Abstract
Electromagnetic metasurface cloaks provide an alternative paradigm toward rendering arbitrarily shaped scatterers invisible. Most transformationoptics (TO) cloaks intrinsically need wavelengthscale volume/thickness, such that the incoming waves could have enough long paths to interact with structured metaatoms in the cloak region and consequently restore the wavefront. Other challenges of TO cloaks include the polarizationdependent operation to avoid singular parameters of composite cloaking materials and limitations of canonical geometries, e.g., circular, elliptical, trapezoidal, and triangular shapes. Here, we report for the first time a conformalskin metasurface carpet cloak, enabling to work under arbitrary states of polarization (SOP) at Poincaré sphere for the incident light and arbitrary conformal platform of the object to be cloaked. By exploiting the foundry threedimensional (3D) printing techniques to fabricate judiciously designed metaatoms on the external surface of a conformal object, the spatial distributions of intensity and polarization of its scattered lights can be reconstructed exactly the same as if the scattering wavefront were deflected from a flat ground at any SOP, concealing targets under polarizationscanning detections. Two conformalskin carpet cloaks working for partial and fullazimuth plane operation are respectively fabricated on trapezoid and pyramid platforms via 3D printing. Experimental results are in good agreement with numerical simulations and both demonstrate the polarizationinsensitive cloaking within a desirable bandwidth. Our approach paves a deterministic and robust step forward to the realization of interfacial, freeform, and fullpolarization cloaking for a realistic arbitraryshape target in realworld applications.
Introduction
The research in electromagnetic invisibility has been long pursued and flourished particularly, thanks to the recent developments of metamaterials^{1}. One approach is to use transformation optics^{2,3}, which essentially consists of designing metamaterials to redirect electromagnetic (EM) waves to flow around a target and thereby renders the target fully invisible. However, this requires to realize complex and even singular constitutive parameters of extreme anisotropy (both electric and magnetic) and inhomogeneity^{4,5,6,7,8}, which is very challenging in practice. Another method is the scattering cancelation with plasmonic metamaterials^{9,10,11,12} and transmissionline coupled network^{13}, requiring sophisticated pairings of each layer to compensate the scattering. Moreover, those devices are usually bulky and not easy to scale up, especially at high frequencies. Recently emerged metasurfaces, a twodimensional equivalent counterpart of metamaterials, have provided unprecedented capacities to control the amplitude, phase, and polarization of scattering EM waves of a target, which is easy for fabrications and facilitates many fascinating applications^{14,15,16,17,18,19,20,21,22,23,24,25,26}. The metasurfaceenabled cloaking has also been proposed and experimentally achieved recently^{27,28,29,30,31,32,33,34,35}. Therein, by wrapping targets with an elaborately designed metasurface, the reflective phase and amplitude of targets can be engineered to mimic specular reflections at a flat mirror as if the object did not exist. With this strategy, both tunable^{36} and intelligent^{37} cloaks were also developed, further advancing the applicative prospect of metasurfaces for cloaking applications.
Nevertheless, all existing metasurface cloaks are limited to a single or few states of polarization (SOP), being vulnerable if the scatterer introduces complex polarizationconversion scattering or if polarizationscanning signals are used in the detection system. Thereafter, achieving a deterministic conformalskin fullpolarization cloaking is in high demand and yet formidably challenging so far. The difficulties are manifolds. First, a designed artificial metaatom may exclusively generate dynamic phases for cloaking at a specific SOP, but it would be not likely to perform under another SOP. Second, isotropic metaatoms (e.g., those with structural rotation symmetry higher than C_{3}) have been utilized to demonstrate the fullpolarization cloaking, simply because they essentially do not distinguish SOP only under a few linear polarization (LP) states^{30,31}. However, the realization of a perfect cloaking interface not only requires the ultimate control on the intensity and wavefront, but also needs to preserve the polarization state of the incident light. For circularly polarized (CP) incident beams, the cloaking effect of the above isotropic strategy would be much diminished at its copolarization component (see Supplementary Section 6). Third, an angleindependent amplitude and phase response is particularly essential for a cloak with arbitrary boundary. The design based on an anisotropic coLP scheme is far insufficient to preserve the EM response as the symmetry would be broken under oblique largeangle incidences, leading to angledistinguished responses. As of today, the realization of fully polarized cloaking at Poincaré sphere remains elusive, letting alone that such cloak is even conformal and ultrathin.
