As three fundamental properties of electromagnetic (EM) waves, polarization, amplitude, and phase are intricately correlative and interact with each other. Among them, polarization, referring to the trajectory of the electric-field vibration [1], has been extensively studied and applied in miniaturized optical systems and integrated photonic circuits. Initially, polarization generation and conversion are based on the linear birefringence effect of the optical crystal [2,3]. The typical devices are polarizers and wave plates, whose operating principle is producing a specific phase shift between the ordinary and the extraordinary components with an appropriate thickness and then superimposing them. Nevertheless, such devices are commonly bulky in size and require high accuracy, and only a few natural materials are alternatives in different bands. More significantly, though with complete modulated polarization, these mature devices barely simultaneously control other EM parameters including amplitude and phase to manipulate complicated wavefronts, which are inconducive to exert potential in modern integrated optical systems.

In recent years, the sudden emergence and rapid development of metasurfaces have rendered an infinite number of possible methods to make such optical devices. Evolving from metamaterials, metasurfaces are regarded as their two-dimensional (2D) planar versions and possess plentiful merits including easy fabrication, small size, and low cost in controlling EM waves [4,5]. By introducing an abrupt field discontinuity, metasurfaces have the remarkable ability to adjust the various properties of the EM waves on demand with a high spatial resolution. Soon afterwards, many fascinating metasurface-based devices and applications have been successively implemented, such as vectorial holograms [6–8], invisible cloaks [9,10], spin and orbital angular momentum generators [11–13], and multifunctional meta-emitters [14,15]. Generally, the currently various metasurfaces can be mainly categorized into three types: reflection metasurfaces (RMs) [16–18], transmission metasurfaces (TMs) [19,20], and transmission-reflection-integrated metasurfaces (TRIMs) [21–24]. The reflection or transmission metasurfaces can work in the reflection or transmission mode to achieve half-space control, while transmission-reflection-integrated metasurfaces can achieve full-space manipulation of EM waves. By contrast, TRIMs tremendously avoid the waste of resources and well meet the requirements of entire-region polarization modulation and multiplexing.

Actually, each polarization utilized in TRIMs can be viewed as one independent information channel in the communication systems, and thus, the storage capacity of the devices can be steadily improved. Ideally, a polarization-modulated and multiplexed TRIM is envisioned with the ability to preserve as much as possible the incident power intensity and convert it into several independently well-defined wave functionalities in full polarization channels. Thereupon, the TRIMs should provide more degrees of freedom (DoFs) and eliminate crosstalk between different polarizations. Notably, considerable efforts have been made to implement full-space bidirectional beamforming applications through tunable structures [25], nested models [26,27], and cascaded surfaces [28–30]. In addition, via ingeniously combining the transmitting and receiving circularly polarized (CP) antennas, some groundbreaking works including dual-mode metalenses [31], multichannel meta-holograms [32], high-efficiency CP folded transmitarray antennas (FTAs) [33], and full-space CP routers [34] were successively achieved. Despite this progress, there are still problems that should be overcome to fully exploit the TRIMs in high-integration wave manipulation. On the one hand, most of them only combine unit cells with different functionalities at respective frequencies or in a narrow bandwidth, causing aperture mismatch, and high-profile and high-complexity limitations of the metasurface. On the other hand, the current endeavors are either linearly polarized (LP) or CP modulated waves, and the operating patterns are limited to single input/single output channels, hindering their application in special scenarios, i.e., full polarization and multiple output. Therefore, rendering arbitrarily polarized modulation with simultaneously tailored wavefronts in broadband and full space while maintaining a simplistic framework is worthy of expectation, but also challenging.

