Fig. 1. Experimental results on the optical memory effect characterized by angles in disordered media^[51]. The patterns on the left show the cross-correlation coefficients of the corresponding images with the reference image, and the patterns on the right show the transmitted speckles. (a) Initial reference speckle pattern for normal incidence; (b) speckle pattern with the laser rotated by 0.01°; (c) speckle pattern with the laser rotated by 0.02°; (d) speckle pattern uncorrelated with Fig. 1(a)

Fig. 2. Angle scattering profile distribution and optical memory effect of disordered media^[37]. (a)‒(c) Angular scattering intensity distribution of disordered metasurfaces with different NA; (d)‒(f) typical angular scattering profile characteristics of conventional disordered media including TiO₂ white paint, opal glass, and ground glass; (g) comparison of angular correlation ranges of different types of disordered media; (h) parametric comparison of key differences between disordered metasurfaces and conventional disordered media in terms of angular scattering profiles and range of memory effect

Fig. 3. Distribution models of random-phase metasurfaces^[67]. (a)(d) Propagation phase disordered metasurface controlled by the nanorod width w and length l; (b)(e) geometric phase disordered metasurface controlled by the nanorod rotation angle θ; (c)(f) composite-phase disordered metasurface controlled by w, l, and θ

Fig. 4. Schematic of far-field distribution of random phase metasurface

Fig. 5. Numerical simulation of far-field scattering from random phase metasurface^[68]. The histograms show the PDFs of far-field intensities in the range of NA=0.9 calculated from I∝Efar2, the red line corresponds to the theoretical prediction of Eqs. (5)‒(6), and the insets show the distribution of far-field intensities calculated in the range of NA=0.9. (a) Simulation of scattering from a continuous random-phase isotropic metasurface under x-polarized light incidence; (b) simulation of scattering from a discrete random-phase isotropic metasurface under x-polarized light incidence; (c) simulation of scattering from a continuous random-phase isotropic metasurface under the incidence of unpolarized light; (d) simulation of scattering from an anisotropic metasurface under the incidence of unpolarized light

Fig. 6. High NA focusing and wide-field-of-view fluorescence imaging based on an engineered disordered metasurface^[37]. (a) High NA focusing; (b) wide-field-of-view fluorescence imaging

Fig. 7. Experimental setup and key information for high-security optical encryption based on disordered metasurface^[46]. (a) Experimental setup; (b) key information

Fig. 8. Application of wavefront control technology based on random phase metasurface. (a) Spectrally interleaved geometric phase metasurface containing two wavelength-dependent functions, i.e., diffuser at 600 nm and lens imaging at 820 nm^[74]; (b) long-range order distribution based on a freeform disordered metasurface^[67]; (c) transparent matte surfaces based on the asymmetric diffusion of white light^[75]; (d) schematic diagram of photonic spin Hall effect in the disordered magnetic metasurface^[76]; (e) spatial coherence structures manipulated by the disordered metasurface and propagation properties of generated beams^[77]; (f) all-Stokes polarization camera based on single-focus imaging using an array of disordered metasurfaces^[45]; (g) schematic diagram of the design of the metasurface with engineering noise and the polarization multiplexing hologram^[78]; (h) disorder-assisted real-momentum topological photonic crystal^[69]

Fig. 9. Different positional disorder models for the metasurface^[66]. (a) Periodic square array; (b) positional disorder parameter perturbed square array; (c) Matérn Ⅲ soft-core point process; (d) Matérn Ⅲ hard-core point process

Fig. 10. Nonlinear effects of positional disordered metasurfaces. (a) Disorder-induced phase transitions in the transmission of dielectric metasurfaces^[66]; (b) dielectric Huygens' metasurface diffusers with critical positional disorder^[81]

Fig. 11. Application of wavefront shaping to positional disordered metasurfaces. (a) Multiple wavefront shaping based on disordered gradient metasurfaces in the near field and far field^[83]; (b) schematic diagrams of the realization of an ultra-high angle selectively engineered disordered metasurface versus a far-field radiation pattern corresponding to small angular changes^[38]; (c) collective lattice resonance of metasurfaces with different types of disorder^[84]; (d) theoretical and experimental investigations on the correlation between topological disorder and strength of surface lattice resonance^[85]

Fig. 12. Structural color generation based on positional disordered metasurfaces. (a) Schematic diagram and colored images of disordered plasmonic system^[86]; (b) prediction of visual appearance of macroscopic objects covered by disordered metasurfaces^[91]; (c) physical concept and design of disordered metasurfaces composed of sub-micronic holes^[92]