Here, we report a ubiquitous approach to obtain conformalskin cloaking for full canonical polarization states described by Poincaré sphere in a halfspace reflection scheme (Fig. 1a) with tailored metaatoms incorporating both dynamic and geometric phases for realworld stealth applications. Importantly, note that the valid cloaking effect for full SOP here does not include the condition of natural light or partially polarized light. Specifically, the wave after impinging onto our metasurface cloak is always precisely deflected to predicted specular reflection directions as if it is grounded by a mirror (Fig. 1b), regardless of incident SOP at any arbitrary point of Poincare spheres (Fig. 1c). The important foundation of fullpolarization cloaking is based on synthesizing identical dualphase patterns in two spindecoupled channels of an anisotropic conformalskin metasurface. Our recipe synergizes the crossLP dynamic and geometric phases based on the sophisticated spindecoupling theory, which serves as the only option to preserve the output polarization state of our proposed skin metasurface cloak, in both LP and CP modes. It completely addresses the tricky issue of partial polarization insensitivity of existing cloaks under few LP states based on isotropic metaatoms. It also completely distinguishes it from other polarizationinsensitive devices based on anisotropic coLP geometric phase^{38,39,40}, where an optimization process is necessary to acquire the delicate polarization insensitivity. Moreover, the threedimensional (3D) cloak is realized by combining a conformal metasurface^{41,42,43,44} and a 3Dprinting technique^{45}, readily extendable to arbitrary complex structures and platforms. This is especially true for the theoretical framework of “conformal boundary optics”, which is very essential to guide conformal design in arbitrary geometries^{43,44}. We believe that our approach offers the deterministic polarizationindependent cloaking for generally conformal objects with costeffective fabrications of the skin metasurface and robustness in angle tolerance, which is of great importance for realworld applications.
Results
Principle of conformalskin cloak for full canonical polarization
Without the loss of generality, we start by cloaking a black metallic bump with an arbitrary boundary described by f(x, y). The purpose of a conformalskin metasurface cloak is to achieve scattering properties, leading to specular reflection at a ground plane modeled by the contour g(x, y), as shown in Fig. 1b. By applying raytracing techniques, the required compensated phase pattern δ targeted at specific polarization \(\left \sigma \right\rangle\) and wavelength λ_{0} can be theoretically calculated as^{29}
Here, k_{0} = 2π/λ_{0} is a freespace wavevector, θ is the wave incidence angle with respect to the ground, and \(\left \sigma \right\rangle\) denotes the SOP of the incident beam, which can be found in Poincare spheres, in the form of Jones’ vectors. Note, for simplicity, we also define that \(\left\langle {\sigma ^ \bot \left \sigma \right.} \right\rangle = 0\) where \(\langle\left. {\sigma ^ \bot } \right\) is its cross (orthogonal) polarization. For the sake of clarity, we explicitly define several SOPs here, which are LP with the electric field along x (\(\left {\sigma _x} \right\rangle = \left[ {1,0} \right]^{\mathrm{T}}\)), along y (\(\left {\sigma _y} \right\rangle = \left[ {0,1} \right]^{\mathrm{T}}\)), and along the intersection of x and y axes (\(\left {\sigma _{\pi /4}} \right\rangle = \left[ {1,0} \right]^{\mathrm{T}}\)), as well as CP for righthanded CP (RCP, \(\left {\sigma _ + } \right\rangle = \left[ {1/\sqrt 2 ,j/\sqrt 2 } \right]^{\mathrm{T}}\)) and lefthanded CP (LCP, \(\left {\sigma _  } \right\rangle = \left[ {1/\sqrt 2 ,  j/\sqrt 2 } \right]^{\mathrm{T}}\)). In general, the function g(x, y) can be set to mimic a fictitious target as an illusion cloak for a particular SOP, but for our proofofconcept demonstrations, we use a constant value to mimic a horizontal ground as carpet cloaking. In the following, we propose the design of a metasurface to provide a wavefront predicted in Eq. (1). Note that the current state of the art in metasurfaces exploits either dynamic or geometric phases to precisely implement the target phase. However, the reflective dynamicphase discontinuity, described by a Jones matrix \(R = \left(\begin{array}{ll}r_{xx}e^{j\varphi _{xx}} & r_{xy}e^{j\varphi _{xy}}\\ r_{yx}e^{j\varphi _{yx}}&r_{yy}e^{j\varphi _{yy}}\end{array} \right)\) under the Cartesian coordinate, is commonly associated with the resonant feature of a metaatom reacting to specific SOP and incident angle. Here, φ_{xx} (r_{xx}) and φ_{yx} (r_{yx}) denote the reflective phase (amplitude) of \(\left {\sigma _x} \right\rangle\) and \(\left {\sigma _y} \right\rangle\) components under excitation of \(\left {\sigma _x} \right\rangle\) (the same nomenclature to other parameters). Minimal change of SOP will induce large or complete phase distortions, thus deteriorating the final performance. This makes the fullpolarization cloak an extremely difficult problem.
