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Abstract
Holography is an advanced imaging technology where image information can be reconstructed without a lens. Recently, multiplexing techniques have been widely adapted to realize multiple holographic images or functionalities in a meta-hologram. In this work, a reflective four-channel meta-hologram is proposed to further increase the channel capacity by simultaneously implementing frequency and polarization multiplexing. Compared to the single multiplexing technique, the number of channels achieves a multiplicative growth of the two multiplexing techniques, as well as allowing meta-devices to possess cryptographic characteristics. Specifically, spin-selective functionalities for circular polarizations can be achieved at lower frequency, while different functionalities can be obtained at higher frequency under different linearly polarized incidences. As an illustrative example, a four-channel joint-polarization-frequency-multiplexing meta-hologram is designed, fabricated, and characterized. The measured results agree well with the numerically calculated and full-wave simulated ones, which provides the proposed method with great potential in numerous opportunities such as multi-channel imaging and information encryption technology.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the continuous in-depth study of electromagnetic (EM) field, researches are aspiring to completely and flexibly regulate the EM waves in multiple intrinsic properties including phase, magnitude, and polarization, etc. Metasurfaces, composed of subwavelength artificial scatterers (meta-atoms), are a class of ultrathin planar electromagnetic devices [1–4]. Taking advantages of interactions between EM waves and meta-atoms, metasurfaces can manipulate EM waves with different degrees of freedoms (DOFs), including amplitude, phase and polarization [1,5–10]. By delicate design of the meta-atom, metasurfaces can arbitrarily manipulate the wavefronts within a thin interface by attaining local and space-variant abrupt electric field changes, breaking the dependence on optical path accumulation. This superior EM field modulation capability of metasurfaces has drawn great attention and has led to abundant fascinating meta-devices, such as metalenses [11–13], chiral detection [14,15], cloaking [16–18] and meta-holograms [19–25].
Typically, most of the previously reported meta-devices could perform one functionality due to the wavelength-dependent behavior. And many great achievements have been made to realize multifunctional or multichannel metasurfaces with multiple DOFs, such as angular momentum multiplexing [26–29], polarization-controlled multiplexing [4,30–34], multi-frequency [35–38], angle-selective multiplexing [39,40] and muti-freedom metasurfaces [41,42]. In particular, polarization multiplexing was employed to increase the information channels of meta-devices, which usually increase to two, corresponding to left/right-handed circularly polarized (LCP/RCP) or x/y-linearly polarized (x-LP/y-LP) waves. Multi-frequency metasurfaces were designed to integrate different functionalities into different operation frequencies, where the information channel number is proportional to the operating frequency number. Furthermore, the interleaved and multi-layer stacking methods are most commonly utilized in multiplexing metasurface design, which may result in the reduction of the working efficiency in each channel, the increased difficulty in processing, and the extra background noises. More recently, single-cell polarization-controlled multiplexing metasurfaces and multi-band metasurfaces are widely investigated [43–47], which show the characteristics of high efficiency, compact structure, easy fabrication and versatile functions. Moreover, researchers have simultaneously regulated multiple DOFs in order to further increase the number of information channels. For example, researchers have developed the multi-channel meta-devices by the combined controls of amplitude and phase, frequency and polarization [48–51]. However, simultaneous and independent manipulation of different DOFs in a single-cell single-substrate-layer metasurface still lacks a straightforward guidance due to the design complexity.
In this work, a reflected dual-band polarization-controlled multiplexing metasurface has been proposed to achieve pure phase modulations in four independent information channels for LCP, RCP, x-LP and y-LP waves. The proposed meta-atom consists of a patterned metallic layer and a ground plane separated by a substrate spacer. The metallic top layer is perforated with a slotted loop and a circular hole, where a double-C-shape split-ring resonator (DCSRR) and a metallic Jerusalem cruciform resonator (MJCR) are placed, respectively. The DCSRR and the MJCR are employed to obtain 2π propagation phase modulations for CP and LP waves at two distinct operation frequencies, respectively. Moreover, combining geometric phase principle, DCSRR could manipulate the phase modulations of the LCP and RCP waves independently and simultaneously, thus realizing the total four information channels for four different polarization types. As a proof-of-concept demonstration, a four-channel meta-hologram has been designed and encrypted via a combined selection of polarization and frequency. The experimental results have good agreements with the calculation and simulation ones, featuring high resolution and no ghost image. The proposed meta-device implies the potential applications of the dual-band polarization-controlled multiplexing single-cell metasurface in high information capacity integrated systems, encryption communication systems, and ultracompact image displays.
