Fig. 1. The structures of carpet cloaking. (a) Schematic of full-space cloaking; (b) Schematic of carpet cloaking ^[40]; (c) The carpet cloaking is designed in a SOI wafer consisting of silicon and silica layers,where C1 is the gradient index cloaking and C2 is a uniform index background ^[41]; (d) The carpet cloaking designed from non-resonant metamaterial cells (left subfigure) and the relationship between unit cell geometry and effective index (right subfigure) ^[42]; (e) Scanning electron microscope images of the carpet cloaking designed from silicon nanopillars distributed in SOI wafers (top subfigure) and different densities of silicon pillars etched on SOI wafers (bottom subfigure) ^[40]; (f) Schematic diagram of the three-dimensional microwave carpet cloaking ^[43]; (g) Blueprint of the 3D carpet cloaking structure,with the 3D cone of light shown in red corresponding to the NA = 0.5 microscope lens ^[44]; (h) The triangular carpet cloaking is made of two calcite prisms glued together ^[45]; (i) Cross-sectional schematic of the cloaking implemented in a silicon nitride waveguide on a low-index nanoporous silicon oxide substrate ^[46]; (j) Experimental sample of a non-magnetic smart metamaterial invisibility cloaking,and the inset shows the effective dielectric constant curve versus Jacobian value ^[47]; (k) A planar electromagnetic wave at 1 GHz frequency passes through the carpet cloaking designed from Zn-Ni-Fe composites (blue) and air (white),surrounded by a background of polytetrafluoroethylene ^[48]; (l) Photographs of the 3D non-Euclidean metasurface carpet cloaking,with insets showing details of the closed metallic rings ^[49]; (m) Photograph of the full-polarization trapezoid conformal-skin cloaking sample,with the inset illustrating the phase profile along the central x-axis ^[50]; (n) Photographs of a sample of the carpet cloaking designed from cured resin cells (left subfigure) and a sample of cured resin cells (right subfigure) ^[51]

Fig. 2. Schematic diagram of TO and TO-based cloaking. (a) Relationship between reference space (left subfigure) and real space (right subfigure) in TO ^[1]; (b) Sphere cross-section of the spherical-shell cloaking ^[1]; (c) Microwave cloaking structure designed by split-ring resonators ^[74]; (d) For the cylindrical cloaking structure with λ = 623.8 nm,the right subfigure shows a small fraction of the cylindrical cloaking,i.e.,the nanowires are all perpendicular to the cylinder’s inner and outer interfaces ^[75]; (e) Concentric layer cloaking structure with alternating layers of medium A (blue) and B (grey) ^[76]; (f) Schematic of infrared cloaking structure sector based on split-ring resonators ^[77]; (g) Photograph of the cloaking structure realized by copper split-ring resonators embedded in a dielectric medium ^[78]; (h) Photograph of the cloaking structure realized by split-ring resonators and metal strips ^[79]; (i) Diagram of the experimental setup for testing cloaking performance: a cat sits in the cloaking structure,and a projector projects a film through the cloaking device onto a screen behind the cloaking device,and parts of the cloaking device can be seen without shadows ^[80]; (j) Diagram of the experimental setup used for infrared cloaking ^[81]; (k) Schematic of multiple antenna environment and the proposed method to coupling reduction (top left subfigure),with antenna 1 radiating in free space (top right subfigure),and antenna 1 radiating in the presence of a cylindrical antenna (antenna 2) (bottom left subfigure),with antenna 2 being covered by a designed cloaking structure (bottom right subfigure) ^[82]; (l) Schematic diagram of an effective simplified cubic cloaking structure in three orthogonal directions in three-dimensional space ^[83]; (m) Diagram of the experimental sample with several copper bars and two aluminum plates ^[84]; (n) Omnidirectional metamaterial cloaking structure and its metamaterial cell design ^[85]; (o) Refractive index distribution of the full-space omnidirectional cloaking structure designed with metal plates and dielectrics ^[86]; (p) Schematic of the cloaking structure with sub-wavelength dielectric channels to achieve a refractive index gradient from 1 to 10,and a uniform dielectric core surrounded by metal plates ^[87]; (q) Schematic diagram of the metamaterial cloaking structure for omnidirectional cloaking ^[88]; (r) Diagram of the experimental sample of a multi-band cloaking structure with metal sheets and two types of dielectrics ^[89]; (s) The two left subfigures show photographs of fabricated four-layer space-compressed TO metamaterial samples,and the right subfigure shows a schematic view of the ideal cloaking based on the designed full-parameter spatial-compression TO metamaterial and the Fabry-Pérot layer ^[90]

Fig. 3. Schematic of the OCM-based cloaking. (a) Propagation of light in the cloaking device,yellow line is the light,the brightness of the green background indicates the refractive index contour,and the invisible region is shown in black ^[91]; (b) Refractive index profile of the cloaking structure that can be used in electro-acoustic double fields ^[92]; (c) Simulation results of two different incident TE polarized waves on two different mapping cloaking structures ^[93]; (d) Optimized refractive index profile (left subfigure) and electric field distribution pattern (right subfigure) based on logarithmic conformal transformation ^[94]; (e) The left subfigure shows the refractive index profile and the ray trajectory of the cloaking structure based on the non-Euclidean transformation,and the right subfigure shows the electric field distribution generated by a Gaussian beam with an incidence angle of π/4 rad on the cloaking structure ^[95]; (f) In three dimensions,some rays turn out to perform two loops in hyperspace that appear in physical space as light wrapped around the invisible interior ^[96]; (g) Invisibility effect with Eaton lens: An Eaton lens is placed in the lower sheet to guide back the incident light,giving the outer region the invisibility effect represented by a black hole. The left and right subfigures show the electric field distributions corresponding to the l = 2 and 40 orders harmonic eigenmodes of the Eaton lens,respectively^[97]; (h) Bidirectional cloaking performance simulation,the boundary of the white area represents the reflector ^[98]