In addition, polarization preservation is another concern of anisotropic coLP system. Synergizing geometric phase (orientation rotation α) and dynamic phase (parametric variation) in an anisotropic coLP geometry (\(r_{xy}\) = \(r_{yx}\) = 0, \(r_{yy} = r_{xx} = 1\) and \(\varphi _{yy}  \varphi _{xx} = 180^\circ\))^{46,47,48} has been successfully implemented for complete distinct phases at two CP states in terms of \(R^{{\mathrm{CP}}}\left(\alpha \right) = \left(\begin{array}{cc}e^{j\left({\varphi _{xx}  2\alpha }\right)}& 0\\ 0 & e^{j\left({\varphi _{xx} + 2\alpha } \right)}\end{array} \right) =\left(\begin{array}{cc}r_{\left {\sigma _+ } \right.\rangle }{e^{j\delta _{\left {\sigma _+ } \right.\rangle} }} & 0 \\ 0 & r_{\left {\sigma _ } \right.\rangle }{e^{j\delta_{\left {\sigma _ } \right.\rangle}}}\end{array} \right)\)_{.} However, it is impossible to achieve fullpolarization cloaking because the polarization in LP operations cannot be preserved, see Supplementary Section 6. Our proposition, instead, exploits crossLP dynamic^{19,49} and geometric phases to preserve the output polarization of the conformalskin cloak in both LP and CP states. Hence, we hereafter adopt a crossLP scheme (\(r_{xx}\) = \(r_{yy}\) = 0) to decouple phases and functions under \(\left {{\upsigma}_ + } \right\rangle\) and \(\left {{\upsigma}_  } \right\rangle\) wave (see the generalized theory for both coLP and crossLP system in Supplementary Section 1). The Jones’ matrix after a rotation of α is formulated as \(R^{{\mathrm{LP}}}\left(\alpha \right) = S^{  1}\left(\alpha \right) \cdot R \cdot S\left(\alpha \right)\) on LP basis, where \(S\left(\alpha \right)\) is a standard rotation matrix. This Jones matrix can be easily transformed to CP basis, given by the relation of \(R^{{\mathrm{CP}}}\left(\alpha \right) = {{\Lambda }}^{  1} \cdot R\left(\alpha \right) \cdot {{\Lambda }}\), with \({{\Lambda }} = 1/\sqrt 2 \left[ {\begin{array}{*{20}{c}} 1 & 1 \\ {  j} & j \end{array}} \right]\). Assuming that crossLP condition \(r_{xy} = r_{yx} = 1\) and \(\varphi _{xy} = \varphi _{yx}\), we immediately achieve \(R^{{\mathrm{CP}}}\left(\alpha \right) = \left(\begin{array}{cc}r_{xy}e^{j\left({\varphi _{xy}  2\alpha + \pi /2} \right)}& 0 \\ 0 & r_{xy}e^{j\left({\varphi _{xy} + 2\alpha  \pi /2} \right)}\end{array} \right) = \left(\begin{array}{cc}r_{\left {\sigma _+ } \right.\rangle }e^{j\delta_{\left {\sigma _+ } \right.\rangle }} & 0\\ 0 & r_{\left {\sigma _ } \right.\rangle }e^{j\delta _{\left {\sigma _ } \right.\rangle}}\end{array} \right)\). This shows that involving both geometric (\(e^{  2aj}\)) and dynamic phase (\(\varphi _{xy}\)) completely decouples the copolarized component of \(\delta _{\left {\sigma _ + } \right\rangle }\) and \(\delta _{\left {\sigma_  } \right\rangle }\). Moreover, it also indicates that crossLP conversion properties of a metaatom determine the efficiency of the entire cloak.
