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Abstract
Metasurfaces are engineered planar surfaces consisting of arrays of resonators for tailoring the electromagnetic wavefronts in a desirable way. However, the spin-locked issue of the geometric metasurfaces hinders simultaneous manipulation of both spins. In this work, a spin-decoupled information metasurface composed of simple C-shaped resonators is proposed to realize two different information channels under the orthogonal circularly polarized (CP) incidences. Based on the encoded digit ‘0’ or ‘1’, the diffusion scattering or a holographic image could be realized under the CP excitation in a broadband frequency range from 9 to 12 GHz. As an illustrative example, a 3-bit polarization-encoded meta-hologram is designed, fabricated, and characterized. The measured results agree very well with the numerical results, which gives the proposed method great potential in numerous applications such as holographic displays and information processing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces have attracted increasing research interest in both science and engineering communities due to their unprecedented capacities in tailoring electromagnetic (EM) wavefronts at subwavelength scales and offering a versatile and compact platform for future micro/nanophotonic devices and systems [1–3]. The three intrinsic properties of output EM waves including phase, amplitude, and/or polarization can be tailored locally by subwavelength meta-atoms at an interfacial surface. A large number of metasurface-based applications have been demonstrated in the past decade [4,5], including metalenses [6,7], meta-holograms [8–10], waveplates [11–13], special beam generators [14,15], and so on. In addition, the information metasurfaces have been paid considerable attention due to their abilities to bridge the physical world and digital world since their emergence [16–18]. As one of the most common types of information metasurface, the digital coding metasurfaces have gradually been developed from original 1-bit or 2-level discretization to N-bit or 2N-level discretization of the full 2π [19,20], which could realize higher quality holographic images or more complicated functionalities. Moreover, information metasurfaces have enabled intriguing functionalities by combining the principles from information science and metasurfaces [21,22].
Generally, due to the dispersive nature, most of the early reported metasurfaces are demonstrated to exhibit a single functionality, which could hinder the current research for metasurfaces toward larger capacities and more information channels within a single compact device. With the explosive demands for large-capacity information transmission in the wireless communications, a number of methods have been proposed, e.g., multi-input multi-output (MIMO) techniques [23,24], multi-tasked devices [19,25,26], and information meta-devices [27]. Thus, the development of multifunctional metasurfaces has been of great interest and importance. Polarization-selective metasurfaces, as one type of the multifunctional metasurfaces, work with the linearly polarized (LP) incidences by adopting the birefringent meta-atoms with different structural sizes or the circularly polarized (CP) excitations by rotating the meta-atoms to impart the required phase profiles for the orthogonal incident waves. Whereas, adjusting the size of each meta-atom in two orthogonal polarization is rather challenging for the fabrication and limited footprint as N-bit phase modulations require 2N different types of meta-atoms. Typically, the size-dependent propagation phases are wavelength-dependent and narrowband. In contrast, metasurfaces operating under the CP incidence rely on the orientation-dependent geometric phases or Pancharatnam–Berry (PB) phases, which could release the fabrication challenges, simplify the design procedure, and broaden the working bandwidth. Besides, the PB phase has intrinsically spin-locked issue, where the realized PB phases for the right-CP (RCP) and left-CP (LCP) incidences possess the same value (2θ) linearly related to the in-plane rotation (θ) of the meta-atom but with opposite signs. In order to address this issue, the combination of both propagation and geometric phases in each meta-atom is proposed to provide a general protocol toward realizing spin-decoupled multifunctional metasurfaces for the orthogonal CP incidences [28–35]. Among these reported spin-decoupled metasurfaces, one of the most intriguing applications is the polarization-encoded or spin-selective meta-hologram [36–40], which could be of great interest from sensing to data storage. Nevertheless, broadband polarization-encoded meta-holograms with high-efficiency still remain largely unexplored so far.
