Spin-encoded wavelength-space multitasking Janus metasurfaces

: The fruitful progress toward geometry (half-space) has facilitated strong aspiration to achieving full-space electromagnetic wave control in both R and T channels. Although it promises large-capacity and integrated functionality, yet imposes prohibitive difficulty and big challenging for extreme wave control (direction of arrival in full space) via an ultrathin flat device. As of today, very limited demonstrations were reported for single-band and linear-polarization operation, significantly limiting the exploitable degree of freedoms (DoFs) for real-world applications. Herein, we report for the first time a triple-layer wavelength-space multitasking scheme for wide-angle and large-capacity detection. Two anisotropic sub-meta-atoms are engineered with high quality factor and simultaneous in-plane and out-of-plane symmetry breaking, facilitating four R and two T spin-conversion channels with high efficiency and insulation. The chirality-assisted Fano effect gives rise to the wide-angle operation and boosted channels. Above features and released DoF would be extraordinary beneficial for large-capability and angle-engineered advanced device. Two proof-of-concept metadevices, i.e., large-scanning kaleidoscopic-beam generator and a wide-angle large-capacity reverser for multi-target tracking, are devised to verify the significance. Numerical and experimental results have approved predesigned advanced functions at six channels with measured efficiency over 75%. Our findings in multi-DoF multitasking of metasurfaces could stimulate great interest in radar applications with versatile beam generation and multi-channel integration. a coordinate by three information of and polarization. Here, the yellow sphere indicating available work with reference numbers marked besides and the gradient panel from light to dark represents the degree of difficulty in realization. The L and C indicate linear and circular polarization (CP), 2L and 2C mean two orthogonal LP and CP wave operations, and R and T indicate reflection and transmission, respectively. Note that the high-efficiency CP operation indicated here requires specific condition of dynamic phases of two orthogonal LP components under LP wave excitations and thus is more difficult than dual-LP operation. Three colours in schematic function represent three synthesized spectrum channels at different operation wavelengths of λ 1 , λ 2 and λ 3 while different angles of each outgoing wave indicate full-space DOA or integrated large-capacity functionalities.

Unfortunately, only the single DoF of spin was employed and most have not involved dynamic phase for near unity efficiency. Intuitively, one may wonder to combine above wavelength-and space-multiplexing strategy in LP case for spin-wave modulation. However, this is particularly challenging or inapplicable since the preservation of high efficiency for concentric sub-atoms with spatially varied orientations is prohibitively difficult across several wavelengths and in both R and T channels. In fact, the criteria are typically mutually exclusive for above compound multitasking. A noninterleaved synergetic strategy by involving different propagation dispersion at different wavelengths [37] or by merging different momentums [38] has significantly enriched the spin-triggered output patterns, however, they were all confined to T channel because the basic monolayer meta-atom (nanobrick) without symmetry breaking is inherently far insufficient for direction selectivity. To date, spin-enabled wavelength-multiplexing or space-multiplexing remains elusive and in its infancy in half space, not to mention the compound multitasking of more than above two DoFs in full space.
In light of aforementioned challenges, here we report for the first time a chirality-assisted multitasking strategy by involving simultaneously in-plane and out-of-plane symmetry breaking for extreme spin-wave manipulations across triple wavelengths and along R&T channels of two-sided metasurfaces in analog to two faces of a Janus. The importance and significance of our concept can be inspected from Fig. 1a, where our work is indicated with high novelty as well as great difficulty in actualization. Our sophisticated two-faced Janus metasurface enables four asymmetric R channels (F1~F4), with two generated at λ1 and λ2 along each face, see the schematic functions shown in Fig.   1b. Moreover, two symmetric T channels (F5 & F6) are naturally formed at λ3 when a spin wave impinges on the meta-plate from both sides. The high efficiency and elegant insulation among these channels are engineered by synthesizing triple R/T channels at each face with high-quality factor, see the inset shown in Fig. 1b, which calls on the elegant design of meta-atoms as further discussed below. Therein, we can engineer an arbitrarily predicted functionality by imposing desired phase patterns in each channel. Most importantly, we can further envision advanced functions for full-range scanning (full-space DOA) by integrating above channel-shifted versatile beams with progressive steering angles, or for large-capacity/complexity kaleidoscopic wavefronts by integrating channel-shifted hetero functions, facilitating large capacity, and great flexibility and versatility.