Theoretically, if we simultaneously impart two independent cloakingphase patterns (\(\delta _{\left {\sigma _ + } \right\rangle }\) and \(\delta _{\left {\sigma _  } \right\rangle }\)), the cloak is expected to operate at any SOP in Poincare spheres. The underlying reason is that any incident polarization state can be described by the superposition of two opposite CP states, i.e., \(\left \sigma \right.\rangle = \chi _ + \left {\sigma _ + } \right.\rangle + \chi _  \left {\sigma _  } \right.\rangle\) with χ_{+} and χ_{−} representing the different proportionality coefficients. By comparing the above matrix \(R^{{\mathrm{CP}}}\left(\alpha \right)\) on two sides, we can obtain two equations: \(\delta _{\left {\sigma _ + } \right\rangle } = \varphi _{xy}  2\alpha + \pi /2\) and \(\delta _{\left {\sigma _  } \right\rangle } = \varphi _{xy} + 2\alpha  \pi /2\). Then the required dynamic crossLPphase patterns \(\varphi _{xy}\) and geometricphase patterns \(\varphi _g = 2\alpha\) to achieve simultaneous invisibility at \(\left {{\upsigma}_ + } \right\rangle\) and \(\left {{\upsigma}_  } \right\rangle\) states are synthesized as
Design of fullpolarization conformalskin cloak
Taking this general principle into consideration, an anisotropic building block is devised to realize \(r_{xy}\) = \(r_{yx}\) = 1 and \(\varphi _{xy} = \varphi _{yx}\) and the aforementioned decoupled phase patterns in Eq. (2). We performed the fullwave numerical simulation of a metaatom using the finitedifference timedomain (FDTD) method. As illustrated in Fig. 2a, the basic block (i.e., the metaatom) utilized for our metasurface cloak can be produced using 3Dprinting technique. It consists of an anisotropic metal–insulator–metal reflective metaatom composed of an ABSM30 plate sandwiched by top quasiIshaped metallic patterns and bottomflat ground etched on two thin flexible substrate boards. We utilize the top circular Ishape resonator oriented along α = 45^{o} to break the symmetry along x and y axes and thus to generate two chiralityassisted characteristic modes (\(A_\parallel\) and \(A_ \bot\)), with major electricfield distribution parallel and perpendicular to principal axis under SOP of \(\left {\sigma _x} \right\rangle\) and \(\left {\sigma _y} \right\rangle\), which can be evidenced by two crossLP \(r_{xy}\) peaks shown in Fig. 2b. These two interelement modes can be judiciously employed and cascaded to engineer a broadband highefficiency crossLP system. Moreover, we change the openangle β to adjust the dynamic phase \(\varphi _{xy}\). As shown in Fig. 2b and Supplementary Fig. S1, the metaatom with α = 45° and β = 10° exhibits a broadband high crossLP rate (\(r_{xy}\) > 0.85) across 8.4–18.9 GHz (a fractional bandwidth of 77%) under θ = 0^{o}. By changing β from 10 to 130°, a continuous phase change of \(\varphi _{xy}\) with a maximum of 180° is achieved across the above entire band. To satisfy a full 2π phase coverage, an additional 180° phase jump is introduced by changing α by 90° without altering \(r_{xy}\) significantly, see Supplementary Fig. S2. All the above results assist to construct the metaatom library for the final cloak design. More importantly, the phase response against the incidence angle θ is quite close at 14 and 15 GHz as depicted in Fig. 2c, which exhibits a maximum phase tolerance of 15° and 20° when θ alters from 0 to 45°. Such a quasiangleindependent phase response is particularly essential for a cloak with arbitrary boundaries, where the phase error induced by different incident angle θ can be minimized. Although slight fluctuation of \(r_{xy}\) is observed at θ = 45°, it is still above 0.85 for all β, which should pose negligible effect in preserving the amplitude of our cloak. The physics of angleinsensitive EM response that lies in the 45° orientation considerably reduces the nearfield coupling strength among adjacent metaatoms (identified from the significantly lowfield intensity at the edge of the metaatom), which contributes mostly to the frequency shift^{50}.
