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Abstract
In recent years, frequency-multiplexed metasurfaces have received extensive attention due to the increasing demand for multifunction integration and communication capacity. However, multi-channel studies achieved with a mono-layered frequency-multiplexed metasurface are limited. Herein, a universal design strategy for a frequency-multiplexed mono-layered geometric phase metasurface is proposed by utilizing Pancharatnam-Berry (PB) phase modulations. The elementary meta-atom is judiciously designed to transmit the cross-polarized component of a circularly polarized incident wave at four distinct frequencies with independent 360° phase shifts and a constant amplitude of 0.48, close to the theoretical limit of 0.5. As a proof-of-concept demonstration, a four-channel meta-hologram is designed to achieve distinct holographic images of “three foci”, “five foci”, “J” and “X” at 7.2 GHz, 9.1 GHz, 10.9 GHz, and 15.2 GHz respectively. The images are projected in the desired azimuth planes by exploiting the time-shifting properties of the Fourier transform. The experimental and full-wave simulation results are in good agreement, which indicates that the proposed strategy has great potentials in various applications, such as multi-channel imaging and information encryption technology.
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1. Introduction
With the rapid development of modern communication systems, tailoring of electromagnetic (EM) wavefronts has attracted great attention due to its importance in wireless communications [1–4]. In the past decades, significant interest has been devoted to metasurfaces composed of artificially designed periodic scatterers, due to their extraordinary ability in manipulating electromagnetic properties such as amplitude, phase, and polarization [5–8]. A metasurface can arbitrarily tailor the EM wavefront by introducing local and space-variant abrupt phase discontinuities at the interface, breaking the dependence on phase accumulation obtained from the propagation effect [9]. Interesting applications based on metasurfaces have been proposed due to the ability in customizing arbitrary EM wavefronts and the advantages of low profile, low fabrication cost, and ease of integration. These applications include anomalous reflection or refraction [10,11], meta-lenses [12,13], EM cloaking [14,15], polarization manipulations [16–19], vortex beam generation [20–23], and holograms [24–27].
In order to meet the increasing demand for higher information capacity and integration, the integration capability of the metasurface needs to be improved. Typically, to uphold metasurface versatility, strategies like polarization multiplexing [28,29], position multiplexing [30], angle multiplexing [31], angular momentum multiplexing [32,33], and frequency multiplexing [34,35] have been proposed. Frequency-multiplexed metasurfaces are designed to integrate various functionalities at different operational frequencies, where the number of information channels is proportional to the number of operational frequencies. More recently, a few frequency-multiplexed metasurfaces have been reported to operate in transmission space [36,37], reflection space [38,39], and full space [40,41]. However, most metasurfaces can only operate at two or three separated frequencies, which limits their information capacity to conform to the trend of highly integrated EM devices. Although four-channel multi-frequency metasurfaces [42] have also been reported, the increase in frequency-multiplexed channels exacerbates the mutual coupling problem between structural resonators, which affects the whole performance of the devices. Hence, the design of a frequency-multiplexed metasurface with multi-channel, high transmission efficiency and low coupling effect is still a challenge.
Here, we propose a strategy for the design of a four-channel geometric phase metasurface, which can modulate the phase of EM wave at four frequencies based on the Pancharatnam-Berry (PB) phase principle. The proposed meta-atom comprises a metallic layer deposited on the top of a thin single layer substrate. The metallic layer consists of four resonators: an outer double C-shaped split-ring resonator (ODCSRR), a modified double C-shaped slot resonator (MDCSR), an inner double C-shaped split-ring resonator (IDCSRR), and a metal ring incorporating an “I” structure (MRI), which are nested together to form the meta-atom. Through the adjustment of the orientation angles of the four resonators, right-handed circularly polarized (RCP) incident waves can be modulated by the meta-atoms, inducing an independent full 2π phase modulation at four distinct frequencies. As a proof-of-concept demonstration, a metasurface showcasing four independent functionalities across four channels is designed and verified through full-wave simulations and experimental measurements. The proposed design enables the realization of four independent meta-holograms at frequencies f1, f2, f3 and f4. Notably, at frequencies f2 and f3, it allows the projection of two distinct holographic images with different azimuthal planes at ± 30°. The proposed monolayer geometric metasurface allows to achieve the high-capacity holographic image operations through direct modulation in frequency-domain. Such strategy is capable of supporting various applications, including ultrafast analog computing devices, high-information-capacity integrated systems, encryption communication systems, and ultra-compact image displays.
