In microwave communication systems, the focusing and imaging have attracted widespread attention due to their application prospects in the information processing and communication fields [1,2]. At the early stage, the focusing and imaging depend mainly on the traditional optical elements regulating the light direction and their combined optical systems, such as the active-plasma lens, Alvarez lens, geometric lens, off-axis interferometers, Fourier transform lens, and spatial light modulators [3–6]. Although obtaining remarkable achievements in the focusing and imaging techniques, the traditional methods still have some limitations of large sizes and complicated systems. To solve the above shortcomings, therefore, it is a highly pressing requirement for novel structures and devices.

Metasurfaces, as artificial structures consisting of two-dimensional arrays of periodic sub-wavelength elements, have attracted considerable attention due to their flexible control of electromagnetic (EM) waves [7]. Owing to their unique properties, metasurfaces have been tremendously applied in diverse fields, such as wavefront control [8,9], cloaking [10,11], sensing and detection [12], and biomedical diagnosis and treatments [13]. For the focusing and imaging, especially, various metasurfaces have been proposed and demonstrated [14–18]. For example, the reflected metasurface based on single-layer bowtie structures can reconstruct single-plane and double-plane holographic images at 13 GHz under the LCP incidence [19]. A reflection metasurface consisting of circular split-ring resonators has been demonstrated for a broadband metalens [20]. However, these metasurfaces can operate in only single-channel mode, which is unfavorable for the large-capacity communications and multifunctional applications. To further improve the channel numbers, two different schemes on the stacked metasurfaces and interleaved metasurfaces have been extensively studied in recent years [21]. Among them, the stacked metasurfaces are created by stacking various structural layers regulated independently to shape different wavefronts [22], while the interleaved metasurfaces are constructed by randomly interspersing several different sub-arrays manipulated independently to implement multiple wavefronts [23]. Generally, the interleaved metasurfaces can be regarded as the integration of two or more metasurfaces without structural overlap. Due to their simple fabrication processes, currently, various interleaved metasurfaces have been widely developed for the wavefront control [24,25]. For example, Zhang et al. experimentally demonstrated a polarization-multiplexing interleaved metasurface composed of rod- and C-shaped slot antennas, and multi-image hiding and seeking are revealed by controlling the polarization states of the incident and detection light [26]. Zhang’s group proposed a dielectric interleaved metasurface composed of two independent anisotropic dielectric meta-atoms for the polarization-dependent metahologram [27]. Yao’s group fabricated the spatially interleaved metasurfaces for the separate vortex focusing of single-frequency dual beams and achromatic focusing [28]. Nevertheless, these interleaved metasurfaces mentioned above suffer from the limitations of the large size and low efficiency, which hinders the development of the high-resolution imaging and integrated systems. Therefore, it is highly desirable for the novel metasurfaces enabling high-efficiency multi-channel focusing and imaging.

To address the above problems, in this paper, we propose and demonstrate polarization-frequency multiplexing non-interleaved metasurfaces for high-efficiency multi-channel focusing and imaging. The meta-atoms of the non-interleaved metasurfaces are constructed by stacking a metallic ground layer, two dielectric layers, a larger cross-shaped metal structure, and a smaller cross-shaped metal structure embedded by a circular metal aperture. By changing the sizes of two cross-shaped structures, the designed meta-atom can obtain an independent complete 2π phase coverage at two different frequency ranges for two orthogonal linear polarization (LP) incidences, realizing polarization multiplexing and frequency multiplexing. Thus, two non-interleaved metasurfaces constructed by the above meta-atoms can realize four-channel focusing and imaging with high efficiency at different operation frequencies by varying the incident polarization states, as displayed in Fig. 1. As a proof, we experimentally fabricate a focusing metasurface composed of 30×30 meta-atoms, and four focal points can be clearly observed, which is in great agreement with simulated results. Therefore, the proposed scheme displays the advantages of high efficiency, multi-channel, and compact size, which paves an avenue for the development of large-capacity compact systems.

Generally, the electric field vector of the plane EM waves that propagate along the z-axis can be described by the expression [EixEiy]=[EixeiφixEiyeiφiy]ei(ωt−kz).Thus, the relation between the input and reflected electric fields can be described by the Jones matrix [ExrEyr]=J[EixEiy](J=R=[rxxrxyryxryy]=[|rxx|eiφxx|rxy|eiφxy|ryx|eiφyx|ryy|eiφyy]).For the birefringent meta-atom, its structure is symmetric about its long axis and short axis, so rxx≠ryy≠0,rxy=ryx=0. When the incident wave is LP, the reflection electric fields can be expressed as [ExrEyr]=[|rxx|eiφxx·Eix|ryy|eiφyy·Eiy],where |rxx| (|ryy|) and φxx (φyy) represent the reflection amplitude and phase response of the meta-atom in the co-polarization channel under the x-LP (y-LP) incidence, respectively. The above expression indicates that the intensity and phase of the reflection electric fields depend only on the amplitude and phase of the co-polarization channel and can be independently controlled. Therefore, the high reflection and independent 2π phase coverage of the meta-atoms can realize the high-efficiency multifunctional devices.