In the proofofconcept demonstrations, we choose a trapezoid platform to initialize our fullpolarization cloak design, while other geometries could also be implemented following our strategy. The metasurfaces are composed of a stacked composite of ABSM30 and a thin F4B metallic ground and are characterized by the width P, and crosssection tilt angle ψ and length L. Given the parameters of the trapezoid bump, the theoretically required dualphase patterns \(\delta _{\left {\sigma _ + } \right\rangle }\) and \(\delta _{\left {\sigma _ + } \right\rangle }\) and followed by the synthesized \(\varphi _{xy}\) and α can be readily achieved. Finally, the layout of our conformalskin cloak composed of spatially varying metaatoms can be mapped by selecting metaatoms from the library according to the target \(\varphi _{xy}\) (β) and α distributions through a program code automatically performed CST Microwave Studio, see the CAD process in “Methods”. Two conformalskin cloaks on 3D trapezoid and pyramid platform are reported with their invisibility property characterized in both nearfield (NF) and farfield (FF) results under different excitation scenarios.
Conformalskin cloak on a 3D trapezoid platform
We first design a conformalskin cloak targeted at 15 GHz on a 3D trapezoid platform, which is characterized by ψ = 22.5°, top/bottom length L_{1} = 143/L_{2} = 387 mm, and height H = 50.5 mm in the tripleside cross section. Figure 3a and Supplementary Fig. S3 show the layout and parametric illustration of our designed cloak wrapped over a trapezoid metallic bump, according to the theoretically calculated phase profile shown in the inset of Fig. 3a. As indicated, our cloak is assembled by triple submetasurfaces with both spatially varied β and α for each metaatom. The spatially varied α with α = 0 and 90^{o} plays a key role as it guarantees the CP polarization insensitivity. The underlying physics is that the phase response of the above specific metaatoms with 0 and 90^{o} orientation under \(\left {\sigma _ + } \right\rangle\) and \(\left {\sigma _  } \right\rangle\) state is the same in terms of equal values of e^{i2α} and e^{−i2α}. Such feature guarantees to preserve both output copolarized phase and amplitude of all metaatoms across the cloak for all SOP in terms of synergizing crossLP dynamic phase through varying β and geometric phase by altering α, which distinguishes our design from any existing metasurface cloak^{29,30,31,32,33,34,35,36,37}. In numerical and experimental characterizations, the bare and cloaked bump are normally illuminated by \(\left {\sigma _x} \right\rangle\), \(\left {\sigma _y} \right\rangle\), \(\left {\sigma _{\pi /4}} \right\rangle\), \(\left {\sigma _ + } \right\rangle\), and \(\left {\sigma _  } \right\rangle\) plane wave incident on xz plane. Here, the polarization angle (\(\phi\)) of an LP light can be arbitrarily engineered by changing the azimuthal illumination angle/rotating the cloak about the vertical axis. Figure 3b–f plots the experimentally measured NF Efield patterns for both bare and cloaked bump at 15.5 GHz by scanning an area of 0.3 × 0.3 m^{2} on xz plane. All NF results are in good consistency with numerical simulations under \(\left {\sigma _x} \right\rangle\), \(\left {\sigma _y} \right\rangle\), \(\left {\sigma _ + } \right\rangle\), and \(\left {\sigma _  } \right\rangle\) planewave illumination (Fig. 1c), except that the center operation frequency has slightly shifted from 15 to 15.5 GHz in the implementation, see NF patterns at other frequencies of a shifted bandwidth in Supplementary Section 3. As expected, Fig. 3b presents the distortion and splitting of light into various directions after reflecting from for a bare bump. In sharp contrast, the signal reflected from our metasurfacecovered bump presents an almost flat and reconstructed wavefront with uniform intensity for all incident polarizations (Fig. 3c–f). With respect to the results presented in ref. ^{29}, where the object is perfectly hidden for \(\left {\sigma _x} \right\rangle\) but completely visible by switching polarization, our approach works for both polarizations and exhibits a desirable operation bandwidth of 2.5/3 GHz (experiment/FDTD) within 14.5–17/14–17 GHz, corresponding to a fractional bandwidth of 16.7/20% (see Supplementary Figs. S4–S6 for more numerical and experimental NF and FF results at other frequencies). Such a level of bandwidth is very remarkable relative to the existing metasurface cloaks^{29,30,31,32,33,34,35,36,37}.