In this work, we propose an ultrathin single-layered reflective information metasurface that synthesizes the propagation and geometric phases to achieve broadband high-efficiency polarization-encoded meta-holograms in the microwave regime. The designed information metasurface is composed of 3-bit spin-decoupled digital meta-atoms, which possess ultrathin profiles with a thickness of 0.14 λ0 at 10.5 GHz and are able to achieve high co-polarization reflectance (average over 0.9). It is known that both the near field and far field scattering properties can be tailored through engineering the coding sequences of an information metasurface. Thus, the coding sequences for various functionalities can be obtained according to the encoded digit ‘0’ or ‘1’ of the incident RCP or LCP wave, which represents the diffuse scattering or a holographic image. As a proof-of-concept demonstration, we have designed polarization-encoded information metasurfaces based on the proposed spin-decoupled meta-atoms: the diffuse scattering for digit ‘0’ under both LCP and RCP excitations, and a holographic image of the letter “L” (“R”) for digit ‘1’ under the RCP (LCP) incidence. In addition, a spin-selective meta-hologram for code “11” is also fabricated and characterized. The measured results agree well with the numerical ones, both of which are consistent with the design goals. The proposed helicity multiplexed meta-holograms feature simplicity, high efficiency, and broad bandwidth, which could be applied in polarization-encoded encryption, anti-counterfeiting, and spin-selective holographic displays, etc.
2. Design of meta-atoms
Figure 1 presents the schematic illustration of the proposed spin-encoded metasurfaces, which consists of 31×31 arrays of simple C-shaped resonators with different sizes and in-plane rotation angles. As shown in the right part of Fig. 1, different functionalities for the LCP/RCP channels can be achieved according to code ‘0’ or ‘1’ of the incident polarization. Taking the LCP channel for example, when the LCP channel is encoded with code ‘0’, the diffuse scattering is assigned for the LCP incidence. Besides, whereas the channel is encoded with code ‘1’, a holographic image of the letter “L” (“R”) for the RCP (LCP) channel can be displayed by the metasurface under the RCP (LCP) incidence.
Fig. 1. Schematic illustration of the proposed polarization-encoded holograms by using reflective information metasurface composed of simple C-shaped meta-atoms. According to the encoded digit ‘0’ or ‘1’, different functionalities can be achieved: diffuse scattering for both LCP and RCP channels with digit ‘0’, and a holographic image of the letter “L” (“R”) for the RCP (LCP) channel with digit ‘1’ (please note that each combination of “00,01,10,11” represents a different metasurface).
In order to realize broadband high-efficiency polarization-encoded information metasurfaces, we propose a reflective subwavelength spin-decoupled meta-atom for the orthogonal circular polarizations, which is required to synthesize both propagation phase and geometric phase. The structure diagram of the proposed meta-atom is shown in the left of Fig. 1, which is composed of a simple C-shaped resonator and ground plane separated by an F4B substrate with a dielectric constant of 2.2 and a loss angle tangent of 0.001. The thicknesses of the metal and substrate are 0.035 mm and 4 mm, respectively, and the radius, width and opening angle of the C-shaped resonator are denoted by r, w and α, respectively. The full-wave commercial software CST Microwave Studio is utilized to simulate the electromagnetic response of the meta-atoms, and the period of the meta-atom is optimized to be p = 9 mm.
To interpret the mechanism of independent phase controls for the two orthogonal circular polarizations, we use propagating phase (${\phi ^{Pro}}$) and PB phase (${\phi ^{PB}}$) to achieve the required phase profiles. Considering that
The propagation phases for the LCP and RCP incidences are identical for the same meta-atom, which means
In addition, the PB phase is realized by rotating the meta-atom, which is linearly corresponding to the in-plane rotation angle. More specifically, if the rotation angle is θ, the PB phase changes for the LCP and RCP incidences are 2θ and −2θ, respectively, which indicates
From the above equations, it can be concluded that once the phase modulations for the LCP and RCP excitations are known independently, the corresponding propagation phase and geometric phase can be determined as follows:
Then, the proper meta-atom size and the rotation angle are chosen to satisfy the required propagation phase and geometric phase.
