Full-space spin-decoupled versatile wavefront manipulations using non-interleaved metasurface

Achieving multifunctional wavefront manipulations of waves with a flat and thin plate is pivotal for high-capacity communications, which however is also challenging. A multi-layer metasurface with suppressed mode crosstalk provides an efficient recipe primarily for circular polarization, but all multiple functionalities still are confined to locked spin states and modes. Here, a multifunctional metasurface with spin-decoupled full-space wavefront control is reported by multiplexing both linear momentumand frequency degree of freedom.We employed vertically cascaded quadrangular patches and crossbars to integrate both geometric and dynamic phases and realized four channels between two spin states and two frequencies in distinct scattering modes (transmission and reflection). For verification, a proof-of-concept metadevice with fourport wavefront manipulations is experimentally demonstrated, exhibiting distinct functionalities including spinand frequency-dependent focusing, quad-beam radiation, anomalous reflections, and Bessel beam generation. Our finding of full-space spin-decoupled metasurfaces would be important for high-capacity communications, multifunctional radar detections, and other applications.

Particularly, metasurfaces are important for compact wireless and optical communications, which allow multitasking or multiple functionalities and significantly boosted information capacity [21,22]. For example, anisotropic metasurfaces with polarization-sensitive EM responses can implement polarization multiplexing based on two orthogonal states, such as linear polarization (LP) basis or circular polarization (CP) basis, for promising satellite communication, especially for microwave frequencies [23]. Here, CP states (also known as spins of EM waves) have been commonly employed to integrate distinct functionalities into single and flat devices based on Pancharatnam-Berry (PB) phase [16,[24][25][26][27][28], which however exhibits intrinsic spin-locked phase profiles. To overcome this issue for more degree of freedom, decoupling two spins is realized by simultaneously employing geometric and propagation phases [18,[29][30][31][32]. Nevertheless, the spin-decoupled strategy only operates in half space (i.e. either transmission or reflection region), showing limited capacity. Very recently, full-space wave control of a CP with a multilayer structure has been demonstrated [33][34][35][36][37], which unfortunately exhibits a spin-locked phase. To date, full-space spindecoupled EM manipulation remains elusive and is rarely demonstrated.
Here, we show a spin-decoupled multitasking strategy with high-efficiency CP wave control in full space. Distinct from any previous literature including unlocked dual-spin [38] and chirality-selective [39][40][41][42] metasurfaces, here we exploit an asymmetric meta-atom with non-interleaved cascading along vertical layered direction. Such a metasurface supports dual sets of spin-decoupled channels across two wavelengths in transmission and reflection mode (Figure 1(a)), respectively, and thus manifests particularly different functionalities as we experimentally demonstrated. Our distinct strategy promises many fascinating applications in fifth generation (5G) communications and paves a way for high-efficiency devices with unprecedented data capacity.

