An Optically Transparent Metasurface for Microwave Amplitude–Phase Manipulation

Abstract

Current microwave metasurfaces predominantly suffer from the disadvantages of optically opaque and phase-only modulation, which inevitably hinder their application potential. Herein, we have proposed a simple but efficient strategy for designing a multifunctional metasurface that is capable of simultaneously achieving visible transparency and microwave amplitude–phase manipulation. The designed meta-atom consists of a metal-frame-based H-shaped resonator and a metallic mesh layer separated by a transparent dielectric substrate, enabling eight-level phase modulation with a π/4 interval and continuous amplitude modulation covering the range of 0–0.9 at 16 GHz. As a proof-of-concept demonstration, a spatially multiplexed complex-amplitude hologram utilizing the designed meta-atom is simulated and experimentally validated. The results show that two distinct holographic images can be reconstructed in different imaging planes, and the measured average optical transmittance attains 63.7% at a wavelength range of 400–800 nm. Our proposed design strategy paves the way to an optically transparent microwave metasurface which is expected to have great potential in application scenarios requiring both visible transparency and microwave wavefront control.

1. Introduction

Metasurfaces, two-dimensional arrays of well-designed artificial meta-atoms, have emerged as a transformative platform for manipulating electromagnetic (EM) waves at the subwavelength scale [1,2,3,4]. Unlike conventional optics that rely on bulky curved components and gradual phase accumulation along the propagation path, metasurfaces enable abrupt phase control across an ultrathin interface, offering seamless integration with miniaturized optoelectronic devices [5]. Although phase-only metasurfaces have enabled unprecedented wavefront shaping, their functionality remains fundamentally constrained by the omission of amplitude degree of freedom—a limitation manifesting in high sidelobe levels and inefficient energy distribution [6,7,8]. In contrast, complex-amplitude metasurfaces transcend these boundaries by synergistically tailoring both phase and amplitude profiles of local meta-atoms [9]. Such a paradigm has realized more sophisticated and high-fidelity wavefront control functionalities that are unattainable with phase-only metasurfaces [10,11,12,13,14,15,16]. For example, Feng et al. developed a transmissive metasurface with independent amplitude and phase control, which was utilized to realize a low-side-lobe metalens antenna. Compared to phase-only metalens antennas, the proposed design achieved a 5.7 dB average sidelobe level suppression [17]. Based on an all-dielectric metasurface with independent and complete manipulation of the amplitude and phase, Yu et al. showed that the quality of holographic images was significantly improved by amplitude–phase control, and they successfully created artifact-free two-dimensional holographic images and controlled the surface textures of three-dimensional holographic objects, which are not attainable in phase-only holography [18]. Very recently, Zhou et al. proposed the concept of multiplexed coherent pixel metasurfaces that can continuously tune the amplitude and phase under incident plane and orbital angular momentum (OAM) waves. Such a strategy realized the multiple degree-of-freedom control of OAM, significantly increasing the data capacity of metasurfaces [7].

Despite the versatile functionalities realized by the simultaneous modulation of amplitude and phase, the aforementioned metasurfaces fail to realize the compatibility of optical transparency. The pursuit of optically transparent metasurfaces has opened new frontiers in aircraft optical windows, vehicle windshields, display screens, and glass curtain walls of buildings, just to name a few. To date, much effort has been devoted to implementing the convergence of optical transparency and microwave manipulation [19,20]. For instance, traditional metallic patches fabricated with printed circuit board technology are replaced by transparent conductive oxides such as indium tin oxide (ITO), generating an orbital angular momentum vortex wave while maintaining high optical transparency [21]. However, the inverse relationship between ITO sheet resistance and optical transparency imposes stringent design trade-offs, and existing ITO-based phase gradient metasurfaces usually exhibit relatively large EM losses [22]. Moreover, ITO films suffer from other limitations such as brittleness, insufficient chemical and thermal stability, high cost, and the scarcity of indium resources, which hinder their widespread application in sophisticated devices requiring stability and flexibility. Another effective method used to further improve optical transparency is the use of ultra-thin metallic meshes. By leveraging meta-atom designs or judiciously tailoring the geometries of conductive meshes, such metasurfaces can manipulate microwave properties, including transmission [23,24,25], absorption [26], and polarization conversion [27], without obstructing visible transparency. Unfortunately, the lithography process for fabricating metallic meshes is undoubtedly time-consuming and high-cost, which is not desirable for metasurface industrialization. Thus, designing and manufacturing an optically transparent microwave metasurface in a low-cost and reliable way remains a big challenge.

