optical frequencies^[431]. (e) Generation of a TM toroidal light pulse (light pulse with toroidal topology, namely, TLP) by a singular plasmonic metasurface excited with radially polarized pulse^[432].

Fig. 37. Diffractive optical elements 75 years: from micro-optics to metasurfaces. We commemorate the 75th anniversary of DOEs by providing a comprehensive overview and forward-looking perspective on the significant milestones, recent advancements, and promising domains within the realms of DOEs.

Fig. 38. Degrees of freedom for light field.

Fig. 39. Roadmap charting the 75-year progression of diffractive optical elements from 1948 to 2023, emphasizing pivotal theoretical and technical breakthroughs while referencing significant works throughout this remarkable expedition.