Theoretical concept and meta-atom design
As shown in Figure 1(b), our proposed metasurface achieves quad-port wavefront control for CP wave incidence at two well-separated frequencies and in transmission and reflection mode, respectively. The quad-port versatile independent functionalities (F 1 , F 2 , F 3 , and F 4 ) require arbitrary different phase profiles ( 1 , 2 , 3 , and 4 ) and hence unlocked dual-spin multiplexing and crosstalk-free dualfrequency multiplexing are necessary. To illustrate working principle, we take transmission mode analyses as an example. Under xand y-polarized wave excitation, the EM response of a meta-atom with mirror symmetry along xand y-direction can be described through transmission/reflection matrix T/R [32].
Here, E in x∕ y /E out x∕ y denotes input/output electric field polarized along x-/y-direction, x / y is transmission phase, R is rotation matrix related to rotation angle of , while . For spin-independent phase control, the transmission matrix of the metasurface should satisfy.
represent two arbitrary orthogonal polarization states, + and − are corresponding required phase, * is complex conjugate, and + and − denote RCP and LCP wave, respectively. For CP wave, by combining equations (1) and (2), the relationship between required dynamic and geometric phases x , y , and and functional phases is obtained as follows (see derive process detailed in Ref. [43]): From this equation, we conclude that spin-independent phase modulation can be achieved by tuning transmission phase properties ( x and y ) and rotation angle ( ) of the meta-atom. Similarly, above criteria is also suitable for reflection mode. Therefore, it is crucial for us to implement spin-decoupled kaleidoscopic wavefront control in both transmissive and reflective modes. In the following, we will implement this target by integrating these dual sets of spin-decoupling at two frequencies.
To minimize spin and mode crosstalk among four information channels, a meta-atom should attain high reflectivity and transmittance with full 2π phases at its operation frequencies. Hence, we propose a high-efficiency spindecoupled meta-atom for multitasking strategy in both R and T schemes, as shown in Figure 1(c). For practical design, we resort to four-layered square patch structures (layers I, II, III, and IV), one-layer frequency selective surface (FSS) (layer V), and one-layer crossbar (layer VI) in a composite meta-atom with negligible crosstalk at low and upper frequencies of f 1 and f 2 (see the inset of Figure 1(c)), where six metallic pattern layers are separated by five F4B substrates. Here, layer V is designed as a circular-slot FSS structure to separate transmission and reflection modes. In previous work, interleaved configurations typically suffer from issue of mode cross-talk and thus low operation efficiency. Therefore, a non-interleaved meta-atom is employed here to suppress spin and mode crosstalk, which is essential to achieve spin and frequency multiplexing [18]. Since a single metallic layer exhibits very low transmission rate and limited phase cover, the four-layer cascaded quadrangular patches with square rings (I, II, III, and IV) are exploited to form Fabry-Perot resonance and thus achieve a full 360 • phase cover and high transmission rate. In addition, the square ring accompanied with metallic quadrangular patch generates dual operation modes and thus considerably extends phase coverage. Layer VI is designed as a crossbar structure with a closed loop to achieve high reflectivity and phase modulation with a 2 cover.
To further verify the physical origin of each mode, current distributions are also calculated. As illustrated in Figure 2(a), under LCP wave excitation, the current is mainly located on the quadrangular patch, accounts for a good transmission window at f 1 = 8.7 GHz due to mutual interaction among four-layered patch. In sharp contrast, a strongly induced current is excited in Figure 2(b) at f 2 = 15.8 GHz and generates a strong resonance between layer V and VI, indicating that the crossbar gives rise to the reflection mode.
We performed finite-difference-time-domain (FDTD) calculations to characterize our devices. The amplitude and phase mapping related to parameters (l w and l t , varying from 5.4 to 9.4 mm) is shown in Figure 2(c), where the transmission amplitude maintains a high value above 0.8 at GHz for xand y-polarized incidence, respectively.
Meanwhile, the transmission phase achieves full 2π coverage. Similarly, in Figure 2(d), the reflection amplitude and phase mapping are also obtained by changing l x and l y within 4-10 mm for xand y-polarized waves, respectively, whereas reflection amplitude is near 1 while reflection phase covers a full 2π range at f 2 = 15.8 GHz. In addition, favorable isolation between two modes is also observed by comparing calculated EM response in different cases, confirming the full-space independent wave manipulation with suppressed mode crosstalk; see more details in Supporting Information Figure S1. Therefore, we can easily get arbitrary phase modulation in both transmission and reflection modes for any desired functionalities in both spin channels and full space. In practice, the frequency ratio and periodicity of proposed meta-atom can be adjusted according to on-demand applications, which can be evidenced in Figure S2.

Full-space quad-channel multichannel metaplexer
As a proof-of-concept demonstration, we design and fabricate a quad-channel spin-multiplexed metasurface, termed as a metaplexer hereafter, by implementing focusing (F 1 ) and quad-beam emissions (

Spin-decoupled wavefront controls in transmission mode
In Figure 3(a), we provide target phase profiles ( 1 and 2 ) of F 1 and F 2 , while x , y , and Ψ are derived by following above theoretical strategy. Here, the alternating projection method is utilized to synthesize phase pattern for F 2 and the detailed process to obtain the appropriate geometrical parameters and rotation angles was presented in Ref. [32]. As a demonstration, we calculated near-field diffraction intensity on y-z and x-y planes with FDTD simulations. The results are shown in Figure 3 Multi-beam antenna arrays promise great potential in radar, satellite communication, and multi-input and multioutput systems. Here, we further realize quad-beam radiation under RCP wave excitation at f 1 . The detailed design method and numerical setup has been shown in Supporting Information Figure S3 (Figure 3(e)). The quad-beam radiation property is also evidenced by the detailed crosssection radiation patterns in two principal planes described in Figure 3  supported by the measured near-field intensity distribution shown in Figure 3(g), where four spots are located in four different positions, conforming the characteristics of quadbeam radiation. The measured aperture efficiency is 33 % for the quad-beam emission, which coincides with 35 % in FDTD calculations. The averaged numerical transmission rate is 85 % (84 %) under LCP (RCP) wave excitation, respectively. All results demonstrate that the proposed metaplexer indeed achieves an independent phase transmission modulation under two orthogonal spin states at f 1 .