In this work, we have presented an approach, simple in concept and in practice, that uses a metal frame to construct an optically transparent meta-atom possessing independent and complete manipulation of the microwave amplitude and phase profiles. To achieve optical transparency, metallic patterns were replaced by an elaborately designed metal frame with a low filling ratio, while the traditional metal backplane of reflection-type metasurfaces was replaced by metallic meshes. Both the metal-frame-based resonator and bottom mesh layer can be easily attained by means of flexible printed circuit (FPC) technology, which is mature and low-cost. Regarding the microwave region, the amplitude was continuously controlled from 0 to 0.9 by in-plane rotation, whereas eight-level phase modulation with an interval of π/4 was realized by changing the geometric size and orientation angle of the H-shaped resonator. It should be noted that the manipulation of amplitude and phase is independent and has low crosstalk, facilitating the implementation of high-quality wavefront control. To demonstrate the advantages of the proposed transparent meta-atom, we designed and experimentally validated a spatially multiplexed complex-amplitude hologram, as shown in Figure 1a. Two holographic images of “WH” and “UT” were separately reconstructed on the different predetermined imaging planes at 16 GHz. The experimental results agree with the theoretical predictions and numerical simulations, validating the capability of the proposed meta-atom for amplitude–phase manipulation. More importantly, in contrast to previous studies [28,29,30,31], the low filling ratio of metal-frame-based resonators and metallic meshes facilitated the high visible transparency (~63.7%) of the entire metasurface.

2. Results

2.1. Design of the Meta-Atom

The schematic of the proposed meta-atom is illustrated in Figure 1b. To achieve visible transparency, first, optically transparent dielectric material polymethyl methacrylate (PMMA) with a thickness of h = 3 mm and a dielectric constant of 2.25(1 – j0.01) is used as the substrate. Next, the metal backplane of a traditional reflection-type metasurface is replaced by metallic meshes with a period of p_m and a linewidth of w_m1. In terms of the top resonant layer, a widely used H-shaped anisotropic configuration is adopted to enable satisfactory polarization conversion efficiency [32,33]. More significantly, the entire metallic pattern of the H-shaped resonator is deliberately replaced by a metal frame with a linewidth of w_m2, as shown in Figure 1b,c. In addition, we denote the two principal axes of the H-shaped resonator as u and v, respectively, and the u axis is rotated counterclockwise by an angle of β with respect to the x axis of the laboratory coordinate system. After the optimization process, other geometric parameters of the designed H-shaped resonator are provided in Figure 1c, and they will not change throughout the paper unless otherwise indicated. Both the top metal frame and the bottom metallic mesh are deposited on a 50 μm thick polyethylene terephthalate (PET) substrate with a dielectric constant of 3(1 − j0.03), which can be easily fabricated by using mature and low-cost FPC technology.