To achieve high-efficiency multi-channel focusing and imaging, the meta-atom must satisfy the requirement of independent phase manipulation in each channel. Here, we design non-interleaved metasurfaces based on the birefringent meta-atoms consisting of five layers: a metallic ground plate, two dielectric layers, a larger cross-shaped metallic structure, and a smaller cross-shaped metallic structure embedded by a circular metallic aperture, as shown in Fig. 1. In this meta-atom, two non-interleaved cross-shaped elements can not only realize dual-frequency operation and small size but also avoid the interlayer crosstalk. By changing the dimensions of the cross-shaped structures, moreover, independent complete 2π phase coverages with high reflection can be obtained at two different frequency ranges under two orthogonal LP incidences. Additionally, the circular metallic aperture can not only avoid the intralayer crosstalk between adjacent meta-atoms but also enhance reflection efficiency. Compared with previously reported structures [21,29], our non-interleaved structures enable not only the polarization-frequency multiplexing but also high reflection efficiency for two orthogonal LP incidences.

To examine the performance of the designed meta-atom, full-wave simulations are performed using the finite-difference time-domain (FDTD) method [30]. Here, the incident x-LP wave is normally illuminated onto the meta-atom along the −z direction, the unit cell boundaries are applied in the x and y directions, and the open add space boundary is applied in the z direction. In the numerical calculations, the optimized size parameters of the meta-atom are as follows: p=10mm, h=2mm, d=0.035mm, r=4.7mm, w=1mm, u1=9.4mm, v1=9.4mm, x1=5.1mm, y1=7.6mm. In addition, the F4B with a dielectric constant ε=2.65 and a loss angle tangent tanδ=1.3×10−3 is used as the dielectric substrates, while the copper with a conductivity of 5.8×107S/m is used as cross-shaped structures, circular aperture grid layer, and ground plate. Figure 2 shows the simulated co-polarization reflection amplitude and phase spectra of the meta-atom with different parameter sizes for LP incidence. Figure 2(a) presents the influence of the parameter u1 on the co-polarization amplitude and phase for x-LP incidence. It is noticed that a complete 2π phase coverage with a reflected amplitude of more than 0.95 can be obtained at 8.0 GHz as the parameter u1 gradually increases from 7.0 to 9.5 mm with interval of 0.5 mm. Similarly, another whole 2π phase coverage with a reflection amplitude of more than 0.98 can be obviously observed at a frequency of 15.0 GHz by gradually increasing the parameter x1 from 3.0 to 8.0 mm with the interval of 1.0 mm, as displayed in Fig. 2(b). Furthermore, similar results can be also achieved at the same frequency for y-LP incidence due to the structural symmetry of the birefringent meta-atom. Additionally, to verify the robustness of the meta-atoms in a non-ideal environment, the reflection amplitude and phase characteristics of the meta-atoms at different incidence angles are further simulated under two orthogonal LP incidences, as displayed in Figs. 2(c)–2(f). It can be observed that with the increase of the incidence angle from 0° to 90°, the amplitudes at 8.0 GHz and 15.0 GHz remain always constant for LP incidence, while below the incidence angle of 60°, the phases at 8.0 GHz and 15.0 GHz stay unchanged. These results indicate that the designed meta-atoms exhibit high insensitivity to the incidence angles, which is favorable for practical applications. According to the amplitude and phase responses obtained above, the non-interleaved meta-atoms with a phase difference of 180° at 8.0 GHz and 15.0 GHz under two orthogonal LP incidences are selected as the meta-atom library, as shown in Fig. 3. Therefore, these results demonstrate that the non-interleaved meta-atoms can execute independent 2π phase coverage with a high reflection amplitude for two operating frequencies and polarization states, realizing frequency multiplexing and polarization multiplexing with high efficiency.

To further explore the multiplexing and crosstalk mechanisms, the electric field distributions of the meta-atom at 8.0 GHz and 15.0 GHz are calculated for LP incidence, as shown in Fig. 4. At 8.0 GHz, strong electric fields are mainly distributed on the edge of the larger cross-shaped metallic structure, whereas the smaller cross-shaped structure exhibits ignorable electric fields, indicating negligible crosstalk between the structural layers, as shown in Figs. 4(a) and 4(b). Moreover, the electric fields on the larger cross-shaped structure are mutually vertical and immune for x-LP and y-LP incidences, thus, realizing the polarization multiplexing. At 15.0 GHz, similar results are also observed for the smaller cross-shaped structure, as shown in Figs. 4(c) and 4(d). Thus, the frequency multiplexing can be also obtained. In addition, the circular metal aperture structure can not only improve the reflection amplitude by the interlayer interaction but also avoid the intralayer crosstalk between adjacent meta-atoms by the screening effect, as demonstrated in previous reports [29,31].