In this work, for the first time, we propose an innovative paradigm and experimental demonstration focusing on broadband TRIM that integrates full-space wavefront manipulation with independent information channels from 8 to 16 GHz, enabling the modulation and multiplexing of arbitrary polarization, as illustrated in Fig. 1. Two chiral meta-atoms with different interior rotations are spatially interleaved to form the tetrameric meta-molecules, which can achieve spin-selective transmission and reflection under predefined CP waves. After tailoring the eigen-polarization responses of each pair of enantiomers, co-polarized reflection and cross-polarized transmission phase shift will cover 2π accordingly along corresponding propagation directions. Consequently, a completely decoupled relation and decorrelation of the two orthogonal basis vectors are obtained in full space. Furthermore, based on EM-field synthesis and decomposition, arbitrary wavefronts in predesigned full-polarization channels can be equivalent to manipulation in respective orthogonal CP channels. Distinguished from the previously demonstrated intense anisotropic particles [35] or multilayer cascaded gratings [36], ours bridges the transmissive and reflective fully polarized controllable wavefronts and features the advantages of high robustness and easy expansion. In particular, several proof-of-concept TRIM prototypes are experimentally verified including a CP beam splitting controller, an LP vortex beams generator, and CP and LP multifoci metalenses. All the simulated and measured results are in good coincidence with the theoretical predictions. The proposed methodology exhibits unprecedented serviceability and can be easily extended to other frequency bands and employed for future-oriented multitask parallel processors.

For the sake of constructing such a brand-new TRIM to manipulate arbitrarily polarized wavefront and EM functionalities in full space, the critical step is to impart independently controllable phase profiles to the generated polarized beams and decompose them into a complete set of orthogonal basis states, both of which can be tailored individually. As illustrated in Fig. 1, in consideration that left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) waves are employed as the orthogonal basis in this study, we in turn elaborately design the chiral meta-atom, with the assistance of the commercial software Computer Simulation Technology (CST) Microwave Studio, which possesses a multilayer configuration consisting of three metallic layers of copper separated by two dielectric layers of F4B, namely, meta-atom A, as presented in Fig. 2(a). The conductivity of each copper metallic film with thickness of 0.035 mm is σ=5.8×107S·m−1, and the relative permittivity and loss tangent of each F4B dielectric spacer with thickness of h1=h2=2.5mm are εr=2.2 and tanδ=0.001. The circular aperture structure in the middle of the meta-atom plays an important role in achieving high-efficiency reflection and transmission for corresponding incident CP waves. The middle metallic structure is a grounded plane, and under that, there is a Rogers adhesive layer (Rogers RO4450F, εr=3.52 and tanδ=0.003) with a thickness of 0.1 mm to bond upper and lower printed circuit boards (PCBs) together, which will not affect the EM property of the meta-atom due to its extremely small thickness. The top and bottom metallic structures are circular patches with a modified L-shaped slot, named RCP antenna and LCP antenna, respectively, and are connected through a metallized via-hole placed at the center of the grounded plane, which is connected to the center points on the top and bottom patch antennas, respectively. The other geometrical parameters of meta-atom A are schematically illustrated in Fig. 2(b). Thereinto, the period of the meta-atom is p=10mm, and the other parameters shown in the meta-atom are r1=0.5mm, r2=4mm, r3=0.8mm, l1=4.3mm, l2=3.2mm, w1=w3=0.96mm, w2=0.66mm, w4=w5=0.71mm, γ1=γ2=45°, gx=1.4mm, and gy=1.6mm.

By delicately optimizing the size of the modified L-shaped slot, along with the relative position between the long and short vertical rectangular sides of that, the CP operations are realized for the top and bottom patch antennas. To be specific, the top patch antenna acts as a receiver to efficiently receive the incident RCP waves due to good impedance matching, and transforms the received energy into guided waves propagating in the metallized via-hole. The bottom patch antenna, as a transmitter, receives the guided waves from the metallized via-hole and radiates them into the transmission space in the form of LCP waves. In addition, the incident LCP waves cannot be received via the top patch antenna and will be radiated into the reflection space in the form of LCP waves. On the other hand, to customize arbitrary phase profiles in these two desired channels, the independent abrupt phase shifts of φtLR and φrLL for the RCP cross-polarized transmission amplitude (tLR) and LCP co-polarized reflection amplitude (rLL) are supposed to be generated, separately. It is not difficult to prove that Pancharatnam–Berry (PB) phase can be generated for both RCP transmitted waves and LCP reflected waves via an exterior rotation method, namely, the rotation of the whole meta-atom structure. However, in such a way, the TRIM will produce intrinsically conjugated phase responses φtLR and φrLL in two independent CP channels. In order to overcome this limitation, independent phase responses are introduced via an ingenious strategy where two patch structures of the meta-atom are separately rotated with different angles, regarded as interior rotations. Here, the orientation of the middle ground layer is fixed without further rotation, while the top and bottom patch layers are respectively counterclockwise rotated with different angles of αA and βA, as denoted in Fig. 2(a). On this basis, the exterior rotation can be viewed as a special case of the interior rotation when αA is equal to βA. The interior rotation of the top and bottom patch antennas for meta-atom A can lead to the required independent phase responses expressed via the following expressions: φrLL=−2αA,(1)φtLR=αA+βA.(2)