Fig. 4. Schematic of the cloaking based on geometrical optics. (a) Schematic diagrams of the cloaking with two L-shaped water tanks and two L-shaped mirrors on the left and right,respectively ^[101]; (b) Demonstration of the principle of quasi-axial invisibility using four optical lenses ^[102]; (c) The cloaking consists of polarizers and mirrors that are attached on glass plates ^[103]; (d) 2D digital integral cloaking setup ^[104]

Fig. 5. Schematic of the cloaking structures based on plasmonic shells. (a) The geometry of the double-shell cloaking structure depicted in the inset,and the four curves in the figure represent the total scattering efficiency for each of the four cases ^[109]; (b) Schematic of a silicon nanowire (grey) hooked up by two gold electrodes (yellow) ^[32]; (c) Photographs of the assembled cloaking structure on the test cylinder with end caps (top subfigure); cross-section of the assembly with the end caps removed (bottom left subfigure); a shell segment edge with copper tape used to form the metallic strip for the metamaterial cloaking (bottom right subfigure) ^[110]; (d) The left subfigure represents a dielectric object reveals its presence to an external observer by scattering the light. The diagram on the right indicates that a shell made from metallic nanoparticles scatters the same amount of light as the core but π out-of-phase. This suppresses the scattered field. It therefore makes the object undetectable ^[111]; (e) Schematic representation of an infinitely long non-magnetic cylinder with dielectric constant ε_c and radius a,coated with a magneto-optical active cylindrical shell with magnetic permeability μ₀ and radius b>a^[112]; (f) Schematic representation of a dielectric sphere with complex dielectric constant wrapped in a graphene shell ^[113]; (g) The dielectric sphere is covered with silver ellipsoids of different distributions and orientations ^[114]; (h) Illustration of the atomically thin graphene layer of surface conductivity σ coating a nano-sized scattering cylinder of relative permittivity ε_d,where the environment medium has a permittivity ε^[115]; (i) Schematic illustration of the difference in light scattering between 3D bare nanospheres (left subfigure) and spheres coated with AuNPs (right subfigure) ^[116]; (j) Schematic representation of zirconium nitride (ZrN) core-shell nanowires under oblique incidence ^[117]

Fig. 6. Schematic diagram of cloaking based artifical structural materials. (a) Examples of patterned metallic geometries that may realize a mantle cloaking^[119]; (b) Diagram of the graphene metasurface ^[122]; (c) The mesh-grid FSS geometry ^[122]; (d) Schematic diagram of a dual-band cylindrical mantle cloaking^[129]; (e) Schematic of a general multilayer infinitely long cylindrical structure ^[36]; (f) The top subfigure shows the schematic diagram of the different layers of the mantle cloaking patch antenna,and the bottom subfigure shows the three-dimensional view of two co-frequency interleaved cloaking arrays ^[127]

Fig. 7. Schematic diagram of invisible sensors. (a) Basic principle of invisible sensors ^[29]; (b) Plasmonic shell used to achieve the cloaking effect simulation of the near-field scanning optical scanning microscope probe ^[31]; (c) Photographs of silicon nanowires surrounded by wrapped gold coating (covered) and silicon nanowires alone (bare) under confocal microscope ^[32]; (d) The left subfigure shows two antennas without the cloaking structure,and the right subfigure shows a scatter-cancelling cloaking structure around one antenna ^[34]; (e) Schematic (left subfigure) and physical photograph (right subfigure) of the simultaneous cloaking of two antennas using a metasurface ^[35]; (f) Photogragh of broadband cloaking of a dipole antenna using a metasurface ^[36]; (g) Cloak of a scanning microscope probe using a scatter-cancelling cloaking mechanism: a conventional probe (top subfigure) and a probe with the introduction of slotted microstructures (bottom subfigure) ^[37]

Fig. 8. Schematic diagram of cloaking structures based on optimization algorithm with experimental verification. (a) Sample view of the six-layer cylindrical cloaking structure and the calculated scattered electrical energy distribution around the bare PEC core and the PEC with the cloaking (yellow ringed area) ^[170]; (b) "Eyelid"-shaped cloaking made of Teflon (white) with the central cloaking region replaced by an aluminum disk ^[138]; (c) Photograph of a sample cloaking structure made of acrylonitrile-butadiene-styrene ^[176]; (d) Schematic of a cloaking structure made of dielectric PLA dielectric square columns ^[171]; (e) Photograph of a sample invisibility cloaking structure made using conventional printed circuit board technology ^[195]; (f) Transmissive metasurface cloaking consisting of two planar metasurfaces labelled Layer 1 and Layer 2 used to hide an internal object,e.g. a cat ^[196]

Table 1. Main differences between full-space and carpet cloaking structures

Table 2. Research history of carpet cloaking with experimental validation

Table 3. Structures of TO-based light-bypassing cloaking

Table 4. Structures of OCM-based light-bypassing cloaking

Table 5. Structures of light-bypassing cloaking based on geometrical optics

Table 6. Structural characteristics and limitations of light bypassing cloaking with different methods

Table 7. Scatter-cancelling cloaking implemented based on plasmonic shells

Table 8. Scatter-cancelling cloaking based on artifical structural materials

Table 9. Structural characteristics and limitations of scatter-cancelling cloaking based on different materials

Table 10. Research progress on invisible sensors

Table 11. Cloaking structures with experimentally verified design based on optimization algorithm