To realize the high-efficiency and multiple multiplexing of the non-interleaved metasurfaces, two different types of non-interleaved metasurfaces (metalens and metaholography) consisting of 30×30 meta-atoms (300mm×300mm) from the above meta-atom library are designed for multi-channel focusing and imaging with high-efficiency, respectively. By regulating the polarization states of the LP incidences, the metalens and metaholography can generate four independent focal points and holographic images at 8.0 GHz and 15.0 GHz, respectively.

For the metalenses [32,33], generally, their spatial phase profile is formulated by φF(x,y)=2πλ(x2+y2+F2−F), where λ is the wavelength of the incidence wave, x and y indicate the center position coordinates of each meta-atom, and F is the focal length. According to the above expression, the phase distributions of the metalens with F1=150mm, F2=200mm, F3=60mm, and F4=100mm at different polarization states and operation frequencies are extracted, as shown in Fig. 5.

Figure 6 exhibits the electric field distributions of four focal points generated by the metalens at LP incidence. At 8.0 GHz, strong electric fields are focused on the xoz-plane to form a focal point with a focal length of F1=146mm under the x-LP incidence, as shown in Fig. 6(a). For y-LP incidence, a focal point with a focal length of F2=193mm can be effectively generated, as shown in Fig. 6(b). However, for 45° LP incidence, two focal points are combined into a focal point with a longer focal depth due to the close focal length between them, as displayed in Fig. 6(c). Such phenomenon results from the fact that the 45° LP can be decomposed into two orthogonal x-LP and y-LP. At 15.0 GHz, two focal points with focal lengths of F3=63mm and F4=101mm can be achieved under two orthogonal LP incidences, as shown in Figs. 6(d) and 6(e). For 45° LP incidence, the above two focal points can be observed simultaneously, as shown in Fig. 6(f). Moreover, the simulated focal lengths agree well with the theoretical values. Therefore, the metalens can generate four independent focal points at 8.0 GHz and 15.0 GHz for LP incidence.

To further examine the working bandwidth of the metalens, the focusing capacities at different frequencies are calculated and analyzed, and the corresponding electric field distributions on the focusing plane (xoy-plane) are shown in Fig. 7. For x-LP incidence, when the operating frequency gradually increases from 7.0 GHz to 8.0 GHz and from 13.0 GHz to 17.0 GHz, respectively, the incidence waves can be efficiently converged in various focusing planes and the corresponding focal length shifts from 96 mm to 146 mm and from 45 mm to 87 mm, as shown in Fig. 7(a). For y-LP incidence, a similar change trend in the focal length can be clearly observed, as shown in Fig. 7(b). Therefore, these results verify that the metalens can realize broadband focal points for two orthogonal LP incidences.

To quantitatively evaluate the focusing performances of the metalens, generally, the numerical aperture (NA), focusing efficiency (η), and diffraction limit (DL) are used to characterize the performances of the lenses. In these parameters, the NA presents the angular range of light collected by the lenses, which determines the optical capacity and spatial resolution of the lenses, η describes the focusing ability of the lenses, and DL is the limit of imaging resolution in an optical imaging system due to diffraction. They can be calculated by the expressions [34–36] η=PFPI=∑pFds′∑pIds, NA=n×sin(arctan(D/2F)), and DL=λ2NA, where PF is the focal point energy in the three times FWHM range, PI is the total energy of the incident light, n is the refractive index of the medium, D is the size of the metasurface, and F is the focal length. For our metalens, the detailed focusing performance parameters are shown in Table 1 for different polarization incidences. It is observed that for y-LP incidence, the metalens can simultaneously obtain a maximum η of 93.19% and a maximum DL of 31.75 mm at 7.5 GHz, while only a maximum NA of 0.97 can be achieved at 13.0 GHz for x-LP incidence. Moreover, all the calculated DLs are larger than the corresponding FWHM values, meaning that our metalens can execute the ultra-diffraction focusing. Additionally, to further verify the focusing superiority of our metalens, a comparison between our results and the previous reports is analyzed, as shown in Table 2. It can be observed that the proposed metalens can realize four independent focal points with high focusing efficiency and large NA at two different frequency ranges.Table 1.