According to Eq. (5), in order to achieve 3-bit spin-decoupled phase modulations for the LCP/RCP waves, the propagation phase is required to achieve 4-bit or 16-level phase regulations within a full phase coverage of 360°, which means that there are 16 meta-atoms to equally divide the 360° with a phase interval of 22.5°. In order to simplify the design process, the width and outer radius of the C-shaped resonators are fixed to be 0.2 and 4 mm, respectively. Thus, only opening angle and rotation angle of the C-shaped resonator are varied to achieved the required propagation and geometric phases. After judicious designs, the amplitude and phase responses of the engineered 16 meta-atoms are shown in Figs. 2(a) and 2(b), respectively, which are determined through the simulations in the CST Microwave studio. It can be seen from Figs. 2(a) and 2(b) that the 16 meta-atoms could achieve an equal phase interval of 22.5° between two adjacent meta-atoms with high efficiency (average over 90%) in the frequency range from 9 to 12 GHz. In addition, the geometric phase can be realized by simply rotating the meta-atom. Figures 2(c) and 2(d) display the amplitude and geometric phase responses by rotating a meta-atom with a step of 10° in the interested frequency band from 9 to 12 GHz, respectively, where the meta-atom with an opening angle of 62.5°. It can be seen from Figs. 2(c) and 2(d) that the geometric phase responses keep twice of the rotation angles with almost unchanged amplitude responses for all the 18 cases. Thus, a total number of 8×8 = 64 meta-atoms required by the 3-bit spin-decoupled information metasurfaces can be obtained, where the structure dimensions of which are detailed in Table 1. It is worth mentioning that the width and the radius of the C-shaped resonators can be adjusted to achieve higher efficiency and broader bandwidth.
Fig. 2. Electromagnetic responses of the C-shaped meta-atom. The simulated (a) amplitude and (b) propagation phase responses for 16 C-shaped meta-toms with different sizes under either LCP/RCP excitations in the frequency range from 5 to 15 GHz. The simulated (c) amplitude and (d) geometric phase responses for 18 C-shaped meta-atoms with in-plane rotation angle step of 10° (the opening angle of the C-shaped meta-atom is 62.5°) under the LCP excitation.
Table 1. The total 64 meta-atoms for the spin-decoupled metasurface with 3-bit phase modulations
Figures 3(a) and 3(b) demonstrate that the full phase coverage of 360° is discretized into 8 digital elements of 1, 2, 3, 4, 5, 6, 7, and 8 with an interval of 45°for the LCP and RCP incidences at 10.5 GHz, respectively, while Figs. 3(d) and 3(e) display the reflection amplitude profiles for the 8 digital elements under the LCP and RCP excitations, respectively. In these figures, the φRR (φLL) and ARR (ALL) denote the reflection phase and amplitude of the meta-atoms for the reflected RCP (LCP) wave under the RCP (LCP) incidence, respectively. Figure 3(c) plots the detailed data of Figs. 3(a) and 3(b) along the black dashed lines therein, in which the phase profile φLL keeps almost constant around 180° for the element ‘5’ under the RCP incidence, whereas the phase profile φRR increases from 0 to 315° with an interval of 45° as the encoded digit for LCP excitation varies from ‘1’ to ‘8’. Moreover, it can be seen from Figs. 3(d) and 3(e) that a large co-polarized reflection over 0.9 can be achieved for the proposed 3-bit spin-decoupled information metasurfaces at the center frequency of 10.5 GHz. Furthermore, Fig. 3(f) plots reflection amplitudes along the black dashed lines in Figs. 3(d) and 3(e), in which the cross-polarized reflection amplitude over 0.95 can be observed for both LCP and RCP states.
Fig. 3. The performance of the proposed 3-bit spin-decoupled meta-atoms. The reflection phases (a) φLL and (b) φRR of the 3-bit spin-decoupled meta-atoms. φYX denotes the reflection phases for the YCP reflected wave under the XCP excitation, and the other symbols are defined similarly. ‘1’- ‘8’ are the coding elements. (c) The cross-sections of (a) and (b) along the black dashed lines. The co-polarized reflection amplitudes (d) ALL and (e) ARR of the 3-bit spin-decoupled meta-atoms. (f) The cross-sections of (d) and (e) along the black dashed lines.
Based on the judiciously engineered 3-bit spin decoupled meta-atoms, we design an information metasurface composed of 31×31 unit cells with a total area of 279×279 mm2, which could diffusely scatter the incident wave for the code ‘0’ under either circular polarization incidence or display a holographic image of the letter “L”/“R” for the code ‘1’ under the RCP/LCP incidence. Moreover, the imaging plane composed of an area of 280×280 mm2 is parallel to the metasurface at a distance of 250 mm away.