The demonstrated mirror reflections indicated by NF results can be further verified from the highly directive singlemode FF specular scattering patterns shown in Fig. 3g, where an excellent agreement is observed between numerical calculation and experimental data. The slightly larger fluctuations of sidelobes and wider width of the main beam in the latter case are attributed to the nonideal plane wave excitation and insufficient directivity of the horn excitation antenna. Nevertheless, when the metasurface cloak is removed, both NF and FF results turn out to be substantially distorted with triplescattering modes directing backward, −45° and 45°, revealing a mirror function of three sides of the trapezoid bare bump. The sharp scattered specular beam with other scattering modes at oblique angles completely suppressed indicates high invisible performance.
Conformalskin cloak on a 3D pyramid platform
The above fullpolarization conformalskin cloak on a 3D trapezoid platform can be further extended to a 3D pyramid platform with the fullazimuthal plane operation. For this purpose, we assembled a cloak composed of five submetasurfaces on a square pyramid with ψ = 22.5°, H = 44.5 mm, and L_{1} = 66/L_{2} = 280.9 mm according to the theoretically calculated phase patterns \(\delta _{\left {\sigma _ + } \right\rangle }\) = \(\delta _{\left {\sigma _  } \right\rangle }\), see Fig. 4a, Fig. 5a, and Supplementary Fig. S7. The theoretically calculated phase profile is symmetric with respect to the center x and y axes. All metaatoms disposed on the top and side tilted faces are constructed automatically in CST Microwave Studio relying on a rigorous calculation of spatial coordinates at each position. Since both dynamic and geometric phases are involved, the metaatoms in two xorientated tilt faces should be deliberately arranged orthogonally, point by point, to those in two yorientated tilt faces aiming to compensate the phase difference induced by spatial variation. To comprehensively evaluate the performances, NF and FF results are recorded in both principal xz and yz planes under five representative polarization states of normally incident plane EM waves. Elegant cloaking performance can be also expected at other azimuthal planes, except for the above two principal planes.
As shown in Fig. 4b–f, we observe desirable flat wavefronts reflected in both planes with almost uniform strength after impinging on the cloak under all inspected SOP. Minor distortions of NF patterns, especially for the unexpected interference, are partially attributed to the nonideal infinite boundary in 3D simulation, which takes lot of computation resources in calculating a largevolume cloak. They are partially induced by the nonuniform scattering amplitudes of those metaatoms at top and fourside surfaces since they are considered to be positioned at different angles with respect to the given illumination. It can be explained in Fig. 2c that the scattering amplitudes will slightly vary under different incident angles. Fortunately, such minimal fluctuation does not pose many penalties on the invisibility, which can be further verified from FF scattering patterns. Wellpreserved specular reflections are observed for all SOP and planes. As shown in Fig. 5b, the fanshape wavefront is clearly observed for the bare bump. However, it is completely flattened on both planes when wrapping the bump with our conformalskin metasurface cloak (Fig. 5c–f). More importantly, such desirable wavefront is achieved under four representative polarization states of \(\left {\sigma _x} \right\rangle\), \(\left {\sigma _y} \right\rangle\), \(\left {\sigma _ + } \right\rangle\), and \(\left {\sigma _  } \right\rangle\). The cloaking performances at other frequencies are also numerically and experimentally evaluated, see Supplementary Figs. S8, S9 for numerical NF patterns, Figs. S10–S13 for measured NF patterns, and Fig. S14 for comparison of farfield scattering patterns between numerical calculations and experimental measurements. The pyramid cloak exhibits almost the same working bandwidth (~20%) relative to its trapezoid counterpart, but circumvents the formidable issue of fullazimuthal operation.