The detailed derivation of such interior rotation strategy for independent phase modulation is provided in Appendix A.

Full-wave simulations are performed with the commercial software CST Microwave Studio to exploit the EM characteristics of the meta-atom. See Section 4 for more details of the simulation setup. Figure 2(c) depicts the side view of the electric-field distributions above and below the meta-atom A under RCP and LCP normal incidence. First, when the RCP waves illuminate the meta-atom, there are apparent electric fields of both Ex and Ey components in the space above and below the meta-atom, indicating that the incident RCP waves can efficiently pass through the meta-atom. Next, in the case of LCP waves illumination, only noticeable electric fields of both Ex and Ey components appear in the space above the meta-atom and are ultralow in the space below that, further proving that the incident LCP waves are completely blocked and subsequently reflected. Also, the electric current distributions at different times t in one sinusoidal period on the surface of the top and bottom patch antennas under RCP and LCP normal incidence are plotted in Figs. 2(d) and 2(e), where the meta-atom can be seen as working in a transmission and reflection mode, respectively. Obviously, in the transmission mode, the currents induced on the top antenna can flow to the bottom antenna through the metallized via-hole; thus, strong currents are motivated on both the top and bottom patch antennas. Meanwhile, the results also show that the excited surface currents rotate clockwise and anticlockwise once in a sinusoidal period along the resonant positions on the top and bottom patch antennas for the transmission mode, resulting in the incident RCP waves being efficiently received from the input port and radiated in the form of LCP waves. However, in the reflection mode, almost zero currents are stimulated on the bottom surface, while for the top layer, intense currents are excited, which are mainly located on the edges of the modified L-shaped slot and the circular patches. In addition, the currents have maximum amplitudes at time t=0 or π/2 and t=π or 3π/2 with opposite vectors.

Therewith, the simulated transmission and reflection amplitudes and phases of the meta-atom A are illustrated in Figs. 2(f)–2(k) to evaluate the performance of that. Figure 2(f) shows the simulated transmission amplitude profiles within the frequency band of 8–16 GHz under normal excitations of RCP waves, from which it can be observed that the cross-polarized transmission amplitude tLR is above 0.8, and reaches a maximum of 0.98 at 9.37 GHz, while other scattering components are tremendously suppressed to a lower level. The simulated cross-polarized transmission phases φtLR with respect to various αA while maintaining βA fixed as 0° and various βA while maintaining αA fixed as 0° are further exhibited in Figs. 2(g) and 2(h). Herein, the results show that the phase response φtLR increases linearly with the increase of αA and βA. Moreover, these two phase profiles exhibit identical tendency with the same slopes. At the same time, the LCP waves normally incident on the meta-atom undergo a high co-polarized reflection rLL with a peak value of 0.99 at 9.41 GHz, as shown in Fig. 2(i). Figures 2(j) and 2(k) present the simulated co-polarized reflection phase φrLL in the same circumstances, where the phase response φrLL equals double the rotation angle αA, while being unaffected via the variation of the rotation angle βA. Based on all of the above theoretical and simulated results, it can be concluded that the phase responses φtLR and φrLL can be separately and freely altered through different combinations of rotational parameters αA and βA. For pursuing TRIM-based complete modulation of the four CP channels to achieve arbitrarily polarized wavefront manipulation, on the one hand, the basic method is to endow the required phase patterns of Lt-Ri and Lr-Li channels with the sweeping of rotation angles αA and βA; on the other hand, a similar method should be utilized synchronously to impart the required phase patterns of Rt-Li and Rr-Ri channels. Fortunately, via applying 180° mirror operation with respect to the yoz plane to the top and bottom patch antennas of the meta-atom A, the newly acquired meta-atom can enable such operations, which is defined as meta-atom B, and the detailed operating mechanisms of that in terms of independent phase modulation can be found in Appendix A. Then, we arrange the two kinds of meta-atoms in an interleaved manner to constitute the tetrameric meta-molecule with a square periodic lattice spaced at 20 mm, as shown in Fig. 1, where one type of meta-atoms is surrounded by the other elements along y-direction.