Chirality-assisted wavelength-space multitasking principle
To begin with, we first elaborate basic principle for wavelength-space multitasking, aiming to afford a solid platform and useful guideline for design. Suppose m wavelength/mode channels and n spatial port channels in our system, then a maximum of m×n information eigen-channels would be achieved. Here, the spatial port channel essentially refers to the main scattering directions in a full space. Intuitively, the information channels grow explosively if more DoFs will be involved, i.e., polarization, wavevector and incidence angle. However, more DoFs implies much more complicated system, which is more challenging in realization. The other tricky issue is how to simultaneously generate and individually manipulate these channels in a subwavelength scale without boosting the element footprint. More importantly, the elimination of the interferences among these modes is substantially crucial for individual control of both dynamic and geometric phases in each mode for advanced high-efficiency wave control. Here, to slightly relax the task but not lose generality, we engineer six R and T channels across three wavelengths of a two-port system.
A chirality strategy involving both in-plane and out-of-plane symmetry breaking was proposed to yield direction-encoded Janus functionalities and circumvent issues of mode interferences among boosted channels, which was previously employed only for polarization control [15], [39], [40] , advancing a step over available applications.

Strategy and meta-atom design
As shown in Fig. 2a, the basic building block utilized for multitasking is a triple-layered thin meta-plate composed of a circular slotted patch sandwiched by two composite metallic structures in top-and-bottom sides. Two types of concentric sub-atoms are adopted to construct the composite pattern, say evolved H structure and dual-gap asymmetry split ring resonator (ASRR). The in-plane symmetry breaking of ASRR is facilidated by deviating one gap from the principal y axis by an angle of β while the other fixed. Such an asymmetry divides the ASRR into two counterparts with different resonant lengths, splitting the original mode into two (Fano effect [41] ), see Supplementary   Fig. S1. This proposal finds strong support from the differently localized current distributions on ASRR at λ1 and λ2 ( Supplementary Fig. S2). The isotropic patch with a centric circular slot etched in the middle layer behaves as a ground plane and thus assists ASRR to afford two R modes at λ1 and λ2. In contrast, it functions as a spatial mode filter and is accompanied with evolved H structure to form an ABA-like T mode at λ3. Besides, the full-fold rotational symmetry of the circular ring shares different orientations of ASRR and evolved H, and thus facilitates both R and T geometric phases with perfect insulation. The out-of-plane symmetry breaking is engineered by designing the two-faced ASRRs with differnet strcutres and orientations, yielding direction-encoded distinct R phase patterns in analog to a Janus.
Typically, we choose chessboard configuration instead of concentric distribution of ASRR and evolved H along a shared optical axis to completely insulate the coupling for individual control [33] .
Quite interestingly, the strong field localization of utilized evolved H in a thin profile enables large quality factor ( Supplementary Fig. S2) which is very beneficial for suppressing the mutual interference. Although increasing the vertical thickness between top and bottom layer enhances the bandwidth occasionally, it yet destroys the high concentration of fields around ASRR and evolved H, which is the key for mode insulation. Plus appropriate mode interval, the encapsulation of evolved H in ASRR guarantees simutaneously independent control and subwavelength scale. The mode interval (ρ=f2/f1) can be arbitrarily engineered by tuning the position of the asymmetric gap (angle β). Large β would lead to large ρ (lower f1 and higher f2), i.e., ρ=1.4 at β=30 o , and ρ=1.78 at β=50 o , see Supplementary Fig. S2. Such a mechanism completely distinguishes our strategy from available harmonic approach [42] or merging concept [19]- [22] . Finally, the high efficiency of spin conversion for triple R and T modes is well engineered by controling the dynamic amplitudes and in both sides. Most importantly, the near-unity spin conversion is inspected in all R/T modes, which is very promising for high-efficiency metadevices. In the following, we will devise two metadevices to demonstrate our wavelength-space multitasking concept and uncover its possible applications.
The triple-layer metallic patterns of each metadevice are fabricated individually on two dielectric boards using printed-circuit-board technique. They were assembled together through adhesives and reinforced through a hot, and finally experimentally characterized through both near-field and far-field measurements, see Supplementary Information (section 5)