Finally, we also evaluated the cloaking performance of our pyramid cloak at oblique incidence by illuminating the sample with light incident along θ = −20° and θ = −30° on xz and yz plane. As shown in Supplementary Fig. S15, the pyramid cloak preserves its mirrorlike farfield scattering patterns for θ = −20° and θ = −30° at four representative frequencies with negligible sidelobes. Degraded cloaking performances occur at large θ, in terms of large sidelobes, wider beam, and reduced bandwidth. This is especially true for the FF scattering pattern obtained at 14.5 GHz and θ = −30°. It should be strengthened that the cloaking performance is inevitably weakened for oblique incidence and offf_{0} operation since the cloak was originally designed at f_{0} for normal incidence according to Eq. (1). Nevertheless, due to the angleimmune and broadband scattering intensity and phase of metaatoms with alternatively changed α = 0° and 90° (small interelement coupling) and the small height of the cloak, all results indicate an elegant angleadaptive cloaking behavior within a bandwidth of 2.5 and 2 GHz for θ = −20° and θ = −30°, respectively. However, for larger incident angles, the cloaking performance would be sharply exasperated due to the magnified phase tolerance and a renewed specific design is necessary. More importantly, our pyramid cloak indeed enables a real 3D operation (fullazimuth operation) under arbitrary azimuthalangle nonsymmetric illumination, see Supplementary Fig. S16, where again similar mirror reflection is clearly inspected under two scenarios of EM wave excitation with \(\phi = 30\)° and θ = 10°, and \(\phi = 40\)° and θ = 20°. Since our conformalskin cloak is ultrathin, the lateral shift of the reflected beams observed in bulk cloaks is automatically diminished.
Discussion
We have proposed and experimentally verified a deterministic strategy of invisible cloaking via a conformalskin metasurface cloak for full polarization described by Poincaré spheres. The challenging polarizationindependent operation is theoretically guaranteed by imposing two sets of cloaking phases on two decoupled orthogonal spins. We have devised two sophisticated trapezoid conformalskin cloaks combining 3D printing and flexible PCB technique. Our proposed method is capable of preserving predesigned scattering signatures (amplitude and phase) across an elegant bandwidth under fully polarized light. Moreover, the constraints of impedance mismatching and lateral shift of reflected beams in existing invisibility cloaks are also mitigated. In principle, there is no cloaking shape and size limitation endowed by the 3Dprinting fabrication. Although the height of our designed prototype cloak is 2.5 λ_{0} tall, further FDTD results indicate that it can be considerably increased provided that the slope angle of the platform ψ < 90°, posing no theoretical limitation on the size of the cloaking region. Furthermore, we have designed two metasurface cloaks in both crossLP and coLP systems based on the available dynamicphase approach, see Supplementary Figs. S17 and S18. The results unanimously confirm that these cloaks cannot preserve polarizations upon either LP or CPstate operations. Table 1 summarizes the feature of some of the experimentally reported metasurface cloaks. To the best of our knowledge, our metasurface cloak with ultrathin thickness of only ~λ_{0}/200, the bandwidth of 20%, and fullazimuth operation, presents the best performance among available passive cloaks. Our paradigm opens up an unprecedented avenue to ultrathin and robust cloaking of arbitraryshape 3D objects, advancing a meaningful step toward realistic applications.