Without loss of generality and for arithmetic simplicity, it is considered that LP waves are normally incident along −z direction upon the tetrameric meta-molecule in the xoy plane with electric polarization 0° off the x-axis, which can be decomposed into a pair of LCP and RCP components with the same amplitude and zero difference. Accordingly, the total electric-field amplitude distributions in both CP co-polarized reflection and cross-polarized transmission channels are equal. The total transmitted and reflected electric fields can be viewed as the collective results of the transmitted and reflected electric fields in each predesigned polarization channel, given as $$\begin{gathered} Etotalmn=Et,totalmn+Er,totalmn \\ =∑j=1JEtj,outmn+∑k=1KErk,outmn \\ =(∑j=1Jζtjmn·Etjmn·ei·(φtjmn+Δφtjlmn))·[1−i]+(∑j=1J1−(ζtjmn)2·Etjmn·ei·(φtjmn+Δφtjrmn))·[1i] \\ +(∑k=1Kζrkmn·Erkmn·ei·(φrkmn+Δφrklmn))·[1−i]+(∑k=1K1−(ζrkmn)2·Erkmn·ei·(φrkmn+Δφrkrmn))·[1i], \end{gathered}$$(3)where mn represents the mn-th meta-molecule and ζ and Δφ denote the amplitude ratio and phase difference for each polarization. The transmission and reflection amplitude and phase of the mn-th meta-molecule are denoted as Etjmn, φtjmn, Erkmn, and φrkmn, in which the former “t/r” of the subscripts indicates the transmission and reflection and the latter “j/k” of those indicates the j-th/k-th modulated polarization. On the basis of the well-designed tetrameric meta-molecule and above-mentioned theoretical analysis, we decompose the wavefronts in the predesigned polarized channels of three different demonstrative cases into LCP and RCP components, subsequently solve the corresponding phase and rotation angles of the top and bottom patch antennas of two pairs of chiral meta-atoms, and eventually interleave and combine them to construct the TRIM. Therefore, the design flow chart of the TRIM can be divided into three steps: (1) phase decomposition, (2) rotation angle mapping, and (3) hybrid arrangement, as depicted in Fig. 3.

The TRIMs with simultaneous polarization and phase control have been widely used to develop far-field beam generators, but the previously reported works have two limitations: (1) different polarization waves are distributed at different frequency bands, and (2) the information channels exist in single LP or CP waves. This inevitably results in the waste of frequency resources and information overload of multi-user communications.

Hence, in order to effectively solve the thorny problem, as the first example, we demonstrate the construction of a single TRIM1, which integrates independent control of orthogonal CP beams splitting in full space for the incident x-LP waves, i.e., transmitted and reflected LCP and RCP dual beams. The designed TRIM1 comprises 16×16 meta-molecules along x- and y-directions with physical dimensions of 320mm×320mm.

