1. Introduction

Metasurfaces, i.e., the planar version of metamaterials, have shown unprecedented ability for manipulating electromagnetic (EM) waves with ultrathin thickness. By introducing field discontinuities across an interface, metasurfaces comprising subwavelength-scaled elements can flexibly control the phase, polarization, and amplitude of EM waves [1–10]. In particular, metasurfaces exhibit the significant advantages of flexible phase-front control over traditional methods through phase accumulations, e.g., curved dielectrics. In this regard, numerous metadevices have emerged in the past decade, such as beam deflectors [11,12], meta-lenses [13,14], vortex beam generators [15,16], and holography [17,18]. To facilitate integration with digital circuit systems, phase-tailoring metasurfaces have recently been developed into digital and coding metasurfaces [17] that connect physics and information science. In general, the 2π phase shift is divided by 2ⁿ to produce n-bit coding elements. Moreover, by introducing a field-programmable gate array and active elements, e.g., PIN diodes, the coding metasurfaces are further developed in a programmable manner, enabling a series of time-multiplexing EM functionalities that may be vital to wireless communication and EM integration. [19,20] Because active elements and hard-ware control systems are used, such metasurfaces are often complex with relatively high energy loss.

Meanwhile, passive metasurfaces enable multiple EM functionalities through various flexible multiplexing techniques, such as polarization [21–25], spin [26–28], frequency [29–31], and direction multiplexing [32], which afford advantages of low cost, low loss, and easy integration. The reliability and flexibility of these multiplexing techniques render multifunctional metasurfaces suitable for numerous applications, including information encryption and high-speed and high-capacity wave processing using an assembly of independent channels. For polarization-controlled multifunctional metasurfaces [21–23], it has been reported that linearly birefringent meta-atoms can be used for decoupling the wave functions of arbitrarily orthogonal linear-polarizations [24,25] or circularly polarizations by combining geometric and propagation phases [26–28]. Frequency-dependent metasurfaces can be used to realize multiple EM functionalities. For example, dual-band metasurfaces are widely employed for achieving dual functionalities, even though most of them can only operate for specified polarizations [29,30]. To achieve more functionalities, multiband metasurfaces are used; however, they are often accompanied by high frequency cross-talk that may affect the device performance [31]. By breaking the out-of-plane symmetry, the chiral metasurface can realize different functions for opposite propagation directions, enabling direction-selective versatile functionalities [32]. Although numerous studies have focused on multifunctional metasurfaces, a bottleneck still exists because most of them utilize a single degree of freedom to enable different wave functions, such as polarization, frequency, and direction, which may limit the information capacity of metadevices. The ultimate goal pursued by scientists and engineers is to integrate as many independent channels as possible in a single metasurface to maximize the information capacity of the metasurface. Notably, the designed polarization channels should be orthogonal to avoid unwanted speckle noise induced by the polarization cross-talk. Hence, the dual-band metasurface can maximally support four different polarization channels. However, few metasurfaces have been realized thus far, particularly those with broad operation bands in all desired polarization channels.

Herein, we propose a dual-band metasurface with two independent functionalities encoded in the orthogonally linear polarization channels at low frequencies, as well as two distinct functionalities in the orthogonal spin channels at high frequencies. An optimized meta-atom composed of quasi-I-shaped and cross-shaped structures is constructed to empower four independent phase responses for different polarizations at the meta-atom level. Subsequently, an assembly involving beam deflection, diffuse scattering, and vortex beam generation is designed to form a multifunctional metadevice, as schematically shown in Fig.  1. Four independent wave functionalities, determined by the incident frequency and polarization, can be observed as the collective result of the secondary scattered wave from the metasurface with a predefined spatial phase distribution.

 

Fig. 1. Conceptual illustration of multifunctional metasurface with four independent polarization channels. Herein, F₁, F₂, F₃, and F₄ represent four independent functionalities, whereas f₁ and f₂ represent different frequency bands. Inset of left panel shows topology configuration of meta-atom.