As mentioned above, the relationship between optical transparency and microwave performance should be balanced, which is mainly affected by the period and linewidth of the top metal frame and the bottom mesh layer. Here we used CST Microwave Studio 2020 commercial software based on the finite element method (FEM) to optimize the geometric parameters of the proposed meta-atom. During the simulation process, periodic boundary conditions were adopted in the x- and y-directions, while an open boundary condition was applied along the z-axis. In addition, adaptive tetrahedral mesh refinement was used to ensure the mesh convergence as well as the numerical accuracy. Figure 2a,b plot the simulated cross-polarized reflection amplitude (|r_yx|) of the designed meta-atom (l = 6.3 mm, β = 45°) with various periods (p_m) and linewidths (w_m1) of the bottom mesh layer, respectively. It is obvious that the bandwidth and efficiency of |r_yx| increase with smaller p_m, whereas w_m1 has almost no influence on the spectral response before 16 GHz. Similarly, the amplitude of r_yx remains intact with the varying linewidths of the top metal frame (w_m2) in the frequency range of 16–20 GHz (Figure 2c), which increases the fabrication tolerance. With the determined period and linewidth of the metal mesh, its optical transmittance can be estimated by T = 1 − S_metal/S_lattice, where S_metal = 2w_mp_m − w_m² and S_lattice = p_m² [34,35]. The calculated optical transmittance of a metallic mesh layer is plotted in Figure 2d, from which we observe that the theoretical optical transparency can exceed 90% when the parameter w_m/p_m is below 0.05. Comprehensively considering the optical transparency, microwave performance, and the FPC manufacturing accuracy, these parameters are finally determined as p_m = 1 mm and w_m1 = w_m2 = 50 μm. From Figure 2, we can also observe that the proposed meta-atom exhibits a broadband amplitude response. Since the Ku-band (12–18 GHz) is aligned with the working frequency range of satellite communications, one of the representative frequencies, 16 GHz, is chosen as the operating center frequency of the proposed metasurface.

In general, for a reflection-type anisotropic meta-atom rotated counterclockwise with an orientation angle β, the local reflection Jones matrix can be expressed as [36,37,38]

$$\mathit{J}=\mathit{R}(-\beta )\left[\begin{array}{cc}{r}_u& 0\\ 0& r_v\end{array}\right]\mathit{R}(\beta )$$

(1)

where r_u and r_v represent the complex reflection coefficients along its u and v principal axes, respectively, and R(β) represents the 2 × 2 rotation matrix denoted by

$$\mathit{R}(\beta )=\left[\begin{array}{cc}\cos \beta & \sin \beta \\ -\sin \beta & \cos \beta \end{array}\right]$$

(2)

From Equations (1) and (2), the two off-diagonal elements of the Jones matrix (i.e., the cross-polarized reflection coefficient) can be derived as

$$\sigma ={\displaystyle \frac{(r_u-r_v)}{2}}\sin 2\beta$$

(3)

Thus, we can conclude from Equation (3) that for a given meta-atom with certain r_u and r_v, the cross-polarized reflection amplitude can be tuned from zero to a maximum value as β is varied from zero to π/4, whereas the phase undergoes a π shift when β is π/2. To quantitatively investigate the influence of rotation angle on the cross-polarized reflection coefficient, we simulated the amplitude and phase of r_yx versus β, as shown in Figure 3a,b, respectively. It can be seen that the simulated results fit the theoretical ones well, verifying that our proposed meta-atom enables the continuous manipulation of amplitude from 0 to 0.9 by varying the rotation angle. In terms of the phase modulation, it can be easily realized by changing the arm length l of the metal-frame-based H-shaped resonator, and an additional π shift can be accomplished by mirroring the meta-atom along the y-axis, as shown in Figure 3c,d. It should be noted that eight-level phase gradient with a π/4 interval is adopted in this work, and the selected parameters marked by asterisks are l = 2.5, 3.4, 4.5, and 6.3 mm. Meanwhile, their cross-polarized reflection efficiencies are all above 0.9, which overcomes the large EM loss disadvantage of ITO-based meta-atoms [22]. To further examine the intrinsic coupling between amplitude and phase modulations, the simulated amplitude and phase of r_yx as a function of both l and β are presented in Figure 3e and Figure 3f, respectively. Intuitively, the amplitude depends only on the rotation angle, whereas a full 2π phase coverage can be realized by changing the arm length and mirroring the structure. Such remarkable characteristics indicate that the amplitude–phase manipulation realized by our proposed meta-atom is independent and has low crosstalk, facilitating the implementation of complex wavefront control functionalities.