Performance Parameters of the Designed Metalens at LP Incidence

Currently, the metaholography enabled by metasurfaces has shown broad application prospects in the data communication and encryption fields. Here, the target images are first dispersed into a number of independent focal points. Then, according to the positional distribution of each focal point, the phases of all meta-atoms in the metasurface are extracted utilizing the Gerchberg-Saxton (GS) algorithm [42–44]. After multiple iterative computations, the phase distribution gradually tends to be smooth. Such metasurface can transform the incident waves into the target images completely, generating the holographic image. For our holographic imaging, thus, its spatial phase profile is formulated by φH(x,y)=arg(∑m=1MeikrnmEmrnm|Em|),where m is the mth focus point in the target image, n is the nth meta-atom of the metasurface, Em is the superposition of the electric field components at the mth focus point of the target image, rnm is the distance between the nth meta-atom and the mth focal point position, and k is the phase constant.

Figure 8 displays the target images and holographic images on the imaging plane (xoy-plane) at 8.0 GHz and 15.0 GHz under two orthogonal LP incidences. The target images of the letters “L”, “O”, “T”, and “U” correspond to the x-LP and y-LP channels at 8.0 GHz and 15.0 GHz, respectively. At 8.0 GHz, the holographic images of the letters “L” and “O” can be clearly recorded at z=80mm for LP incidence, as shown in Figs. 8(a) and 8(b). However, at 15.0 GHz, the images of “T” and “U” can be obtained at z=200mm for LP incidence, as shown in Figs. 8(c) and 8(d). Moreover, the reconstructed holographic images agree well with the target images. To further evaluate the imaging quality, here, the imaging efficiency is defined as the part of incident wave energy that contributes to the holographic image [45,46]. The calculated imaging efficiencies for the four holographic images (“L”, “O”, “T”, and “U”) are 62.57%, 66.23%, 69.88%, and 71.21% respectively, which are higher than the previous results [47,48]. Additionally, all four holographic images can be generated in a broadband frequency range, as shown in Fig. 9. Therefore, these results demonstrate that our non-interleaved metasurface can implement four high-efficiency independent holographic images at two broadband frequency ranges by changing the polarization state of the incident waves.

To further verify the accuracy of simulated results, a focusing metasurface with a total size of 300mm×300mm is fabricated by utilizing the traditional planar printed circuit board (PCB) technology. Figure 10(a) exhibits the optical image of the fabricated sample, where the red dashed box displays the enlarged view of the partial meta-atoms. The near field measurements are performed in the microwave anechoic chamber, as shown in Fig. 10(b). The conical absorbing materials are put around the anechoic chamber to shield EM interference. A microwave LP emitting a horn and a receiving probe placed at an appropriate distance away from the metasurface are used as the wave source and detector, and connected to a two-port vector network analyzer (VNA), respectively. Moreover, in order to reduce the interference of the incident wave, the LP emitting horn and the receiving probe are set in front of the metasurface with a deviated angle of 15° from the normal direction.

Figure 11 exhibits the measured focusing performances of the fabricated focusing metasurface at 8.0 GHz and 15.0 GHz for two orthogonal LP incidences. At 8.0 GHz, an obvious focal point can be detected in the plane of z=146mm (xoy-plane) for x-LP incidence, while for the y-LP incidence, the incident waves are converged on the focusing plane of z=193mm, as shown in Figs. 11(a) and 11(b). At 15.0 GHz, similarly, two focal points with focal lengths of F3=63mm and F4=101mm can be observed for LP incidence, respectively, as shown in Figs. 11(c) and 11(d). Their corresponding focusing efficiencies are 72.13%, 75.58%, 57.93%, and 69.94%, respectively. These measured results further demonstrate that the designed focusing metasurface can effectively converge incident waves at different positions by changing the operation frequency and polarization state. Moreover, the experimental results are well consistent with simulated results. The slight discrepancy between them arises mainly from the fabrication error [49].

In conclusion, we have successfully proposed and demonstrated the polarization-frequency multiplexing non-interleaved metasurfaces for high-efficiency multi-channel focusing and imaging. The designed meta-atoms are composed of a metallic ground layer, two dielectric layers, a larger cross-shaped metal structure, and a smaller cross-shaped metal structure embedded by a circular metal aperture. By engineering the two cross-shaped structures, independent full 2π phase coverage can be obtained at two different frequency ranges under two orthogonal LP incidences. Based on the above designed meta-atoms, two various non-interleaved metasurfaces (metalens and metaholography) are constructed to respectively implement four independent focal points (F1=146mm, F2=193mm, F3=63mm, and F4=101mm) and four different letter images (“L”, “O”, “T”, “U”) at two broad frequency ranges by changing the polarization state of the LP incidence. Their largest focusing efficiency, NA, and the imaging efficiency can attain 93.19%, 0.97, and 71.21%, respectively. As an experimental proof, we fabricate a focusing metasurface by the PCB technology and find that the measured results are well consistent with the simulated results. Therefore, the proposed polarization-frequency multiplexing non-interleaved metasurfaces show broad application prospects in low-loss and multi-channel communication integrated systems.