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2. Theory and meta-atom design

First, a meta-atom capable of modulating the independent phase in two frequency bands is designed. Previous metasurface technologies have suggested various methods for realizing dual-band operation, including dual-layer structures [30], multi-order mode generation [33], and combinations of multiple elements with different geometries [34]; however, they only support a few polarization channels. In this study, we integrate a cross-shaped structure and four quasi-I-shaped patterns in a single metallic layer to form the meta-atom, which affords advantages of simple structure configuration, easy fabrication, potential in broadband performance, and capability of introducing independent phase responses for orthogonally polarized incidence. Because the resonances of the cross- and quasi-I-shaped structures are closely associated with their geometric footprint, the periodicity of the cross-shaped structure is set as twice that of the quasi-I-shaped structure, providing the possibility for independent phase modulations in the two bands. Specifically, the cross- and quasi-I-shaped structures resonate at low and high frequencies, respectively. The optimized topology configuration of the meta-atom is schematically shown in the inset of Fig.  1(a), where the metallic pattern and ground plane are separated by a substrate (FR4 Epoxy Glass Fabric Laminated Sheet) with a dielectric constant of 4.3 and a loss tangent of 0.01. In the next section, we will first discuss the reflection properties of the meta-atom at low frequencies and then present the design of the desired EM responses at high frequencies. Additionally, the frequency and polarization cross-talk will be investigated.

The cross-shaped structure is well known for its linearly birefringent properties. In other words, the lengths of the two arms along the x- and y-directions, denoted as l_x and l_y in the inset of Fig.  1(a), respectively, can be adjusted to impose independent phase shifts to x- and y-linearly polarized (LP) waves, respectively. To verify this, commercial software CST Microwave Studio is used to investigate the reflection properties of the designed meta-atom using a frequency-domain solver. Unit-cell boundary conditions are applied along both the x- and y- directions, and the variation of the meta-atom’s EM responses are observed under normal x- and y-LP incidence by tuning parameters l_x and l_y, respectively. Furthermore, other geometric parameters of the meta-atom are fixed as h = 2.5 mm, p = 11 mm, d = 3.5 mm, α = 76°, and φ = 45°. The wire width of the arc is set to 0.4 mm, whereas that of the connecting rod to 0.2 mm. Four sets of parameters are selected to achieve independent 1-bit phase manipulation for x- and y-LP incidence. The reflective amplitude and phase of the meta-atom under x-LP incidence are plotted in Figs.  2(a) and 2(c), respectively. High-efficiency co-polarized reflection can be observed in the range of 6–10 GHz, and a phase difference of 180° around 8 GHz is realized under x-LP illumination. More importantly, the phase responses under x-LP incidence are only determined using l_x, as shown in Fig.  2(c), where a change in the parameter l_y does not affect the phase curve for x-LP incidence. Moreover, owing to the rotational symmetry of the meta-atom, the same high-efficiency co-polarization reflection is achieved for y-LP incidence, as shown in Fig.  2(b). Figure  2(d) illustrates a phase difference of 180° around 8 GHz under y-LP incidence, as determined using only l_y. The results above show that a 1-bit coding phase is independently obtained for x- and y-LP incidence by correspondingly tuning l_x and l_y, with negligible polarization cross-talk.

 

Fig. 2. Performance of meta-atom in low-frequency band. (a) Reflection amplitude and (c) phase of meta-atom under x-LP incidence. (b) Reflection amplitude and (d) phase of meta-atom under y-LP illumination.

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Next, we explain the construction of 1-bit digital phases for left-hand circular polarization (LCP) and right-hand circular polarization (RCP) in the high-frequency band. In this regard, the parameters of the quasi-I-shaped structure are tuned to achieve decoupled phases for LCP and RCP waves, in addition to the abovementioned scheme for LP waves in the low-frequency band. In our previous study [28], we discover that by synthesizing the Jones matrix of the meta-atom, two half-wave plates with a phase difference of 90° can form a 1-bit coding metasurface independent of orthogonal spins. Hence, the cross-polarized reflection coefficients and phases of the meta-atom under y-polarized incidence in the high band are investigated by fixing l_x and l_y at 10.2 mm but increasing α from 76° to 140°. The simulation results are shown in Figs.  3(a) and 3(b). The near-unity cross-polarization reflectivity exhibited in Fig.  3(a) shows that each meta-atom functions as a half-wave plate. In addition, a phase difference of 90° across the frequency band from 14 to 17 GHz is depicted clearly in Fig.  3(b). Hence, the capability of the proposed meta-atom in generating independent 1-bit phase modulation for two orthogonal spins is validated using the abovementioned spin-decoupled strategy. By tuning the rotation angle φ, the phase difference between different meta-atoms can be manipulated. The optimized parameters of the meta-atom for forming the 1-bit spin-decoupled coding phases are listed in Table  1. The reflection curves of these meta-atoms under RCP illumination are shown in Figs.  3(c) and 3(e), whereas those under LCP illumination are shown in Figs.  3(d) and 3(f). The high efficiency of the reflectivity is clearly indicated, where most amplitudes exceed 0.9, and a free combination of 0° and 180° phases can be obtained in the 13–17 GHz band. Using these four meta-atoms, a spin-decoupled 1-bit metasurface capable of channeling independently different circularly polarized waves can be formed. Moreover, excellent polarization isolation between the LCP and RCP waves is demonstrated; i.e., the phase responses for the LCP wave imposed minimal effect on the RCP responses, and vice versa.