To begin with, as shown in Figs. 4(a) and 4(b), the ideal spatial phase profiles for the above wavefront manipulation in both the Lr-Li channel of meta-atom A and Rr-Ri channel of meta-atom B are separately calculated and discretized into pixels, where a 1-bit encoding strategy including 0 and π is employed. To simplify the presentation, the reflection phases of 0 and π are defined as codes 0 and 1, respectively, which is the same for the transmission phase. Next, the spatial reflection phase distributions of the meta-molecules on the top layer of TRIM1 are then obtained through interleaving those of the two kinds of chiral meta-atoms, as presented in Fig. 4(c). Once the reflection phase distributions are obtained, the suitable rotation angles α1 of the meta-molecules on the top layer of TRIM1 can be determined, as depicted in Fig. 4(d). For the cross-polarized transmitted waves, Figs. 4(e) and 4(f) exhibit the calculated spatial phase profiles in both the Lt-Ri channel of meta-atom A and Rt-Li channel of meta-atom B, and the final transmission phase distributions of the meta-molecules on the bottom layer of TRIM1 are shown in Fig. 4(g). Once the transmission phase distributions are obtained, combined with the known α1, the rotation angles α2 of the meta-molecules on the bottom layer of TRIM1 can be determined according to Appendix A, as illustrated in Fig. 4(h). In the light of the generalized Snell’s law, the deflection angle θ of the dual scattering beams can be calculated as follows: θ=±sin(λ0/Γ)−1,(4)where λ0 is the free-space wavelength of operation frequency and Γ is the period of the coding pattern covering 2π phase range. In the designed examples, based on Figs. 4(a), 4(b), 4(e), 4(f), and Eq. (4), the theoretical deflection angles of the desired dual scattering beams in the Lr-Li channel, Rr-Ri channel, Lt-Ri channel, and Rt-Li channel at 11 GHz are ±20° in the ϕ=0° plane, in the ϕ=90° plane, in the ϕ=90° plane, and in the ϕ=0° plane. For verification, full-wave simulation with open boundary conditions applied for all directions is conducted to record the far-field distributions. See Section 4 for more details of the simulation setup. The simulated 3D normalized far-field scattering patterns are displayed in Figs. 4(i) and 4(j), from which we can observe that in the corresponding CP channels, the reflected and transmitted beams are split into dual beams symmetrically at the predesigned deviation angles, which are in good consistence with theoretical predictions, confirming the manipulation principle of independent control of CP beams splitting in full space.

In the experimental process, the TRIM1 prototype identical to the simulation model is fabricated through a standard commercial PCB technique, and the photographs of the top and bottom layers are presented in Figs. 4(k) and 4(l) with an inset exhibiting the enlarged view of 2×2 meta-molecules. See Section 4 for more details of the prototype fabrication. The far-field experiments of the prototype are implemented on a rotary platform in the microwave anechoic chamber. See Section 4 for more details of the experimental setup. The measured 2D normalized far-field scattering patterns of the prototype in Figs. 4(m)–4(p) reveal that the scattering beams with deflection angles approximately pointed to the theoretical values are generated in the corresponding CP channels and ϕ-planes, and the discrepancy of deflection angles between theoretical and experimental results does not exceed 1°. In addition, the broadband performance of the prototype is measured and provided in Appendix B. Notably, the measured results coincide well with the simulation analysis, in both of which the deflection angles remain consistent with the theoretical predictions. The small discrepancies of the beam direction and slight fluctuations in the scattering curves of the experimental results can be attributed to imperfect fabrication processing and measurement deviations, such as misalignment between the center of the horn antennas and prototype. All in all, the capability of independent control of CP beams splitting enabled by the proposed TRIM1 is successfully demonstrated. Additionally, it should be noted that the designed TRIM for independent beams splitting control is not constrained to LP waves illumination, but can operate under elliptically polarized (EP) waves excitation with the form of EP output state, which is provided in Appendix C.

Vortex beams have promising prospects in future communication applications, which have frequently been reported in extensive literature. By defining the orbital angular momentum (OAM) as l, the azimuthal phase distribution exp(−jlφ) of the spatial wavefront is related to the azimuthal angle phase φ. Vortex beams with orthogonal modes can simultaneously transfer at the same frequency band without interferences. Therefore, they will tremendously enhance the communication capacity without increasing the frequency bandwidth.