2. Principle and meta-atom design
Figure 1 presents a schematic illustration of the proposed four-channel meta-hologram device based on a frequency-multiplexed monolayer geometric phase metasurface. When an RCP wave illuminates the metasurface, different wavefront manipulations with the cross-polarized component (i.e., left-handed circularly polarized (LCP) component) can be performed in the transmission space at different working frequencies (7.2, 9.1, 10.9 and 15.2 GHz) according to the geometric phase principle. It constructs the holographic “five foci” image, spatially shifted “three foci” image, spatially shifted “J” image, and holographic “X” image at four different frequencies. It can be seen from Fig. 1(b) that ODCSRR, MDCS, IDCSRR, and MRI resonators are nested together to form the proposed meta-atom, which comprises a patterned metallic layer printed on a single-layer substrate. The orientation angles of the ODCSRR, MDCS, IDCSRR and MRI are denoted as θ1, θ2, θ3, and θ4 with respect to the x-axis, respectively. According to the PB phase theory [43], the cross-polarized component of the metasurface is able to produce additional 2θ phase shift. Therefore, a full 2π phase coverage can be obtained by rotating the meta-atom resonator from 0 to π.
Fig. 1. (a) Schematic demonstration of the proposed four-channel meta-hologram based on a frequency-multiplexed mono-layered geometric phase metasurface. A normally RCP incident wave is used to illuminate the metasurface and four independent holographic images including “five foci”, “three foci”, “J”, and “X” are reconstructed at f1, f2, f3, and f4 with the cross-polarized wave (LCP wave) in the transmission space, respectively. (b) Different resonators used to construct the proposed four-channel geometric meta-atom.
Besides, the substrate is chosen to be the commercially available F4B (dielectric constant ɛr = 2.2, loss tangent tanδ = 0.001, and thickness h = 2 mm) with copper (conductivity σ = 5.96 × 107 S/m, and thickness t = 0.035 mm) cladding. The parameters of the four-channel geometric phase meta-atom are optimized using the CST microwave studio commercial software, resulting in a frequency spacing of minimum 1.8 GHz between each channel, which helps to reduce the coupling and crosstalk between different channels. The geometric parameters of the ODCSRR, MDCS, IDCSRR, and MRI are optimized to be r1 = 5.7 mm, w1 = 0.3 mm, g1 = 0.3 mm, rc1 = 4.9 mm, wc1 = 1 mm, r2 = 4.5 mm, w2 = 0.3 mm, g2 = 0.7 mm, r3 = 3.6 mm, w3 = 0.3 mm, g3 = 0.3 mm, rc2 = 2.7 mm, wc2 = 0.3 mm, r4 = 1.9 mm, w4 = 0.3 mm, β = 120°. The periodicity of the meta-atom is p = 12 mm.