 

Fig. 3. Performances of meta-atom in high-frequency band. (a) Cross-polarized reflection coefficient and (b) phase of meta-atom under y-polarized incidence. (c) Co-polarized reflection coefficient and (d) phase of meta-atom under LCP incidence. (e) Co-polarized reflection coefficient and (f) phase of meta-atom under RCP incidence.

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Table 1. Geometric parameters of coding elements for LCP and RCP in higher band.

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Negligible frequency cross-talk is an important criterion for frequency multiplexing. Hence, the isolation between the two operating bands is evaluated. As depicted in Figs.  4(a) and 4(b), the reflection responses for the LCP and RCP waves at high frequencies are determined by the geometry of the quasi-I-shaped structure, which is not affected by the arm length adjustments of the cross-shaped structure, demonstrating that the operation at low frequencies does not affect that at high frequencies. Meanwhile, Figs.  4(c) and 4(d) show that modulation of the quasi-I-shaped structure imposes minimal effect on the reflection properties in the low-frequency band. In summary, low polarization and frequency cross-talk are observed on the proposed metasurface, providing four independent polarization channels for wave manipulation at the meta-atom level.

3. Design and performance of multifunctional metadevice

As a proof of concept, distinct phase distributions are imposed in four polarization channels to actualize four independent EM functionalities, which are then interpreted by real meta-atoms with spatially varying distributions. The emergent far-field three-dimensional (3D) patterns, which are twin-beams along the diagonal direction, diffusive scattering, twin vortex beams in the xoz plane, and twin-beam in the yoz plane, are schematically illustrated in Figs.  1(b), 1(c), 1(d) and 1(e), respectively.

 

Fig. 4. Cross-talk performance between two operating bandwidths. Co-polarized reflection coefficients and phases of meta-atom under (a) LCP and (b) RCP incidence with tailored cross-shaped structure. The parameters are fixed as α = 76° and φ = 135°. Co-polarized reflection coefficients and phases of meta-atom under (c) x- and (d) y-polarized incidence with modulated quasi-I-shaped structure. The parameter l_y is fixed as 10.5 mm and parameter l_x is fixed as (c) 8.5 mm and (d) 10.2 mm.

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The desired phase profile for beam deflection under normal incidence can be deduced from the generalized Snell laws as follows [2]:

The first functionality, denoted as F₁ in Fig.  1(b), is set as twin-beam deflection with (θ_r1, φ_r1) = (−30°, −45°) and (θ_r2, φ_r2) = (30°, 135°) under x-LP illumination at low frequencies. Hence, the phase profile for obtaining F₁ can be determined using Eq.  (1) and then discretized into a 1-bit coding pattern, as shown in Fig.  5(a). Diffusive scattering, denoted by F₂ in Fig.  1(c), is imposed on the y-LP channel at low frequencies. A supercell composed of 2 × 2 identical meta-atoms is used and the metasurface contains 16 × 16 supercells. The random phase profile shown in Fig.  5(b) is employed to destroy the planar incident wavefront and redistribute the incidence into numerous directions such that diffusive scattering can be achieved to reduce the backward radar cross section (RCS) of the metadevice. The third functionality (denoted as F₃) for LCP at high frequencies is set to generate twin vortex beams, and the phase profile is depicted in Fig.  1(d). To design such a phase profile, a spiral phase profile is superimposed onto the anomalous deflection described by Eq.  (1), and it can be expressed as

