Figures & data
Figure 1. Modelling of disorder in metasurfaces based on (a) geometric parameters and (b) correlation. (a) Illustration of ordered metasurface and metasurfaces with disorder in the size, position and both, respectively. (b) Illustration of statistically modelled disorder with different correlation [Citation18].
![Figure 1. Modelling of disorder in metasurfaces based on (a) geometric parameters and (b) correlation. (a) Illustration of ordered metasurface and metasurfaces with disorder in the size, position and both, respectively. (b) Illustration of statistically modelled disorder with different correlation [Citation18].](/cms/asset/ce0b5b11-4e47-4b03-8c2d-1649161229e6/tapx_a_2234136_f0001_oc.jpg)
Figure 2. Disordered metasurfaces for resonance manipulation applications. (a) Resonant metasurfaces for the study of the interplay of order and disorder at oblique incidence. As shown in panel i, the photonic metasurface is composed of sandwich-type nanoparticles, with different arrangements, periodic, disordered and amorphous metasurfaces are prepared, which exhibit different optical response, for example, different transmission spectra in panel ii [Citation30]. (b) Metal split metasurfaces with quasicrystal, periodic and random arrangements for the study of near-field surface plasmons. The schematic diagrams of the three types of metasurfaces and corresponding simulated surface plasmon distributions at different frequency are presented in panel i, ii and iii, respectively [Citation31], where the propagation modes of SPs for quasicrystal and periodic metasurfaces are denoted by the arrows and there is no propagation of regular SPs for random metasurface. (c) SiGe random metasurfaces based on Mie resonances for antireflection. By modifying the fabrication process, three samples with different statistical distribution of particle diameter are prepared (panel i), resulting in different reflectance and transmission spectra, as shown in panel ii and iii. Panel (c) is adapted with permission from REF [Citation32]. Copyright 2018, American Physical Society. (d) Collective lattice resonances in metasurfaces with different types of disorder. Four types of disorder are studied (panel i). As the extinction spectra shown in panel ii, different types of disorder lead to diverse resonances. Panel (d) is adapted with permission from REF [Citation33]. Copyright 2019, the Optical Society.
![Figure 2. Disordered metasurfaces for resonance manipulation applications. (a) Resonant metasurfaces for the study of the interplay of order and disorder at oblique incidence. As shown in panel i, the photonic metasurface is composed of sandwich-type nanoparticles, with different arrangements, periodic, disordered and amorphous metasurfaces are prepared, which exhibit different optical response, for example, different transmission spectra in panel ii [Citation30]. (b) Metal split metasurfaces with quasicrystal, periodic and random arrangements for the study of near-field surface plasmons. The schematic diagrams of the three types of metasurfaces and corresponding simulated surface plasmon distributions at different frequency are presented in panel i, ii and iii, respectively [Citation31], where the propagation modes of SPs for quasicrystal and periodic metasurfaces are denoted by the arrows and there is no propagation of regular SPs for random metasurface. (c) SiGe random metasurfaces based on Mie resonances for antireflection. By modifying the fabrication process, three samples with different statistical distribution of particle diameter are prepared (panel i), resulting in different reflectance and transmission spectra, as shown in panel ii and iii. Panel (c) is adapted with permission from REF [Citation32]. Copyright 2018, American Physical Society. (d) Collective lattice resonances in metasurfaces with different types of disorder. Four types of disorder are studied (panel i). As the extinction spectra shown in panel ii, different types of disorder lead to diverse resonances. Panel (d) is adapted with permission from REF [Citation33]. Copyright 2019, the Optical Society.](/cms/asset/ed40f050-2fc6-41b4-bebd-14ace6ecd99f/tapx_a_2234136_f0002_oc.jpg)