Large-scanning kaleidoscopic-beam generator
Highly-directive multi-beam emission system with large cover especially for a full-space span promises great potentials in radar, satellite-based communication, SAR, smart antenna, and multiple-input multiple-output systems. However, available approaches typically require a complicated beam-forming network. Here, we devised and characterized a passive metadevice that is capable of manifesting kaleidoscopic beams for full-space DOA without any network. Such an advanced large-scanning capability is unbelievable before our wavelength-space concept and distinguishes completely from current anisotropic scheme capable of manipulating EM wave in two reflection channels under dual-orthogonal LP [43]- [45] and spin waves [23]- [26] . The compound plate is predesigned with six spatial wavevectors covering both principal planes and directing at (Φ, θ)=(0 o , Supplementary Fig. S7. Then, the resulting reflection/deflection angles θ=sin -1 (ξ/k0) can be readily predicted as a function of ξ according to the generalized Snell's law [2]. As is expected in Fig. 3(b), six spatial beams with two and four wavevectors are clearly inspected across Φ=0 o and Φ=90 o plane in full space from both numerical and experimental far-field patterns. The beam-steering property can be further evidenced from the near-field Eσ+ or Eσ-patterns shown in Fig. 3(e), where oblique planar wavefront is clearly inspected. Most importantly, these wavevectors are precisely directed along target angles predicted by theory with an angle error of ±1 o (Fig. 3d), indicating negligible interference among these well-insulated channels. The FDTD calculated and measured efficiency evaluated as the ratio between the powers carried by the reflected/refracted beam and the total power integrated over full space is more than 92%/84% in all six R-T channels. The slightly reduced efficiency in experiment case is attributable to the higher sidelobes induced by the slightly distorted phase patterns. Such level of high-efficiency and advanced full-space scanning is extremely difficult for an active phased array, not to mention the existing passive metasurfaces [29] [32] for high-efficiency spin conversion at one single R or T channel.

Wide-angle large-capacity reverser
In the following, we demonstrated another more advanced function, called a reverser, by using our Janus metasurface, which enables to reverse predefined in-plane components of momentum in both R (retroreflector) and T (negative refractor) channels. Such an integrated reverser can be considered as another alternative for full-space DOA. Retroreflector is an important device in the discipline of navigation safety, target labeling, RCS/visibility enhancement, remote sensing and satellite communication. It allows the reflection of the EM wave propagating back along its oblique incident direction. Available approaches such as corner reflector and Luneburg lens have been reported, however, the bulk size, large weight and nonplanar configuration have hindered its real-world applications since it does not meet the native compatibility for integration and miniaturization. Employing metasurface for such a task has been an intriguing issue most recently [46]- [50] , especially for the adaptive retroreflector, which is only demonstrated by mechanically altering the geometry of reconfigurable C-shaped resonators [48] or switchable metagrating [49] .
Nevertheless, large-angle retroreflection particularly in full space is still extremely challenging for a passive metasurface, not to mention the proposed compound large-capacity reverser which promises great potential applications in multi-target tracking. Here, we engineer a full-space reverser that integrates retroreflection at f1 and f2 and negative refraction at f3 inspired by our wavelength-space multitasking concept. More importantly, the retroreflections at f1 and f2 in forward and backward channels can be independently modulated, see Fig. 4a.
The design of retroreflector origins from the conservation of tangential momentum in the transverse plane. To flip the in-plane component of the momentum of incident light (p||), we need to impart an exact momentum (pm=-2p||) on the gradient metasurface for compensation, which follows the condition . Therefore, the reflective and transmissive phase patterns of the full-space retroreflector should fulfil , where n is the total number of meta-atoms along transverse direction. To engineer a multispectral retroreflector and negative refractor at large incidences, we require that the EM response, especially the manifested phase of the meta-atom is insensitive to the incident angle .
To begin with, we first evaluate the angle-immune EM response of the composite meta-atom to , as shown in Fig. 2e and Supplementary Fig. S8. The R/T spin-conversion coefficients in all channels deteriorate slightly as θi increases. Nevertheless, all intensity is inspected more than 0.9 at f1, f2 and f3 even at θi=60 o . Moreover, the phase response is preserved almost constant at three target bands (grey region) despite slight deviation at off-resonant frequencies at θi=60 o . All inspected phenomenon reveals an elegant angle-immune EM response which is essentially important for a retroreflector at large incidence angle. Similar angle-insensitive EM property can be also expected when the incidence is along yz plane, see Supplementary Fig. S9. More interestingly, the symmetry-breaking in ASRR is beneficial for the incidence-angle insensitivity, see EM response of the SRR meta-atom without symmetry-breaking portrayed in Supplementary Fig. S10, where a sharp reflection dip with amplitude and phase fluctuations appears when θi≠0 o . The physics behind the angle-immune behaviour of ASRR is because similar electric and magnetic dipole modes are excited with stable intensity for different θi.
The integrated multitasking retroreflector and negative refractor is predesigned at both sides of the metasurface for both R/T channels, see the schematic functionality shown in Fig. 4a. Here, the intriguing with respect to the available report which is confined to 20 o [48] . Finally, the released DoF indicates that we can also engineer achromatic retroreflector and nega-refractor in the same incidence at f1 and f3.