Spin-decoupled wavefront controls in reflection mode
In the following, we demonstrate other functions, i.e., beam deflection (F 3 ) and Bessel beam generation (F 4 ) in reflection mode under LCP and RCP wave excitation, respectively at f 2 by using our multichannel metaplexer.
The desired decoupled phase ( 3 and 4 ) of F 3 and F 4 is shown in Figure 4(a), more details can be referred to Figure S4 in Supporting Information. In our design, the metaplexer is excited by a CP horn radiating LCP wave and the distance between it and the CP horn is set as F = 192 mm to suppress side-lobes, which guarantees highly directive beam generation. Here, the direction of beam is predefined  Figure 4(b) and (c), respectively. A pencil beam with extremely low side-lobes is precisely directed in predesigned direction. Numerically calculated and experimentally measured far-field scattering patterns at = 0 • cross plane are plotted in Figure 4(d), showing a clear deflection beam with = 30 • . Here, a slight deviation may be caused by the finite size effect, fabrication error, and background noise. The conversion efficiency of beam deflection is simulated and measured as 91.2 % and 90.1 %, respectively.
Bessel beam, as a classical non-diffraction beam, owns general advantages of long energy transmission distance and wide focusing range compared with other types, promising great potential in communication systems [44]. Here, we demonstrate a Bessel beam generation in RCP channel at f 2 . To generate a Bessel beam using metasurfaces, the abrupt phase profile should be in a cone shape. The phase distribution ( 4 ) described as: Figure 4(a), where = 15 • is base angle of equivalent axicon, is wavelength, p is the period of meta-atom and m (n) denotes the number of each meta-atom away from the center of metaplexer along x-(y-) axis. The calculated near-field intensity in y-z plane in Figure 4(e), shows a nondiffraction beam with excellent performance with a propagation length longer than 15 . Furthermore, corresponding electric field intensity (of reflection) in x-y plane at z = 200 and 300 mm above the metaplexer is illustrated in Figure 4(f) and (g), respectively, where a bright central maximum appears in the center, exhibiting a good zero-order Bessel beam. Such a good performance is also supported by measurement results, as shown in Figure 4(h)-(j). In Figure 4(h), longdistance non-diffracting propagation behavior is observed, which coincides well with characteristics of a Bessel beam. In addition, as shown in Figure 4 Figure S5, all exhibiting similar patterns and confirming the non-diffraction long energy propagation property of zero-order Bessel beam. The averaged numerical reflection rate is about 95 % (96 %) under LCP (RCP) wave excitation, respectively. The efficiency of the Bessel beam is measured as 89 % while is calculated as about 91 % in FDTD simulations. All results clearly illustrate kaleidoscopic wavefront manipulation in four information channels based on spin-frequency multiplexing in full space, further verifying our concept and design. Moreover, we further explore the polarization purity of each designed functionality by investigating field distributions at its co-polarized spin state, see Figures S6 and S7.

Conclusions
We have proposed and demonstrated a full-space versatile wavefront manipulation based on spin-decoupled multichannel metasurface. In this regard, a composite meta-atom of six metal layers and five substrate layers was devised, in which the middle FSS structure is utilized to guarantee upper four-layers quadrangular patch with square rings working in transmission mode at f 1 and bottom crossbar with a closed ring in reflection mode at f 2 , respectively. Thanks to elegant design for a suppressed spin and mode crosstalk, four information channels can be controlled independently in two orthogonal CP states, leading to independent full-space spin-decoupled kaleidoscopic wavefront manipulation. As proof of concept, a well-designed multitask metaplexer that exhibits four independent functionalities was experimentally demonstrated. Both numerical and experimental results qualify our proposed full-space strategy as a solid platform to realize spin-and modemultiplexing systems with high information capacity, even our findings can be readily extended to more diverse wavefront modulations by introducing more eigenchannels associated with each piece of information, such as incidence direction and wavevector. We believe that our proposed fullspace multitask metaplexer should provide new avenues and more degree of freedoms in designing multifunctional devices with high data capacity, promising great potential applications in the next-generation wireless communication systems.

Experimental characterization
To experimentally demonstrate our concept, a sample was fabricated by using the standard printed circuit board technique, where six-layer metallic patterns were printed individually on five dielectric boards, then assembled together through adhesives and finally reinforced through a hot press. As shown in Figure 5(a), in beam deflection and quadbeam radiation far-field measurements, the fabricated sample was placed in center of a rotation platform, where a small size LCP or RCP spiral horn working at 4-18 GHz was employed as feeding source to excite the fabricated metaplexer. The metaplexer was aligned with feeding horn by a 3D-printed frame with a distance of F = 192 mm. Meanwhile, an LCP or RCP horn was selected as receiving antenna at a reasonable distance of 3 m to record EM field information (amplitude and phase) by freely rotating 180 • with a step of 1 • around the sample. The feeding horn and receiving antennas were connected to two ports of an AV3672B vector network analyzer. In Figure 5(b), for near-field measurements of quad-beam radiation, the metaplexer was excited by an RCP horn from forward incidence, and a 6 mm-long monopole antenna, functioning as the receiver, was placed at 240 mm away from the metaplexer on another side. To obtain a near-field intensity distribution in x-y plane, a monopole antenna was connected with a 2D electronic step motor which can move automatically in a maximum area of 0.3 m × 0.3 m with a step resolution of 5 mm. In Bessel beam near-field measurements, the metaplexer was launched by an RCP lens antenna. Similarly, a monopole antenna was selected as the receiver to obtain reflection field information in area of 162 mm × 162 mm and 162 mm × 400 mm with a step resolution of 5 mm. By altering relative position of the metaplexer and 2D monitor, near-field distribution in y-z and x-y planes can be obtained. In all reflection near-field contour maps, incident signal in free space was deducted from total fields.

Supporting Information
Discussion for crosstalk among different modes; discussion for frequency ratio and periodicity of proposed metaatom; detailed design method and numerical setup for quadbeam radiation; reflection beam deflection phase calculation; additional information for Bessel beam; discussion for purity of each designed functionality by examing the field distribution at its co-polarized spin state.