Figure 3. Disordered metasurfaces for wavefront manipulation applications. (a) Ferromagnetic-disordered metasurfaces for investigating the stochastic photonic spin Hall effect (PSHE). Panel i illustrates the PSHE from a spatially fluctuated metasurface under an external magnetic field, which has a typical spin shift. The calculated probability distributions of PSHEs along with spin shift and the measured standard deviation of PSHEs as a function of the spatial fluctuation are shown in panel ii and iii, respectively. Panel (a) isadapted with permission from REF [Citation41]. Copyright 2020, Wang B. et al, under exclusive licence to Springer Nature Limited. (b) Bilayer plasmonic metasurfaces with optical chirality induced by rotational disorder. The schematic diagrams and scanning electron microscopy (SEM) images of the bilayer metasurfaces are shown in panel i, whose chirality is proved by the measured transmittance and ellipticity spectra. Panel (b) is adapted with permission from REF [Citation42]. Copyright 2018, American Chemical Society. (c) Multifunctional silicon metasurface based on order – disorder interleaving approach. In panel i, the schematic diagrams and SEM images of the interleaving metasurface are presented. The results of wavelength-dependent imaging at 600 nm and 820 nm are shown in panel ii. Panel (c) is adapted with permission from REF [Citation43]. Copyright 2018, American Chemical Society. (d) Metasurfaces with engineered noise for high-capacity polarisation multiplexing. Panel i illustrates the design of the polarisation-multiplexed metasurfaces. The SEM images of the fabricated metasurface are shown in panel ii (scale bars from left to right: 500 nm, 250 nm). The measured holographic images in 11 independent channels of linear polarisation states are shown in panel iii, where the polarisation orientations are denoted by the arrows. Panel (d) is from REF [Citation44], reprinted with permission from AAAS. (e) Metasurface in randomly flipped configuration for antiglaring application. Panel i demonstrates the concept of antiglaring. The schematic diagrams of the metasurface is shown in panel ii, whose imaging results in transmission and reflection directions are presented in panel iii, verifying the antiglaring function [Citation45].(f) Disordered metasurface with long-range-order via a topology optimisation approach. The disordered supercell metasurface and topology-optimised freeform metasurface as well as their diffraction intensity distributions are shown in panel i and ii, respectively, confirming that the phase fluctuation is suppressed by applying the topology optimisation. Panel (f) is adapted with permission from REF [Citation46]. Copyright 2022, Wiley-VCH GmbH. (g) Perfect optical diffusers via dielectric Huygens’ metasurfaces with positional disorder. The pair correlation functions and SEM images of the three types of disordered metasurfaces are presented, indicating that the long-range order is maintained by the perturbed array while the uniform-types metasurfaces exhibit ideal-gas-like long-range order and limited short-range order. Panel (g) is adapted with permission from REF [Citation47]. Copyright 2021, Advanced Materials published by Wiley-VCH GmbH.
![Figure 3. Disordered metasurfaces for wavefront manipulation applications. (a) Ferromagnetic-disordered metasurfaces for investigating the stochastic photonic spin Hall effect (PSHE). Panel i illustrates the PSHE from a spatially fluctuated metasurface under an external magnetic field, which has a typical spin shift. The calculated probability distributions of PSHEs along with spin shift and the measured standard deviation of PSHEs as a function of the spatial fluctuation are shown in panel ii and iii, respectively. Panel (a) isadapted with permission from REF [Citation41]. Copyright 2020, Wang B. et al, under exclusive licence to Springer Nature Limited. (b) Bilayer plasmonic metasurfaces with optical chirality induced by rotational disorder. The schematic diagrams and scanning electron microscopy (SEM) images of the bilayer metasurfaces are shown in panel i, whose chirality is proved by the measured transmittance and ellipticity spectra. Panel (b) is adapted with permission from REF [Citation42]. Copyright 2018, American Chemical Society. (c) Multifunctional silicon metasurface based on order – disorder interleaving approach. In panel i, the schematic diagrams and SEM images of the interleaving metasurface are presented. The results of wavelength-dependent imaging at 600 nm and 820 nm are shown in panel ii. Panel (c) is adapted with permission from REF [Citation43]. Copyright 2018, American Chemical Society. (d) Metasurfaces with engineered noise for high-capacity polarisation multiplexing. Panel i illustrates the design of the polarisation-multiplexed metasurfaces. The SEM images of the fabricated metasurface are shown in panel ii (scale bars from left to right: 500 nm, 250 nm). The measured holographic images in 11 independent channels of linear polarisation states are shown in panel iii, where the polarisation orientations are denoted by the arrows. Panel (d) is from REF [Citation44], reprinted with permission from AAAS. (e) Metasurface in randomly flipped configuration for antiglaring application. Panel i demonstrates the concept of antiglaring. The schematic diagrams of the metasurface is shown in panel ii, whose imaging results in transmission and reflection directions are presented in panel iii, verifying the antiglaring function [Citation45].(f) Disordered metasurface with long-range-order via a topology optimisation approach. The disordered supercell metasurface and topology-optimised freeform metasurface as well as their diffraction intensity distributions are shown in panel i and ii, respectively, confirming that the phase fluctuation is suppressed by applying the topology optimisation. Panel (f) is adapted with permission from REF [Citation46]. Copyright 2022, Wiley-VCH GmbH. (g) Perfect optical diffusers via dielectric Huygens’ metasurfaces with positional disorder. The pair correlation functions and SEM images of the three types of disordered metasurfaces are presented, indicating that the long-range order is maintained by the perturbed array while the uniform-types metasurfaces exhibit ideal-gas-like long-range order and limited short-range order. Panel (g) is adapted with permission from REF [Citation47]. Copyright 2021, Advanced Materials published by Wiley-VCH GmbH.](/cms/asset/57bf9a6f-df20-4b64-8b57-d2673933024f/tapx_a_2234136_f0003_oc.jpg)
Figure 4. Structural colour realized by using disordered metasurfaces. (a) High-purity colour display achieved by combining a disordered nanostructure system and an external Fabry–Perot cavity. The schematic of the clusters-on-spacer sample is shown in panel i, which is endowed with a rainbow-like photonic image (panel ii) by varying the thickness of the spacer. The generated colour in CIE 1931 ×y chromaticity diagram is shown in panel iii [Citation61]. (b) Disordered metasurfaces with FP-cavity configuration for generating humidity-responsive structural colour. Panel i demonstrates the schematics of the chitosan hydrogel FP-cavity in humid and dry states, whose reflectance spectra vary with the humidity in the environment (panel ii) [Citation62]. (c) the quasi-independent control of the colours of the specular and diffuse components by using disordered metasurfaces. The schematics of the disordered metasurface for visual appearance is shown in panel i, whose SEM images and photographs under different incident and detection angles are presented in panel ii. Panel (c) is adapted with permission from REF [Citation63]. Copyright 2022, Vynck K. et al, under exclusive licence to Springer Nature Limited. (d) Material-insensitive structural colours achieved by using plasmonic disordered metasurfaces. The SEM image of the cross-section of the disordered metasurface is shown in panel i, and panel ii demonstrates the colour-map of the corresponding metasurfaces with different materials and thicknesses of the spacer. Panel (d) is adapted with permission from REF [Citation64]. Copyright 2021, Wiley-VCH GmbH.