Here, m is the mode of the generated vortex beam. With the goal set as twin vortex beams with (θ_r1, φ_r1, m) = (20°, 0, 2) and (θ_r1, φ_r1, m) = (−20°, 180°, 2), the spatial phase distribution for obtaining F₃ can be acquired by discretizing Eq.  (3), as illustrated in Fig.  5(c). As for the RCP incidence at high frequencies, a twin-beam deflection with (θ_r1, φ_r1) = (30°, 90°) and (θ_r2, φ_r2) = (−30°, −90°) is implemented as the design example; meanwhile, the corresponding phase profile shown in Fig.  5(d) is acquired using Eq.  (1) and discretizing the result into a 1-bit coding pattern. Subsequently, these four phase profiles are interpreted by real meta-atoms based on the one-to-one mapping relationship between the phase response and structure parameters of the meta-atoms under linearly and circularly polarized incidences; the corresponding distributions of the coding states are shown in Fig.  5(e). In particular, the distribution of the cross-shaped structures can be achieved straightforwardly by combining the phase profiles shown in Figs.  5(a) and 5(b), that is to arrange the parameters l_x and l_y of each meta-atom according to the phase profiles shown in Figs.  5(a) and 5(b), respectively. As for the distribution of the quasi-I-shaped structures, it can be obtained by referring to the coding states shown in Table  1. Once the distributions of the cross- and quasi-I-shaped structures are determined, the metadevice is fixed and fabricated, as shown in Fig.  5(f).

 

Fig. 5. Phase distribution and metasurface configuration. Phase profiles for (a) x- and (b) y-polarizations at lower frequency. Phase profiles for (c) LCP and (d) RCP at higher frequency. (e) Coding sequence of quasi-I-shaped structures. (f) Photograph of fabricated prototype. Inset shows enlarged view of four supercells.

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To validate the design principle and the proposed metasurface, full-wave simulations and experimental verifications are performed on the multitasking metasurface sample shown in Fig.  5(f). The sample covering an area of 352 × 352 mm² is utilized, which is sufficiently large to accommodate the plane-wave-like incident beam. The simulation is performed with open (add space) boundary conditions applied along all directions of the metasurface sample using the time-domain solver in CST Microwave Studio. The performances under normally x-LP incidence at low frequencies are shown in Fig.  6. Figure  6(a) depicts the normalized 3D far-field scattering pattern at 8 GHz, where the incident wave is separated into two symmetric beams tilted at the same deflection angle, consistent with our expectations from the theoretical analysis. The beam deflection performance is quantitatively evaluated based on the simulated and measured 2D scattering patterns in the diagonal plane at 8 GHz, as shown in Fig.  6(b). The measured results agree with the simulated ones, i.e., an anomalous deflection angle of ${\theta _r} ={\pm} 23^\circ$, which is consistent with theoretical result of 23.3°. The measured beam width is slightly larger than the simulated value, primarily because the radiation wave generated from the horn antenna is not exactly an ideal plane wave illumination. To analyze the bandwidth performance of the proposed metasurface, we plot the two-dimensional (2D) scattering patterns as a function of the frequency and deflection angle, as shown in Fig.  6(c). The 2D hot graph, green dashed lines, and white circles represent the simulated, theoretical, and measured beam deflection angles, respectively. The simulated and measured deflection angles agree well with the theoretical ones and indicate an ambiguous deflection effect across the band from 7 to 8.5 GHz, demonstrating the broadband performance under x-LP illumination.

 

Fig. 6. Performances of proposed metasurface for (a–c) x- and (d–f) y-LP incidence. (a, d) Simulated 3D scattering pattern at 8 GHz. (b) Simulated and measured normalized scattering patterns in diagonal plane at 8 GHz. (c) Normalized scattering patterns in diagonal plane within 6–10 GHz. (e) Simulated and (f) measured backward scattering reduction results under oblique incidence.