According to the principle of optical path reversibility, the phase distribution of the electric field on the metasurface can be calculated according to the Rayleigh-Sommerfeld diffraction propagation formula. For the code ‘0’, a random phase distribution is adopted to generate the diffusive scattering. Besides, for the code ‘1’, the meta-hologram generated by Computer Generated Hologram (CGH) is given by
Figures 4(a) and 4(c) show the target images (i.e., the letters “L” and “R”) for the RCP and LCP incidences, respectively. While Fig. 4(b) (Fig. 4(d)) displays the required 3-bit total phase distribution for generating the target holographic image shown in Fig. 4(a) (Fig. 4(c)), which is the superimposition of the digitized phase distribution from the GS algorithm and the compensation phase.
The designed spin-encoded metasurface with the code sequence are first numerically calculated through MATLAB by treating each meta-atom as a point source. Figures 5(a) and 5(e) show the computed images for the code sequence of “11” for the RCP and LCP states at the center operation frequency of 10.5 GHz, respectively. The image plane with an area of 280×280 mm2 is placed parallel to the metasurface at a distance of 250 mm away. It can be seen from Fig. 5(a) (Fig. 5(e)) that a holographic image of the letter “L” (“R”) can be observed clearly for the RCP (LCP) incidence, where the calculated field intensity is outlined with the white dashed line. Then, the designed metasurface is simulated by the full-wave simulation software CST Microwave Studio. In the simulations, the feeding source is a CP horn antenna impinging normally on the metasurface at a distance of 600 mm, and the electric field monitors at 9, 10.5 and 12 GHz are set to record the simulated electric fields. Because the image plane is designed between the antenna and metasurface at a distance of 250 mm away from the metasurface at 10.5 GHz, the positions of the imaging plane at 9 and 12 GHz should be adjusted accordingly to find the proper distances for obtaining high-quality images. After an optimization process, the positions of the imaging plane at 9 and 12 GHz are determined to be 170 and 300 mm, respectively. Figures 5(b)–5(d) show the reflected LCP electric field intensities under the RCP excitation on the different imaging planes at 9, 10.5, and 12 GHz, respectively. It can be seen from Figs. 5(b)–5(d) that the holographic image of letter “L” can be observed at the distances of 170, 250, and 300 mm away from the metasurface, respectively. Similarly, Figs. 5(f)–5(h) demonstrate the holographic image of letter “R” under the LCP excitation. It can be concluded from Fig. 5 that the numerical calculations are in good agreement with the full-wave simulations, both of which agree well with the design goals.
Fig. 4. (a)The target image (“L”) and (b) the corresponding phase distributions under the RCP incidence. (c)The target image (“R”) and (d) the corresponding phase distributions under the LCP incidence.
Fig. 5. The calculated result at 10.5 GHz with a distance of 250 mm under the (a) RCP and (e) LCP incidence. The simulated result at 9 GHz with a distance of 170 mm away from the metasurface under the (b) RCP and (f) LCP incidence. The simulated result at 10.5 GHz with a distance of 250 mm away from the metasurface under the (c) RCP and (g) LCP incidence. The simulated result at 12 GHz with a distance of 300 mm away from the metasurface under the (d) RCP and (h) LCP incidence. (The scale bar in each figure is 70 mm.)
Moreover, the total coding sequences of “00”, “01”, “10”, and “11” for the polarization-encoded metasurfaces are demonstrated at 10.5 GHz in Fig. S1 in Supplement 1, where the first and second digits refer to the incident RCP and LCP waves, respectively. In Supplement 1, Fig. S1 demonstrates that the incident CP waves can be diffusively scattered with code ‘0’, and a holographic image of letter “L” (“R”) can be clearly observed under the RCP (LCP) excitation with code ‘1’, which verifies the proposed method.