![Figure 4. Structural colour realized by using disordered metasurfaces. (a) High-purity colour display achieved by combining a disordered nanostructure system and an external Fabry–Perot cavity. The schematic of the clusters-on-spacer sample is shown in panel i, which is endowed with a rainbow-like photonic image (panel ii) by varying the thickness of the spacer. The generated colour in CIE 1931 ×y chromaticity diagram is shown in panel iii [Citation61]. (b) Disordered metasurfaces with FP-cavity configuration for generating humidity-responsive structural colour. Panel i demonstrates the schematics of the chitosan hydrogel FP-cavity in humid and dry states, whose reflectance spectra vary with the humidity in the environment (panel ii) [Citation62]. (c) the quasi-independent control of the colours of the specular and diffuse components by using disordered metasurfaces. The schematics of the disordered metasurface for visual appearance is shown in panel i, whose SEM images and photographs under different incident and detection angles are presented in panel ii. Panel (c) is adapted with permission from REF [Citation63]. Copyright 2022, Vynck K. et al, under exclusive licence to Springer Nature Limited. (d) Material-insensitive structural colours achieved by using plasmonic disordered metasurfaces. The SEM image of the cross-section of the disordered metasurface is shown in panel i, and panel ii demonstrates the colour-map of the corresponding metasurfaces with different materials and thicknesses of the spacer. Panel (d) is adapted with permission from REF [Citation64]. Copyright 2021, Wiley-VCH GmbH.](/cms/asset/5ef1224d-42ba-4a3c-ac1c-6e35fedc09eb/tapx_a_2234136_f0004_oc.jpg)
Figure 5. Energy related applications of disordered metasurfaces. (a) Broadband perfect absorbers based on disordered titanium nitride metasurface. Panel i demonstrates the schematic and the top-view SEM image of the perfect meta-absorber. The absorption spectra of the disordered metasurfaces with and without TiN coating are shown by cyan and black curves, respectively, in panel ii [Citation84]. (b) Enhanced broadband photon confinement in two-dimensional disordered media. The schematic of the random film is shown in panel i. The absorption spectra of the bare and random films are shown by black and blue curves, respectively, in panel ii. Panel iii presents the distributions of the electromagnetic energy density in the sample at different frequencies. Panel (b) is adapted with permission from REF [Citation89]. Copyright 2012, Springer Nature Limited. (c) Absorber-coated plasmonic metasurfaces with abundant optical modes. The planar Ag with rough organic coating in panel i supports Mie-absorption-induced scattering. The scattering modes supported by AgNPA/Ag metasurface with semi-crystalline and amorphous organic coatings are shown in panel ii and iii, respectively [Citation90]. (d) a hybrid disordered metasurface for tailoring optical modes to facilitate water splitting reactions. The schematic and photographs of hybrid disordered metasurfaces are shown in panel i. Panel ii illustrates the photoelectrochemical measurement system for water splitting assisted by the disordered metasurface. The corresponding evolution of H2 and O2 as well as the H2-evolution action spectrum are presented in Panel iii. Panel (d) is adapted with permission from REF [Citation91]. Copyright 2018, Shi X. et al. (e) an OLED with improved device stability obtained by enhancing the decay rate using a disordered metasurface. The schematic of the disordered metasurface and the atomic-force micrograph of the Ag nanocubes on the top are shown in panel i and ii, respectively. The measured results of the lifetime and efficiency of the three samples are presented in panel iii. Panel (e) is adapted with permission from REF [Citation92]. Copyright 2020, Fusella M. A. et al, under exclusive licence to Springer Nature Limited. (f) a EQE-improved GaN LED assisted by the Ag disordered metasurface. The field distributions of the bare substrate and the three different metasurfaces are shown in panel i. The far-field intensity and the transition spectra at different incident angles for the three different metasurfaces are shown in panel ii and iii, respectively [Citation93].
![Figure 5. Energy related applications of disordered metasurfaces. (a) Broadband perfect absorbers based on disordered titanium nitride metasurface. Panel i demonstrates the schematic and the top-view SEM image of the perfect meta-absorber. The absorption spectra of the disordered metasurfaces with and without TiN coating are shown by cyan and black curves, respectively, in panel ii [Citation84]. (b) Enhanced broadband photon confinement in two-dimensional disordered media. The schematic of the random film is shown in panel i. The absorption spectra of the bare and random films are shown by black and blue curves, respectively, in panel ii. Panel iii presents the distributions of the electromagnetic energy density in the sample at different frequencies. Panel (b) is adapted with permission from REF [Citation89]. Copyright 2012, Springer