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The simulated 3D scattering pattern for the y-LP incidence at 8 GHz is shown in Fig.  6(d), where the y-LP beam is randomly redirected to numerous directions to invoke diffuse scattering, indicating that backward scattering can be reduced significantly. To characterize the performance of the scattering reduction, the far-field radiation patterns of the sample are measured in a standard microwave anechoic chamber, where the transmitting and receiving horn antennas are placed symmetrically on two sides of the yoz plane. Additionally, a metallic plate of identical size is measured as the reference. The simulated and measured results for the y-LP incidence are plotted, as shown in Figs.  6(e) and 6(f), respectively. The backward RCS reduction is measured from 5° to 40° at an interval of 5°. The measured results agree relatively well with the simulated ones, demonstrating that the backward scattering can be suppressed by more than 10 dB over the range of 7.4–8.7 GHz as the oblique incident angle increases up to approximately 30°. Some non-negligible loss induced by realistic material, imperfect fabrication, and measurement may cause the additional peaks of the measured results in the neighborhood of 7.7 GHz for near-normal incidence (0°−15°), which make no difference on the performance of F₂. Inevitably, with an increase in the incident angle, the performance of backward scattering reduction deteriorates gradually. However, 6-dB scattering suppression remains from 7.4 to 8.7 GHz when the oblique angle reaches up to 40°, demonstrating a robust angular performance for y-LP incidence.

Figure  7(a) shows the simulated 3D scattering pattern at 15 GHz under the illumination of the LCP plane wave. As shown, two vortex beams are generated in the xoz plane, consistent with the function predesigned for LCP incidence. Figure  7(b) shows the simulated spiral phase profiles of the generated beams, where the vortex beams carrying orbital angular momentum with modes of ±2 are observed. To further validate our design, a far-field experiment is carried out to measure the performance of the vortex beams. The normalized scattering patterns in the xoz plane are shown in Fig.  7(c), where the results are calibrated to the maximum value of a metallic plate of identical size for a clearer depiction. The green line represents the theoretical deflection angle, whereas the white circles represent the measured angles of the energy null of the vortex beams. It is evident that the measured results agree well with the simulated ones, proving that the deflection angle of the vortex beam is approximately ${\theta _r} ={\pm} 19^\circ$, consistent with the theoretically designed one. In addition, the generated twin vortex beams can be observed clearly across the 13–17 GHz band, confirming the broadband characteristic of the designed metasurface under LCP incidence.

 

Fig. 7. Performances of proposed metasurface under illumination of (a–c) LCP and (d–f) RCP wave. (a, d) Simulated 3D scattering pattern at 15 GHz. (b) Phase profiles of conical beams deflected in xoz plane at 15 GHz. Normalized scattering patterns in (c) xoz and (f) yoz plane within 13–17 GHz band. (e) Simulated and measured normalized scattering patterns in yoz plane at 15 GHz.

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Finally, the performance of the designed metasurface under RCP illumination at high frequencies is investigated experimentally. The simulated normalized 3D scattering pattern at 15 GHz depicted in Fig.  7(d) shows a twin-beam in the yoz plane, as predicted by theoretical calculations. A comparison of the simulated and measured normalized scattering patterns in the yoz plane is shown in Fig.  7(e). The measured results are consistent with the simulated ones, validating the deflection effect with a deflection angle of ${\theta _r} ={\pm} 29^\circ$. The 2D scattering patterns in the yoz plane as functions of frequency and detection angle are shown in Fig.  7(f). As shown, the 2D hot graph, green dashed lines, and white circles represent the simulated, theoretical, and measured beam deflection angles, respectively. The simulated and measured results are consistent with the theoretical results, verifying the broadband anomalous deflection performance under RCP incidence.

4. Conclusion

In summary, we proposed a quad-channel shared aperture empowered by a frequency-polarization multiplexing metasurface; it imparts four distinct phase profiles in four polarization channels, enabling two independent functionalities for two orthogonal LPs at low frequencies and two decoupled functionalities for different spins at high frequencies. Excellent beam control was demonstrated both in simulations and experiments, as evident by four different functions achieved on a shared metasurface aperture that included beam deflections, diffuse scattering, and vortex beam generation. The measured results agreed well with the numerically simulated and theoretically calculated results. We envision that the proposed concept can be extended to triple- and multiple-band coding metasurfaces as well as to other frequencies, e.g., terahertz and optical spectra, thereby realizing frontier research pertaining to information processing, encryption communication, etc.