Conclusions
To    (e) Experimentally measured NF patterns (E field) in xz and yz planes for functions of F1~F6. Here, the reflection or refraction angle is defined with respect to the normal within -90 o~9 0 o and all measured results intensity are normalized against its maximum.

FDTD calculations
All numerical designs and characterizations are performed through FDTD simulations based on a commercial software package. Specifically, the reflection/transmission amplitudes/phases are obtained by studying a single meta-atom with periodic conditions imposed at its four boundaries and a Floquet port assigned at a distance of 15 mm away from the xy-plane where the meta-atom is placed. In the far-field and near-field calculations, we characterized the two entire metadevices consisting of 32 × 32 and 30 × 30 meta-atoms, with open boundary conditions set at its four boundaries in the xy-plane. In all cases, the metadevice/meta-atom is illuminated by normally incident LCP and RCP plane wave.

Additional results for the composite meta-atom
The frequency ratio (f2/f1) between two R modes can be progressively controlled by adjusting the position of the asymmetry gap (angle β), see Fig. S1. As can be seen, large β would lead to large frequency interval/ratio, namely, lower f1 and higher f2. Moreover, the efficiency slightly deteriorates when β increases. Nevertheless, we obtain a high efficiency of more than 0.91 and a frequency ratio of 1.4 (f1=7 and f2=9.8 GHz) at β=30 o , and a larger frequency ratio of 1.78 (f1=6.5 and f2=11.6 GHz) at β=50 o .

Figure S1
Illustration of the frequency ratio control over f1 and f2 by the asymmetry gap β.
To gain an insight into the principle of multiband operation, we afford FDTD calculated current distributions on the meta-atom, see Fig. S2. As can be inspected, the current is densely distributed around the left longer part of ASRR at f1, whereas it is strongly localized around the right shorter part at f2, accounting for the two reflective operation band. Moreover, the current intensity is mainly concentrated near the top-and-bottom evolved H patterns and centre annular slot at f3, indicating an ABA transmission response. The origin of above three operation modes gives us a clear guideline for individual control.

Figure S2
Current distributions on the meta-atom at three representative frequencies of f1, f2 and f3.
Given the clear origin of three resonances, the key for meta-atom design is how to maintain the high efficiency of spin conversion. Fig. S3 plots the frequency spectrum of the composite meta-atom under x and y linearly-polarized (LP) EM wave excitation for both reflection and transmission, respectively. As is appreciated, high reflection rate (|ryy|≈|rxx|>0.88) and transmission (|tyy|≈|txx|≈1) rate are clearly observed at f1, f2, and f3 for both co-polarized components in two cases.
Moreover, the phase difference (φyy-φxx) between them is around 180 o across three bands. Therefore, we conclude that the high spin conversion efficiency can be well engineered by controling birefringent response of the anisotropic ASRR and evolved H structure under LP excitation.     Figure S7 portrays the full layout of the top, middle and bottom layer of the full-space kaleidoscopic-beam generator. As can be seen, the ASRR varies spatially along x and y direction in the top and bottom layer, respectively, whereas the evolved H patterns varied synchronously along y direction in both layers. The circular slotted patch in the middle layer are the same at all positions.