2.2. Multiplane Complex-Amplitude Hologram

In this section, as schematically shown in Figure 4a, the designed meta-atom featuring continuous amplitude control and eight-level phase control at 16 GHz is utilized to generate a spatially multiplexed complex-amplitude hologram that can reconstruct different holographic images of “WH” and “UT” with z₁ = 130 mm and z₂ = 270 mm away from the metasurface, respectively. In the microwave region, the Rayleigh–Sommerfeld diffraction formula is adopted to calculate the near-field distribution diffracted by the metasurface, which can be expressed as [39,40]

$$U(x,y,z)={\displaystyle \frac{1}{i\lambda }}{\displaystyle {\iint }_{S_0}U(x_0,y_0,0)}\cos (\delta ){\displaystyle \frac{\exp (ik\left|\mathit{r}\right|)}{\left|\mathit{r}\right|}}d{S}_0$$

(4)

where λ and k are the wavelength and wavevector, respectively, U(x, y, z) and U(x₀, y₀, 0) represent the complex-amplitude distributions on the imaging plane S and metasurface plane S₀, respectively, $\left|\mathit{r}\right|=\sqrt{{(x-x_0)}^2+{(y-y_0)}^2+z^2}$ represents the distance between points (x, y, z) and (x₀, y₀, 0), and cos(δ) = z/|r| is the inclination factor. By considering the inverse propagation operator, the field distribution on the metasurface plane can be calculated as

$$U(x_0,y_0,0)={\displaystyle \frac{1}{i\lambda }}{\displaystyle {\iint }_{S}U(x,y,z)\cos (\delta )\frac{\exp (-ik\left|\mathit{r}\right|)}{\left|\mathit{r}\right|}dS}$$

(5)

Using Equations (4) and (5), the complex-amplitude distributions at a single imaging distance can be obtained. Furthermore, the spatially multiplexed technology is utilized to enhance the information capacity, which can be obtained by using the superposition theorem denoted by [41,42]

$$U_{\mathrm{tot}}(x_0,y_0,0)={\displaystyle \sum _{i=1}^N{U}_i(x_0,y_0,0)}$$

(6)

where U_tot(x₀, y₀, 0) represents the required total field distribution on the metasurface. Here we choose the letters “WH” and “UT” as the target images to be separately generated in two imaging planes of 130 mm and 270 mm apart from the metasurface, and the target images and metasurface contain 45 × 45 number of pixels covering an area of 360 × 360 mm². Calculated from Equations (4)–(6), the normalized continuous amplitude distribution and the discretized eight-level phase distribution of the metasurface are obtained, as shown in Figure 4b,c, respectively. By mapping the meta-atoms with different arm lengths l and rotation angles β to the calculated amplitude–phase profile accurately, the final arrangement of the entire metasurface can be attained.

Figure 4. (a) Schematic of the designed multiplane hologram. (b,c) Calculated continuous amplitude distribution and digitized eight-level phase distribution of the metasurface with 45 × 45 number of pixels at 16 GHz.

Figure 4. (a) Schematic of the designed multiplane hologram. (b,c) Calculated continuous amplitude distribution and digitized eight-level phase distribution of the metasurface with 45 × 45 number of pixels at 16 GHz.