Materials and methods
Numerical characterizations
All numerical designs and FDTD characterizations are performed through the numerical simulation package CST Microwave Studio. Specifically, in calculations of the reflection amplitudes/phases of the metaatom, especially in generating the reflection response database, we impose periodic boundary conditions at its four bounds, and with a Floquet port placed at a distance 15 mm away from the metaatom plane in the frequencydomain solver of the commercial software. In NF and FF numerical characterizations of the polarizationsensitive and fullpolarization triangle, trapezoid, and pyramid cloaks, metasurfaces composed of 30 × 1 and 48 × 1 spatially varied metaatoms along two slopes are utilized in timedomain solver with periodic boundary condition assigned to y sides to reduce the calculation volume, while four open boundaries set along x and z axes. In fullwave FDTD evaluations of the cloaking performance, all boundaries of the square pyramid are arranged as open conditions.
Sample preparing and fabrication
The cloak sample is prepared based on a fourstep dualsided fabrication process by combining 3Dprinting and PCB technique. The supporting trapezoid platform with specific tilt angle is prepared using 2.5mmthick 3Dprinting polymer material ABSM30 (dielectric constant ε_{r} = 2.7 and loss tangent tanδ = 0.005) through 3Dprinting technique, see Supplementary Fig. S17. The top and bottom metallic patterns and ground of our metasurface cloak are fabricated individually on two 0.1mmthick flexible F4B dielectric boards (ε_{r} = 2.65 and tanδ = 0.001) using the PCB technique. A CAD process is established, which can automatically construct all metallic patterns through program codes in a commercial software based on reflection response and position database of each metaatom. After all PCB boards and supporting platforms are ready, the next step is to align and attach each flexible board to two sides of the ABSM30 platform to form an entirety through adhesives. Finally, they are shaped and reinforced by clamps for several hours. Such an assembling process avoids metalizing the 3Dprinted substrates through thinfilm sputtering.
Microwave experiments
All farfield (FF) and nearfield (NF) experiments are performed in a microwave anechoic chamber to avoid possible interference from the environment, see the experimental setup shown in Supplementary Fig. S18. Two pairs of highly directive LP or CP antenna emitting Gaussian wave are utilized as receiver and transmitter. The doubleridged horn exhibiting a voltage standingwave ratio (VSWR) less than 2.5 within the frequency range 1–18 GHz is utilized as the LP antenna. By altering the orientation of the emitting antenna with respect to the fixed sample, a LP wave excitation can be readily realized with several representative polarization angles of 0, 30, 45, and 90^{o}. For CP wave excitation, the sample is illuminated by a horn with an axial ratio of less than 3.5 dB, and a voltage standingwave ratio of less than 2.5 within 8–18 GHz.
In all NF contour maps, a 10/15mmlong monopole, functioning as the receiver, is placed between the 1mdistanced sample and horn, and is connected to an AV3672B Agilent vector network analyzer to record the static EM signals. It is fixed to a 2D electronic step motor that can move automatically in a maximum area of 1.2 × 1.2 m with a step resolution of 5 mm. To guarantee the pure scattering signature, the incident signal in free space is deducted from the total fields. In the FF scattering pattern measurements, the cloak sample and the receive horn to record signals are fixed on a large rigid foam that is capable of rotating freely along the foam’s axial center. The transmitting horn is placed 6 m away to afford desired excitations.
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Acknowledgements
This work was supported by the National Defense Foundation of China (2019JCJQJJ081), the Youth Talent Lifting Project of the China Association for Science and Technology (17JCJQQT003), the Key Program of Natural Science Foundation of Shaanxi Province (2020JZ33), the Key Principal’s Fund of Air Force Engineering University (XNLX19030601), the National Key Research and Development Program of China (2017YFA0700202), and the National Natural Science Foundation of China (61701082).
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H.X.X. conceived the idea, theoretically designed and fabricated the samples, and performed the FDTD simulations. H.X.X. Y.W., C.W., M.W., and S.W. conducted the experiments. G.H. and Y.H. analyzed the results and made additional efforts in preparing the paper. H.X.X., G.H., P.G., and C.W.Q. wrote the paper with input from all authors. P.G., W.H., and C.W.Q. supervised the project. All authors discussed the results and commented on the paper.
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Xu, HX., Hu, G., Wang, Y. et al. Polarizationinsensitive 3D conformalskin metasurface cloak. Light Sci Appl 10, 75 (2021). https://doi.org/10.1038/s41377021005078
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DOI: https://doi.org/10.1038/s41377021005078
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