Nature Limited. (c) Absorber-coated plasmonic metasurfaces with abundant optical modes. The planar Ag with rough organic coating in panel i supports Mie-absorption-induced scattering. The scattering modes supported by AgNPA/Ag metasurface with semi-crystalline and amorphous organic coatings are shown in panel ii and iii, respectively [Citation90]. (d) a hybrid disordered metasurface for tailoring optical modes to facilitate water splitting reactions. The schematic and photographs of hybrid disordered metasurfaces are shown in panel i. Panel ii illustrates the photoelectrochemical measurement system for water splitting assisted by the disordered metasurface. The corresponding evolution of H2 and O2 as well as the H2-evolution action spectrum are presented in Panel iii. Panel (d) is adapted with permission from REF [Citation91]. Copyright 2018, Shi X. et al. (e) an OLED with improved device stability obtained by enhancing the decay rate using a disordered metasurface. The schematic of the disordered metasurface and the atomic-force micrograph of the Ag nanocubes on the top are shown in panel i and ii, respectively. The measured results of the lifetime and efficiency of the three samples are presented in panel iii. Panel (e) is adapted with permission from REF [Citation92]. Copyright 2020, Fusella M. A. et al, under exclusive licence to Springer Nature Limited. (f) a EQE-improved GaN LED assisted by the Ag disordered metasurface. The field distributions of the bare substrate and the three different metasurfaces are shown in panel i. The far-field intensity and the transition spectra at different incident angles for the three different metasurfaces are shown in panel ii and iii, respectively [Citation93].](/cms/asset/46d21040-e9b5-424e-bb19-16760a86f4e9/tapx_a_2234136_f0005_oc.jpg)
Figure 6. Applications of disordered metasurfaces in nonlinear optics and state/phase transition. (a) Tunable nonlinear photoluminescence generation via disordered metasurfaces. The distributions of normalized standard deviations for the three samples are shown in panel i. The average NPL intensity distributions for metasurfaces with gold filling fractions of 0.29 and 0.58 associated with local field enhancements (panel ii), interfering delocalized plasmonic modes (panel iii) and combined results (panel iv) are also presented . Panel (a) is adapted with permission from REF [Citation108]. Copyright 2021, American Chemical Society. (b) Manipulating the radiation of second-harmonic generation via nonlinear quasicrystal metasurfaces. Panel i shows the SEM images of the three quasicrystal metasurfaces, whose measured linear and nonlinear diffractions are also presented in panel ii and iii, respectively. Panel (b) is adapted with permission from REF [Citation109]. Copyright 2019, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (c) the transition from spin Hall to random Rashba effect realized by increasing the disorder in geometric phase metasurfaces. In panel i, the photonic transition is illustrated by using ordered, weakly disordered and strongly disordered metasurfaces. Panel ii illustrates the obtaining of the twisted metasurface by combining the helical phase and disordered phase. The metasurfaces with distorted helical phase distributions and corresponding measured intensities in momentum space are shown in panel iii. Panel (c) is from REF [Citation110], reprinted with permission from AAAS.
![Figure 6. Applications of disordered metasurfaces in nonlinear optics and state/phase transition. (a) Tunable nonlinear photoluminescence generation via disordered metasurfaces. The distributions of normalized standard deviations for the three samples are shown in panel i. The average NPL intensity distributions for metasurfaces with gold filling fractions of 0.29 and 0.58 associated with local field enhancements (panel ii), interfering delocalized plasmonic modes (panel iii) and combined results (panel iv) are also presented . Panel (a) is adapted with permission from REF [Citation108]. Copyright 2021, American Chemical Society. (b) Manipulating the radiation of second-harmonic generation via nonlinear quasicrystal metasurfaces. Panel i shows the SEM images of the three quasicrystal metasurfaces, whose measured linear and nonlinear diffractions are also presented in panel ii and iii, respectively. Panel (b) is adapted with permission from REF [Citation109]. Copyright 2019, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (c) the transition from spin Hall to random Rashba effect realized by increasing the disorder in geometric phase metasurfaces. In panel i, the photonic transition is illustrated by using ordered, weakly disordered and strongly disordered metasurfaces. Panel ii illustrates the obtaining of the twisted metasurface by combining the helical phase and disordered phase. The metasurfaces with distorted helical phase distributions and corresponding measured intensities in momentum space are shown in panel iii. Panel (c) is from REF [Citation110], reprinted with permission from AAAS.](/cms/asset/06d15848-f51d-4582-96af-1b4b7641507c/tapx_a_2234136_f0006_oc.jpg)