In the second illustrative example, a proof-of-concept demonstration of generating LP versatile vortex beams through TRIM2 in full space under excitations of x-LP waves was designed and implemented. The designed TRIM2 has overall dimensions of 400mm×400mm in the xoy plane and 20×20 meta-molecules.

As schematically shown in Fig. 1, this metadevice can yield vortex beams in x-LP, u-LP, y-LP, and v-LP output channels in the reflection and transmission spaces, where u-LP and v-LP waves can be equivalent to a ϕ=45° counterclockwise rotation of x-LP and y-LP waves, respectively. In order to simplify the calculation, we define the topological charges in the four reflection polarization channels and four transmission polarization channels separately as l=+2 and l=−2, and the designed vortex beams for x-LP and y-LP (u-LP and v-LP) states at 11 GHz are emitted to θ=−27° and +27° (θ=+27° and −27°) in the ϕ=90° (ϕ=0°) plane in the reflection and transmission spaces. Subsequently, the anticipated phase profiles necessary for the above functionality are meticulously calculated and merged through Eq. (3). Figures 5(a) and 5(b) depict the ideal spatial phase profiles for the above wavefront manipulation in both the Lr-Li channel of meta-atom A and Rr-Ri channel of meta-atom B, and Figs. 5(c) and 5(d) present the corresponding spatial distributions of reflection phase φ1 and rotation angles α1 of the meta-molecules on the top layer of TRIM2. Also, the required spatial phase profiles in both the Lt-Ri channel of meta-atom A and Rt-Li channel of meta-atom B are calculated, as depicted in Figs. 5(e) and 5(f), and the corresponding spatial distributions of reflection phase φ2 and rotation angles α2 of the meta-molecules on the bottom layer of TRIM2 are deduced afterwards, as illustrated in Figs. 5(g) and 5(h). The simulated 3D normalized far-field scattering patterns are shown in Figs. 5(i) and 5(j), from which the vortex beams that behaves as a concave center x-LP, u-LP, y-LP, and v-LP states with anomalous deflection angles of −27° in the ϕ=90° plane, +27° in the ϕ=0° plane, +27° in the ϕ=90° plane, and −27° in the ϕ=0° plane deviated from the z-axis can be observed in the reflection (transmission) spaces. The simulated results are almost in accordance with the theoretical predictions despite the appearance of some sidelobes mainly attributed to the inevitable coupling between the two kinds of chiral meta-atoms.

To further experimentally validate the performance of the proposed TRIM2, another prototype identical to the simulation model is fabricated, as shown in Figs. 5(k) and 5(l). The inset shows the enlarged illustration of 2×2 meta-molecules. Figures 5(m)–5(p) present the measured 2D normalized far-field scattering patterns of the prototype at the designed frequency of 11 GHz through utilizing the same method mentioned in Section 2.B. Because the eight vortex beams have different polarization states, we measure the scattering patterns for two orthogonal CP waves, and then transform them to obtain the normalized total scattering pattern in terms of power density. The measured results show that the vortex beams for v-LP and u-LP (x-LP and y-LP) states with anomalous deflection angles of −27° and +27° in the ϕ=0° (ϕ=90°) plane are generated in both the reflection and transmission spaces. Moreover, the relatively high degree of coincidence of the curve trend exhibited in Figs. 5(m)–5(p) further proves that the simulated and measured results are in good agreement, verifying the good performance of the proposed TRIM2 in generating LP versatile vortex beams. To investigate the near-field behavior of the vortex beams in each polarization channel, the 2D normalized amplitude and phase distributions of the electric field of the reflective and transmitted wavefronts are also quantitatively detected and numerically characterized, which are provided in Appendix D. What is more, the broadband performance of the prototype is measured and provided in Appendix E.