Following the above design process, the multiplane complex-amplitude metasurface hologram was fabricated and experimentally verified. The top layer of the metal-frame-based H-shaped resonator and the bottom metallic mesh layer were composed of 18 μm thick copper grids with an electrical conductivity of 5.8 × 10⁷ S/m, which were deposited on 50 μm thick PET films and fabricated by the mature and low-cost FPC technology. The microscopic images of the top metal frame layer and the bottom metallic mesh layer are shown in Figure 5b,c, demonstrating a mesh linewidth of approximately 45 μm, which is slightly narrower than the designed value (50 μm). From the previous analyses in Figure 2, such a slight discrepancy hardly affects the polarization conversion efficiency. In addition, an ultrathin optically clear adhesive was used for interlayer adhesion between the PET and PMMA substrates. Figure 5a illustrates the photograph of the fabricated metasurface with an overall dimension of 360 × 360 mm², through which the logo below the sample can be clearly seen, indicating its visual clarity. Next, a UV/Vis/NIR spectrometer (Lambda 750) was used to quantitatively analyze the optical transmittance of the fabricated sample in the wavelength range of 400–800 nm, as shown in Figure 5d. Also, the optical transmittance spectra of PMMA, top layer with PMMA, and bottom layer with PMMA are plotted for a clear comparison. Owing to the low filling ratio of the designed metal frame, the top layer exhibits a high transmittance of over 86%. Meanwhile, the average transmittance of the bottom metal mesh layer attains ~71%. For the entire metasurface, an average optical transmittance of 63.7% is realized at 400–800 nm, showcasing the efficacy of our proposed meta-atom consisting of a metal frame and mesh for realizing visible transparency.

In the microwave region, the performance of the designed metasurface was first verified by numerical simulations using the time-domain solver in CST Microwave Studio 2020. In the simulations, open (add space) was used as boundary conditions in the x-, y-, and z-directions, and the metasurface was illuminated by a normal incident plane wave with the electric field polarized along the x direction. Another y-polarized probe operating at 16 GHz was used to record the near-field intensities. The simulated cross-polarized electric field intensity distributions at the distance of z₁ = 130 mm and z₂ = 270 mm are shown in Figure 6g,h, respectively, indicating good agreement with the theoretical calculations obtained from MATLAB R2017b (Figure 6e,f). Next, a two-dimensional (2D) near-field scanning system was used to experimentally determine the metasurface performance, as shown in Figure 6a,b. To match the operating frequency (16 GHz) of the designed metasurface, an emitting WR-62 waveguide antenna connected to a vector network analyzer (VNA, Keysight N5227B) was used to generate a linearly polarized quasi-plane wave for illuminating onto the metasurface sample with the help of a large-diameter dielectric lens. In addition, a movable probe connected to the VNA was used to detect the electric fields with a step of 1 mm. The entire scanning plane of the probe system was placed between the emitting antenna and the sample, with two distances of 130 mm and 270 mm away from the sample. It is worth mentioning that the whole measurement setup was surrounded by microwave-absorbing materials to eliminate reflection losses. The obtained experimentally measured cross-polarized electric field intensity distributions at the observation planes of z₁ = 130 mm and z₂ = 270 mm are plotted in Figure 6i and Figure 6j, respectively. Specifically, a holographic image displaying “WH” appears at the first imaging plane of 130 mm (Figure 6i), while at a distance of 270 mm, a holographic image of “UT” is clearly observed (Figure 6j). We note that the measured holographic images closely match the corresponding calculated and simulated results. Further, a signal-to-noise ratio (SNR), which is defined as the ratio of the peak intensity in the holographic image to the standard deviation of the background noise [43,44], was used to evaluate the quality of the metasurface hologram. For the experimentally reconstructed image at z₁ = 130 mm (Figure 6i), the SNR is 13.65, whereas the experimental SNR for the image at z₂ = 270 mm (Figure 6j) is 7.49, proving the effectiveness of the amplitude–phase manipulation realized by the proposed meta-atoms.