Figure S7
Layout of the triple-layer full-space kaleidoscopic-beam generator based on our chirality-assisted wavelength-space multitasking concept. The top row is the CAD model while the bottom row is the photograph of fabricated sample.

Angle-insensitive performance for wide-angle large-capacity reverser
In the main text and previous section, we learned that our composite meta-atom exhibits desired high efficiency of spin conversion under three well-insulated R and T channels mainly under normal incidence. Here, in addition to Fig. 2e we further verify such angle-immune response can also be preserved in two principal incident planes. Figs. S8 and S9 portray the reflection and transmission coefficients in xz and yz plane across a broadband spectrum. As is expected, the transmissive and reflective amplitude and phase is maintained constant at three grey regions over a large range of incident angles even when θi is up to 60 o in both planes, indicating a large-angle EM behavior.  In fact, the symmetry-breaking in ASRR is found to account for the angle-immune EM property.
As a proof, we additionally afford the FDTD calculated scattering spectrum for the meta-atom loaded with partial-symmetry SRR under oblique incidence for sharp contrast. The angel-sensitive EM response can be inspected from Fig. S10. As is shown in Figs. S10a and S10b, we only observe one reflection peak around 8.2 GHz when θi=0 o and there appears a sharp reflection dip when the EM wave is obliquely incident. Such an amplitude dip is also accompanied with a sharp phase fluctuation across the phase spectrum, indicating an angle-sensitive EM behavior of the partial-symmetry meta-atom. The effect of oblique incidence (θi=20 o ) to the PB phase near 8.2 GHz can be inspected from Figs. S10c and S10d. As is indicated, it is hardly to achieve a linear PB phase response which is two times of the rotation angle ψ1 when ψ1 varies from 0 o to 150 o in steps of 30 o .
The sharp phase shift under tilt incidence deteriorates the regular PB phase at normal incidence. The sharply varied intensity of excited electric and magnetic dipole modes among different θi for SRR meta-atom without symmetry-breaking gives rise to the giant contrast of EM response under large-angle incidence.

Figure S11
Layout of the triple-layer multitasking full-space retroreflector and negative refractor based on our chirality-assisted wavelength-space multitasking concept. The middle layer is the same with that of fabricated kaleidoscopic-beam generator.

Fabrication and experimental setup
The triple-layer metallic patterns of each metadevice are fabricated individually on two dielectric boards using printed-circuit-board (PCB) technique. They were then assembled together through adhesives and finally reinforced through a hot press. In near-field (NF) experiments, the fabricated sample was launched by two types of dual-spin CP horns with voltage-standing-wave ratio (VSWR) less than 2.5 and axial ratio less than 3.5 across 4~8 GHz and 8.2~12.4 GHz, they were fixed with a distance of 0.7 m, see the experimental setup shown in Fig. S12. A 15 mm-long monopole antenna, functioning as the receiver, was placed behind the sample, and connected to an AV3672B vector network analyzer to record the static EM signals. The monopole was fixed to a 2D electronic step motor that can move automatically in a maximum area of 0.7 m×0.7 m with a step resolution of 10 mm. In far-field (FF) experiments, the transmitted horn was placed on one artificially-controlled arm, while the received horn was fixed on the other arm of rotary table which is automatically rotated around the sample in a circumference and controlled by an electronic motor. For transmission measurement, the sample is enveloped by a mass of radiation-absorbing materials to avoid possible diffractions from the edge of the sample. Under this circumstance, the signal emitted from the horn transmits only through the aperture window while the residual diffractive energy is almost completely blocked.

Figure S12
Illustration of the experimental setup for (a) NF and (b) FF measurements.