Eventually, we provide simulated and experimental demonstration of TRIM3 for generating CP and LP multifoci in full space under illuminations of x-LP waves, as schematically shown in Fig. 1. The multifoci characteristic, a particular case of holographic imaging, has been an appealing technique for its capability of modifying light for 3D displays and information storage. The strong desire to increase the information capacity with an ultrathin metasurface has stimulated the messianic motivations for the development of the multifoci multiplexing technique, including wavelength, polarization, and active components, but most of them are constrained to single polarized input/output. Herein, our proposal can achieve four preset focal spots with distinctive representative polarized states in the reflection and transmission space via a single ultrathin metasurface, which might promote the applications of microwave metrology and encryption/decryption.

The designed TRIM3 comprises 16×16 meta-molecules along x- and y-directions and occupies a total area of 320mm×320mm. Here, the focal length is set as F=180mm (or z0=±180mm) apart from the center of the metasurface in both reflection and transmission cases. On the other hand, the positions of the focal spots (x0, y0) in the focal plane z0=+180mm (z0=−180mm) at the frequency of 11 GHz are defined as (−100mm, 0 mm), (0 mm, −100mm), (+60mm, 0 mm), and (0 mm, +60mm) for LCP, RCP, x-LP, y-LP focal spots in the reflection (transmission) space, respectively.

In our design, the electric-field intensities at the LP focal spots are intentionally set as twice those at CP focal spots. Thereafter, the anticipated phase profiles necessary for the above functionality are meticulously calculated and merged through Eq. (3). Figures 6(a) and 6(b) depict the ideal spatial phase profiles for the above wavefront manipulation in both the Lr-Li channel of meta-atom A and Rr-Ri channel of meta-atom B, and Figs. 6(c) and 6(d) present the corresponding spatial distributions of reflection phase φ1 and rotation angles α1 of the meta-molecules on the top layer of TRIM3. Also, the required spatial phase profiles in both the Lt-Ri channel of meta-atom A and Rt-Li channel of meta-atom B are calculated, as depicted in Figs. 6(e) and 6(f), and the corresponding spatial distributions of reflection phase φ2 and rotation angles α2 of the meta-molecules on the bottom layer of TRIM3 are deduced afterwards, as illustrated in Figs. 6(g) and 6(h). For verification, full-wave simulation with open boundary conditions applied for all directions is conducted to record the near-field distributions. See Section 4 for more details of the simulation setup. The numerically simulated normalized electric-field intensity distributions in the plane z0=±180mm at 11 GHz are presented in Figs. 6(i) and 6(j), both of which are calculated via E=Ex2+Ey2. Apparently, different focal spots located at (−100mm, 0 mm), (0 mm, −100mm), (+60mm, 0 mm), and (0 mm, +60mm) are generated with the desired polarization states in the reflection and transmission spaces.

To further experimentally validate the performance of the proposed TRIM3, the last prototype identical to the simulation model is fabricated, as shown in Figs. 6(k) and 6(l). The inset shows the enlarged illustration of 2×2 meta-molecules. Thereafter, the normalized electric-field intensity distributions on the focal xy plane are measured via a 3D field mapping system, which is provided in Appendix F. See Section 4 for more details of the experimental setup. The simulated and measured electric-field intensities at the CP focal spots are approximately one half of those at LP focal spots, with all of them located at the designed positions in the focal plane. Some slight background noise distributed around the focal spots mainly results from the crosstalk of other needless CP output components at predesigned frequency and imperfection in processing and measurement. To give a clear comparison, we portray the simulated and measured normalized field intensities scanned along the line of y=0mm or x=0mm in the plane z0=±180mm, as shown in Figs. 6(m)–6(p). As for the quality of the focal performance, we have further calculated the full width at half maximum (FWHM) of the focal spots with different polarization states, the values of which for both simulated and measured results stand in between 1.05λ0 and 1.72λ0. The measured and simulated results are in good agreement and they are both almost consistent with the theoretical predictions, clearly proving that the relatively high-quality focal spots with four polarization states can be generated and controlled independently in both the reflection and transmission spaces. In addition, the broadband performance of the prototype is measured and provided in Appendix G.