Furthermore, according to the alternatively arranged metal and slot structures, the coupling or crosstalk between any two structures is minimized. Here, the metal structures are ODCSRR, IDCSRR, and slot structure is MDCSR. The metal structures excite mainly the electric resonance, which is strongly coupled to the electric field, while the slots excite the magnetic resonance, which is more related to the magnetic field. Due to the different coupling mechanisms of the electric and magnetic fields, the alternating arrangement allows the adjacent electric and magnetic resonance structures to be relatively independent, thus reducing their mutual influence [44–46]. It is worth mentioning that our design also incorporates a metal ring as an absorber in the MRI resonator, which reduces the coupling between the “I” element and the IDCSRR. The surface current and electric field distributions of the resonators are analyzed at the four frequencies when excited by a RCP incident wave, as shown in Figs. 2(a)-(d). At 7.2 GHz and 10.9 GHz, the electric fields and surface currents are mainly concentrated near the metal structures. At 9.1 GHz, the electric fields and surface currents are primarily concentrated within the gap of the MDCSR. The electric fields and surface currents are predominantly concentrated in both the metal ring and the “I” structure of the MRI resonator, when the frequency is 15.2 GHz. In summary, the induced maximum current at each operation frequency that reaches the metal boundaries can flow along the ring and not pass into the adjacent structures, which performs as an equivalently infinite ground plane and considerably minimizes the cross-talk among resonators. Consequently, the designed meta-atom enables independent phase modulation at four different operational frequencies by individually rotating the corresponding resonator. The amplitude and phase of the meta-atom with transmitting LCP wave for a normally incident RCP illumination are shown in Figs. 2(e)–2(h), where the orientation angles of four resonators (i.e., θ1, θ2, θ3 and θ4) are changed from π/8 to π with an interval of π/8. It can be observed that the cross-polarized transmission amplitudes at the four frequencies hold almost constant (> 0.48), which are close to the theoretical limit maximum of 0.5 [47–49]. Furthermore, it can be observed that the phase shift of the meta-atom is twice the rotation angle of the resonator, achieving a full phase coverage of nearly 2π. As a result, high transmission efficiency and full 2π phase shift are obtained by adjusting the four angles θ1, θ2, θ3 and θ4, allowing to achieve 3-bit phase encoding with the designed meta-atom. Throughout this process, a total of 32 coding meta-atom structures are extracted, as depicted in Fig. 3, where the rows show distinct resonator configurations at the different frequencies and the columns indicate the rotation angles for each resonator. The digital states denoted as 000, 001, 010, 011, 100, 101, 110 and 111 correspond to the orientation angles of the four resonators, namely, π/8, π/4, 3π/8, π/2, 5π/8, 3π/4, 7π/8, π, respectively.
Fig. 2. Electric field distributions, surface current distributions and transmission characteristics of the meta-atom under an RCP incident wave illumination at 7.2 GHz, 9.1 GHz, 10.9 GHz, and 15.2 GHz, respectively. (a)-(d) Electric field energy distributions and current distributions. (e)-(h) Simulated cross-polarized transmission amplitudes and phase responses while varying θ1, θ2, θ3 and θ4 from π/8 to π with a step interval of π/8.
In order to ensure the effectiveness of the designed four-channel geometric phase meta-atom for the independent modulation of EM waves, the crosstalk on the LCP transmission characteristics of the meta-atom under a normally incident RCP illumination is investigated, as presented in Fig. 4. More intuitively, Fig. 4(a) shows the cross-polarized transmission amplitudes and phases of the meta-atoms at 7.2 GHz for different rotation angles θ2, θ3, and θ4, while θ1 is kept constant and equal to 3π/8. It can be clearly observed that both the amplitude and phase curves are almost overlapped, indicating that modulating θ2, θ3, and θ4 have no effects on the transmission characteristics of the meta-atom at 7.2 GHz. Similar amplitude and phase manipulation can be achieved in the cross-polarized transmission when θ1, θ3 and θ4 changes while θ2 is fixed (θ1, θ2 and θ4 changes while θ3 is fixed, θ1, θ2 and θ3 changes while θ4 is fixed), as shown in Figs. 4(b)–4(d). As a result, independent phase control is achieved at four frequencies by adjusting the four angles θ1, θ2, θ3 and θ4, correspondingly, thereby demonstrating that the crosstalk between the four resonators is negligible. It should be noted that the channel capacity can be improved by further increasing the number of resonators. Considering the design complexity and the fabrication cost, four resonators are designed here as a proof-of-concept. This convenient way of manipulating phase responses without interfering with the phase profiles in other frequency bands is of great interest for designing multi-band meta-devices with independent phase modulations.