For the purpose of experimental verification, a spin-selective meta-hologram sample is fabricated by using the standard printed circuit board (PCB) technique. Figure 6(a) displays the picture of the fabricated sample composed of 31×31 meta-atoms. The inset image of Fig. 6(a) is the enlarged view of a small section of the fabricated sample. The experiments are conducted in a microwave anechoic chamber with the two-dimensional (2D) near-field scanning setup shown in Fig. 6(b), where a horn antenna and a waveguide probe are utilized to emit a linearly-polarized (LP) wave and detect the reflected wave with a step of 2 mm, respectively. The horn antenna and a waveguide probe are connected to the transmitting and receiving ports of a vector network analyzer (VNA). In order to reduce the possible diffractions from the measurement environment, the supporting rod of the probe is wrapped with the foam, and the horn antenna is placed 600 mm away from the metasurface. The x- and y-polarized components of the reflective field (rxx, ryx) on the imaging planes can be obtained by emitting x-polarized wave from the horn antenna, while the corresponding components (rxy, ryy) can be recorded through emitting y-polarized wave. Thus, the reflective co-polarized CP components can be reconstructed from the four components (rxx, ryx, rxy, ryy) by the following equations:
Fig. 6. (a) The photo of the fabricated sample of the spin-selective meta-hologram (the inset shows the zoomed in view of a small section of the sample.). (b) The experimental setup for the measurement. The measured result at 9 GHz with a distance of 170 mm away from the metasurface under the (c) RCP and (f) LCP incidence. The measured result at 10.5 GHz with a distance of 250 mm away from the metasurface under the (d) RCP and (g) LCP incidence. The measured result at 12 GHz with a distance of 300 mm away from the metasurface under the (e) RCP and (h) LCP incidence. (The scale bar is 70 mm.)
Therein, rLL (rRR) represents the reflective LCP (RCP) field under the LCP (RCP) excitation. Figures 6(c)–6(e) plot the measured reflected electric field intensities at 9, 10.5, and 12 GHz on the corresponding imaging planes of z = 170, 250, and 300 mm under the RCP excitation, respectively. Once again, the holographic images of “L” can be clearly observed at the corresponding measured planes, which agree very well with the simulated results displayed in Figs. 5(b)–5(d). As can be seen from Figs. 6(f)–6(h) and Figs. 5(f)–5(h), similar conclusions can be drawn for the LCP excitation. The distortion and noise affected the measurements when synthesizing the CP components from the LP components, which necessitates the relocation of waveguide probe after changing the polarization of the horn antenna. Besides, the fabrication tolerance and imperfect material property of the substrate could cause slight deviation between simulation and measurement.
In order to evaluate the quality of the reconstructed holographic images in the propagation path, we adopt the correlation coefficients (Co) between the reconstructed images and the target image at each frequency as the major criterion. According to [41], The Co is defined as:
Table 2. Evaluation of reconstructing quality for the proposed method at different frequencies.
3. Conclusion
To summarize, we proposed a broadband polarization-encoded information metasurface with an ultrathin profile of 0.14 λ at 10.5 GHz and high co-polarized reflectance (>0.9) from 9 to 12 GHz. The spin-decoupled meta-atom of the polarization-encoded metasurface is composed of a simple C-shaped resonator printed on a grounded substrate. The 3-bit spin-decoupled phase modulations for the LCP and RCP excitations can be achieved by superimposing the 4-bit propagation phases and the geometric phases, realizing by varying the opening angles and rotation angles of the C-shaped resonator, respectively. According to this principle, higher-bit spin-decoupled metasurfaces can be realized by constructing the proper meta-atoms with only considering the propagation phases firstly, which could greatly simplify the design process. In addition, diffuse scattering and meta-hologram can be realized according to different code of ‘0’ and ‘1’ for both circular polarizations, respectively. Random phase distribution on the metasurface is constructed for the diffuse scattering, while the phase distributions for the hologram consist of the phase distribution from the GS algorithm and compensation phase for collimating the spherical wave. Thus, there are four scenarios for the presented polarization-encoded metasurfaces, including diffuse scattering for both LCP and RCP incidences with code “00”, diffuse scattering for one CP state and meta-hologram for the other state with code “01” or “10”, and spin-selective meta-holograms with code “11”. All four scenarios are numerically verified through full-wave simulations. Moreover, the spin-selective meta-hologram is also validated by experiments, and the simulated and measured results agree very well with the design goals in a broad bandwidth from 9 to 12 GHz. Furthermore, the proposed method could be readily extended to other frequency regimes due to its simplicity and low cost, which could greatly expand the research scope of the proposed method for applications such as holographic displays, encryption, and data storage, etc.
Funding
National Natural Science Foundation of China (62171186, 61971392); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare no conflict 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.
Supplemental document
See Supplement 1 for supporting content.
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