In summary, we propose a generic methodology for achieving arbitrarily polarized independent wavefront manipulation in full space within 8–16 GHz via a single TRIM. A pair of meta-atoms with spin-selective scattering properties is elaborately designed and arrayed in an interleaved manner to construct the tetrameric meta-molecule, which can flexibly and individually tailor the phase response with high amplitude in both orthogonal CP co-polarized reflection and cross-polarized transmission channels. As proofs of concept, three meta-devices based on merged phase modulation, including a CP beam splitting controller, an LP vortex beams generator, and CP and LP multifoci metalenses, have been designed, simulated, and measured at microwave frequency, which have exhibited excellent performance. The proposed TRIM with advanced functionalities goes beyond the previous attempts for specific polarized or single input/output functions. More encouragingly, the operational paradigm can be readily extended to higher frequency spectra such as millimeter-wave and terahertz regions to realize more fascinating phenomena and useful functionalities once the meta-molecules working in corresponding bands are well designed. The proposed metasurface lays a solid foundation for efficiently customizing full-space independent wavefronts with desired polarization states within a shared aperture, which is promising to be applied to ultracompact and integrated systems.

In this work, all simulations were performed using CST Microwave Studio. The simulations of the meta-particle were carried out by the finite-difference frequency-domain (FDFD) technique, in which the boundary conditions of the “unit cell” were set along x- and y-directions, and two Floquet ports were fixed at ±z-directions. The full-wave simulations of the TRIM were implemented via the finite-difference time-domain (FDTD) technique. The boundary conditions of “open (add space)” were set along x-, y-, and z-directions, and a plane wave source encoded with predesigned polarizations was fixed at +z-direction for normal incidence. Through adding the “far-field” and “E-field” monitors in the frequency band of 8–16 GHz with an interval of 0.2 GHz, the corresponding far-field scattering patterns and near-field distributions can be obtained and recorded.

The TRIM prototype was fabricated by a standard PCB technique, which can be divided into approximately three steps: (1) the designed circuit patterns are respectively portrayed on the top dielectric substrate with single-clad copper and the bottom dielectric substrate with double-clad copper via photolithography technology, and the unneeded copper is dissolved through chemical solvent to obtain the desired circuit patterns; (2) the top and bottom structural layers are connected via a hot pressing process utilizing adhesives and drilled via mechanical craft; (3) the surfaces of the prototype are processed with tin plating to improve corrosion resistance.

The far-field and near-field experiments are conducted in a standard microwave anechoic chamber to avoid unwanted scatterings and the noise influence from the surrounding environment, and more details of the experimental setups of reflection and transmission characteristics are provided in Appendix H. For far-field scattering pattern measurement, a pair of 6–18 GHz dual-LP wideband horn antennas and a pair of 8–18 GHz dual-CP wideband horn antennas are utilized as the transmitter and the receiver to produce the required incidence and measure the output EM characteristics. The fabricated prototype is vertically placed on the supporting foam upon the experimental platform, and the transmitter and the receiver are placed at a distance of 25λ0 away from the prototype, mimicking the quasi-plane waves within the frequency band of interest. Both the transmitter and the prototype are mounted on a rotary platform capable of mechanical rotating in the horizontal plane, and the receiver is fixed to measure the wave energy at various azimuthal angles with a fixed interval of 1°. For near-field mapping measurement, the LP horn antenna as the transmitter is placed 25λ0 apart from the prototype, which is vertically set on the supporting foam on the experimental platform, and the scanning coaxial probe as the receiver is placed in front of and behind the prototype with distance of focal length z0 for measuring the reflection and transmission performance, respectively. More specifically, the probe located in the center of the focal plane is driven by the motion controller with a fixed step of 5 mm along both x- and y-directions to measure the amplitude and phase profiles of the electric field in the predesigned region, and the measurement system can record x-LP and y-LP electric field data synchronously. Accordingly, on the basis of the formula E=Ex2+Ey2, the total normalized electric-field distributions can be obtained. In both measurement systems, the transmitters and the receivers are connected to an Agilent N5224A vector network analyzer, which is adopted to measure the complex S21 parameters including the amplitude and phase.