Fig. 4. Crosstalk on the LCP transmission characteristics of the proposed meta-atom under a normally incident RCP illumination when rotating (a) θ2, θ3 and θ4 at 7.2 GHz, (b) θ1, θ3 and θ4 at 9.1 GHz, (c) θ1, θ2 and θ4 at 10.9 GHz, and (d) θ1, θ2 and θ3 at 15.2 GHz.
3. Design of four-channel meta-hologram
The meta-atoms are then arranged in arrays according to certain rules to form the phased-encoded metasurface, which can realize four different holographic imaging at four operating frequencies. As a proof-of-concept demonstration, the weighted Gerchberg-Saxton (WGS) algorithm [50] and the angular-spectral method (ASM) algorithm [51] are utilized for the design of holographic imaging at the four frequencies as follows. First, the phase of images “five foci” and “three foci” are reconstructed at 7.2 GHz and 9.1 GHz, respectively, by applying the WGS algorithm:
Second, the phase of target images “J” and “X” are respectively obtained at 10.9 GHz and 15.2 GHz by using a modified ASM algorithm:
where U0 (x, y) is the electric field distribution of the target image, H (kx, ky) is the target transfer function, expressed by: where z represents the perpendicular distance between the imaging plane and the metasurface, kx and ky are the spatial frequencies of x and y, respectively. Thus, efficient imaging can be achieved from the WGS and ASM algorithms at different imaging distances and frequencies.To achieve spatially shifted holographic images, the phase distribution of the shifted target image is determined by superimposing the original target image’s phase with the phase associated to the offset angle [52], as expressed by:
The four-channel holographic metasurface is designed using 20 × 20 coding meta-atoms with a total size of 240 × 240 mm2. To visualize the four different holographic images, the “five foci” and “X” imaging distances are set as z1 = 40 mm and z4 = 55 mm at 7.2 GHz and 15.2 GHz, respectively. The phase distribution of the metasurface is calculated and encoded by the WGS and ASM algorithms, as shown in Figs. 5(a)-(b). Similarly, the “three foci” and “J” imaging distances are set as z2 = 80 mm and z3 = 60 mm, with offset angles θr = 30° and θr = −30° at 9.1 GHz and 10.9 GHz, respectively. The phase coding distribution of the metasurface is calculated with the offset phase superposition, as shown in Figs. 5(c)–5(d).
Fig. 5. Phase-encoding layouts and simulation results of the four-channel meta-hologram under an RCP wave illumination. Phase-encoding distributions of: (a) “five foci”, (b) “X”, (c) “three foci”, and (d) “J” images. Full-wave simulated intensity of the transmitted LCP electric field on the image planes: (e) z1 = 40 mm at f1 = 7.2 GHz, (f) z4 = 55 mm at f4 = 15.2 GHz, (g) z2 = 80 mm at f2 = 9.1 GHz and θr = 30°, and (h) z3 = 60 mm at f3 = 10.9 GHz and θr = −30°.
The geometric phase metasurface illuminated by an RCP incident wave is simulated and the LCP electric field intensity distributions in the observation plane θr = ± 30° and the xoy plane are extracted. A “five foci” image and an “X” image are observed for ${z_1}\textrm{ = 40 mm}$ at 7.2 GHz and for z4 = 55 mm at 15.2 GHz, respectively, as shown in Figs. 5(e)-(f). The “three foci” image is reconstructed on the z2 = 80 mm plane at 9.1 GHz with the offset angle θr = 30°, as shown in Fig. 5(g) and the “J” image is reconstructed on the z3 = 60 mm plane at 10.9 GHz with the offset angle θr = −30°, as shown in Fig. 5(h).