3. Discussion

In practical applications, oblique incidence scenarios are common. Thus, it is essential to analyze the incident-angle stability of the proposed meta-atoms. Figure 7a,b present the cross-polarized reflection amplitude and phase versus rotation angle under different incident angles of θ = 0°, 30°, and –30°. We note that the monotonically increasing amplitude and almost unchanged phase versus the rotation angle are observed at large incidence angles of ±30°. In addition, as can be seen from Figure 7c,d, the cross-polarized reflection amplitudes of the selected meta-atoms #1–8 are above 0.9 when the incident angles are ±30°, whereas the phase modulation with a π/4 interval is almost insensitive to the incident angle. Thus, the independent and complete manipulation of amplitude and phase responses of the proposed meta-atoms can be preserved under oblique incidence scenarios of θ = ±30°, showcasing a remarkable property of oblique-incidence stability which is essential in practical applications.

Without loss of generality, broadband performance validation across the Ku-band (12–18 GHz) is presented in Figure 8. It can be seen that a holographic image of “WH” appears at the imaging planes of 85, 100, 130, and 160 mm under the frequencies of 12, 14, 16, and 18 GHz, whereas another holographic image of “UT” is observed at distances of 200, 240, 270, and 290 mm under the corresponding frequencies, demonstrating the excellent broadband holographic imaging performance of the proposed metasurface. We also note that the observing plane increases with the operating frequency, which can be easily explained by the different phase accumulation of wave propagation related to different frequencies [39,45].

Table 1. Comparison of the proposed metasurface and its counterparts.

Ref.	Material	Center Frequency	Manipulation Approach	Function	Optical Transparency
[28]	Metal	11.1 GHz	Amplitude–phase	Beamforming	None
[29]	Metal	28 GHz	Amplitude–phase	OAM generation	None
[30]	Metal	13 GHz	Amplitude–phase	Airy beam generation	None
[31]	Metal	13 GHz	Amplitude–phase	OAM generation	None
[46]	ITO	24.5/41 GHz	Phase	Hologram	46%
[47]	ITO	20 GHz	Phase	OAM generation	Yes
This work	Metal frame	16 GHz	Amplitude–phase	Hologram	63.7%

compares the performance of the proposed metasurface with previously reported counterparts. First, amplitude–phase manipulation was realized by refs. [28,29,30,31] by using metal-based meta-atoms. However, the optically opaque properties restrict their applications in optical windows. Next, refs. [46,47] focused on realizing optical transparency by replacing the metal resonator with ITO configuration, whereas their wavefront control capabilities were limited to a single degree of freedom, i.e., the phase-only modulation. In contrast to previous studies, our proposed metasurface not only enables independent and complete control of amplitude and phase in the microwave region, but also maintains relatively high optical transparency. Additionally, the metal-frame-based resonator fabricated by the mature and low-cost FPC technology is particularly beneficial for practical applications, which may promote the industrialization of metasurfaces.

Despite the achievements of the proposed metasurface, the existing limitations lie in the non-tunable performance and limited operating channels in the microwave region. Thus, future research may focus on integrating stimuli-responsive elements (e.g., varactor, graphene, and vanadium dioxide) with meta-atoms to realize dynamical tunability [48], or utilizing polarization-multiplexed and angle-multiplexed technologies to expand the information capacity [49,50,51].

4. Conclusions

In conclusion, a new type of multifunctional metasurface simultaneously possessing high visible transparency and microwave amplitude–phase manipulation was proposed. A metal frame with ultra-narrow linewidth was adopted to construct the anisotropic resonator, whereas the reflective backplane of the meta-atom was replaced by metallic meshes, facilitating high visible light transmittance of 63.7% at 400–800 nm. In terms of the microwave frequencies, based on in-plane rotation and geometric size variation, continuous amplitude modulation covering a range of 0–0.9 and eight-level phase gradient with a π/4 interval was enabled at 16 GHz. Utilizing the fascinating capability of independently manipulating the amplitude and phase, a spatially multiplexed meta-hologram capable of reconstructing two holographic images in distinct imaging planes was experimentally demonstrated, showing good agreement with the numerical simulations. We believe our proposed metasurface provides a robust and generalized path towards realizing the compatibility between visible and microwave bands, which is required for future smart windows, wireless communications, and data storage systems.