4. Experimental verification
In order to verify the feasibility of the proposed four-channel meta-hologram, the geometric phase metasurface sample is fabricated using the conventional printed circuit board technique. A single-face copper-cladded metasurface based on a monolayer substrate is realized, which has a total size of 240 × 240 mm2, as shown by the photograph in Fig. 6(a). Experimental tests are performed in a microwave anechoic chamber, whose schematic description is schematically illustrated in Fig. 6(b). To approximate the simulated incidence conditions, a 2-18 GHz broadband horn antenna is placed far enough at 1.5 m (about 36λ relative to the lowest operational frequency of 7.2 GHz) from the meta-hologram in the experiments such that it is illuminated by quasi-plane waves. The LCP transmitted electric fields in the image planes are measured using an EFS-105-12 fiber-optic active near-field probe, which has a small purely dielectric head of 6.6 × 6.6 mm2, allowing to have negligible field perturbation. The horn antenna and probe are both connected to an Agilent 8722ES vector network analyzer (VNA). The probe moves in small increments of 2 mm in the xoy plane to obtain a full two-dimensional spatial distribution of the electric field.
Fig. 6. Experimental results of the four-channel meta-hologram. (a) Photograph of the fabricated metasurface sample. (b) Description of the experimental measurement setup used to scan the transmitted electric field. Measurement results of the hologram: (c) at 7.2 GHz, (d) at 15.2 GHz, (e) with the offset angle of 30° at 9.1 GHz, and (f) with the offset angle of −30° at 10.9 GHz.
The “five foci” and “X” images at 7.2 GHz and 15.2 GHz are measured in the xoy plane at 40 mm and 55 mm from the metasurface, and results are shown in Figs. 6(c) and 6(d), respectively. The “three foci” and “J” holograms are recorded at 9.1 GHz and 10.9 GHz in the observation planes situated at distances of 80 mm and 60 mm from the metasurface. These measurements are conducted with offset angles of 30° and −30°, and the corresponding outcomes are depicted in Figs. 6(e) and 6(f). It can be observed from Figs. 6(c)–6(f) that the measured results are consistent with the theoretical predictions and simulation results, demonstrating that the designed coding metasurface can focus electromagnetic wave energy to the target region to produce high-quality holographic images. It should be noted that the electric field energy distributions of the “three foci” and “J” images, exhibit slight deviations from the simulation results, arising from the fabrication tolerance and the alignment angle of the metasurface with respect to the illuminating horn antenna.
5. Conclusion
In summary, we propose a frequency-multiplexed mono-layered metasurface based on the geometric phase principle, designed to enable four-channel holography under RCP incident waves illumination. Leveraging the distinctive design of the patterned metal layer, we effectively mitigate coupling among the four resonators, ensuring that each resonator operates exclusively at its designated frequency. Independent and complete control of the EM wavefront phases at the different frequencies is achieved by adjusting the rotation angle of the corresponding meta-atom resonator. As a proof-of-concept demonstration, a four-channel meta-hologram is designed to display four different holographic images. The experimental results agree very well with the theoretical predictions and full-wave simulations. Reconstructing the image of the corresponding channel requires precise control of both the frequency and polarization of the incident waves. Furthermore, the high capacity and complex holographic images can be achieved by directly modulating frequency, offering new possibilities for display in free space. Our method supports various applications, including ultrafast analog computing devices, high-capacity integrated systems for information storage, encrypted communication systems and ultra-compact image displays.
Funding
Natural Science Foundation of Heilongjiang Province (LH2022F053); National Natural Science Foundation of China (62171153, 62275063); Scientific and technological development project of the central government guiding local (SBZY2021E076); Postdoctoral Research Fund Project of Heilongjiang Province of China (LBH-Q21195); Fundamental Research Funds of Heilongjiang Provincial Universities of China (145209151); Open project of State Key Laboratory of Millimeter Waves (K202309).
Acknowledgments
The authors would like to thank Harbin Institute of Technology and Univ Paris Nanterre for the measurement service.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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