2. Principle and structure design
2.1 Polarization-controlled multiplexing principle
While designing polarization-controlled multiplexing metasurface, anisotropic meta-atoms are widely utilized for manipulating two orthogonal polarized waves. By adjusting the anisotropic resonance in metallic metasurfaces, independent phase manipulations of x-LP and y-LP waves can be easily achieved, which are named as propagation phases. In contrast, the independent phase manipulations of the orthogonal circularly polarized (CP) waves (i.e., LCP and RCP) need to combine both the propagation and geometric phases, where the geometric phase or PB phase results in an equal amplitude and opposite sign of LCP and RCP phases, expressed as $\phi _{LCP}^{PB} ={-} \phi _{RCP}^{PB} = 2\theta$, where θ is the orientation angle of the anisotropic structure with respect to x-axis. To further interpret the mechanism of the circular-polarized multiplexing metasurface, the total phases for the LCP and RCP could be written as
where ${\phi ^{\textrm{Pro}}}$ and ${\phi ^{PB}}$ represent the propagation phase and PB phase, respectively. Considering that the propagation phases for the LCP and RCP are identical for the anisotropic meta-atom (i.e., $\phi _{LCP}^{Pro} = \phi _{RCP}^{Pro} = {\phi ^{Pro}}$), it is concluded that the corresponding propagation phase and geometric phase could be calculated by the certain combination of ΦLCP and ΦRCP, which is expressed as follows:Therefore, the orientation angle of the meta-atom could be determined by
When a 2-bit phase modulation for the circular-polarized multiplexing is required, the propagation phases and the orientation angles of the total number of 4 × 4 = 16 meta-atoms are listed in Table 1, where it can be seen that a 3-bit or 8-level propagation phase regulation is needed.
Table 1. Total 16 meta-atom for the circular-polarized multiplexing metasurface with 2-bit phase modulations (unit: degree)
2.2 Dual-band polarization-controlled multiplexing meta-atom design
Figure 1(a) shows the schematic illustration of the four-channel multifunctional meta-hologram. It can be seen from Fig. 1(a) that an incidence impinges normally on the meta-hologram, and the reflected co-polarized (i.e., LCP, RCP, x-LP and y-LP) electric fields are recorded, displaying four holographic images at two preset frequencies of f1 and f2. Figures 1(b) and 1(c) demonstrate the three-dimensional (3D) and top views of the proposed dual-band polarization-controlled multiplexing meta-atom, which is composed of a bottom ground and a top patterned metallic layer separated by a spacer with a thickness of ts. The top layer is perforated with an annular loop and a circular hole, in the centers of which a DCSRR and an MJCR are located, respectively.
Fig. 1. (a) Schematic of the proposed four-channel multifunctional meta-hologram under both a linearly polarized (LP) and a circularly polarized (CP) illuminations, and the reflected co-polarized components of the electric fields are recorded. The meta-hologram generates joint-polarization-frequency-selected holographic images of ‘U’ / ‘S’ at f1 and ‘T’ / ‘C’ at f2, respectively. (b), (c) The three-dimensional view and top view of the proposed meta-atom.
The opening angles, radii, and widths of the DCSRR in the annular loop are denoted as α1, α2, r1, r2, w1 and w2, respectively. The orientation of the DCSRR is denoted as θ with respect to the x-axis. Besides, the lengths and width of the MJCR’s branches are denoted as l1, l2, l3, l4, and w3. Furthermore, the radius and the widths of the loop are rL and wL, respectively. The radius of the hole and the periodicity of the meta-atom are denoted as rc and p, respectively. As an illustrative example, we choose the operating frequencies of the dual-band metasurface as f1 = 7.5 GHz in the C band and f2 = 13 GHz in the Ku band. The metal and substrate are set as copper (σ = 5.96 × 107 S/m, tm = 0.035 mm) and F4B (εr = 2.2, tan δ = 0.001, ts = 4 mm), respectively. To obtain the required phase modulations at two frequencies, numerical simulations are carried out by CST Microwave Studio, where the periodic boundary conditions are applied in both the x- and y-directions and the Floquet-port excitation under the CP or LP incidence is adopted in the -z-direction.
By micro-tuning the geometric parameters of the DCSRR and MJCR, the 3-bit propagation phases for CP waves and 2-bit propagation phases for LP waves can be obtained at 7.5 and 13 GHz, respectively. It should be noticed that while the θ is changed from 0 into 90°, the propagation phases for both LCP and RCP waves are shifted 180° simultaneously and remain equal, which indicates that 3-bit propagation phase for CP wave at 7.5 GHz is only required to cover 135° range at a holding angle of θ = 0. The rest of phase coverages can be achieved by simply rotating the previous meta-atom by θ = 90°, which could greatly reduce the design complexity. In order to simplify the design process, the radius and width of the annual loop, and the radius of the circular hole are fixed with [rL, wL] = [5.5, 1.2] (unit: mm), and rc = 4.1 mm, respectively. Besides, the widths of both DCSRR and MJCR are chosen as w1 = w2 = w3 = 0.2 mm. After a judicious design process, the radii, opening angles, and orientation of the 8 DCSRR are optimized as r1 = [5.1, 5.1, 5.2, 5.1, 5.1, 5.1, 5.2, 5.1], r2 = [4.7, 4.7, 4.8, 4.7, 4.7, 4.7, 4.8, 4.7,] (unit: mm), α1 = α2 = [25, 65, 110, 150,25, 65, 110, 150], θ = [0, 0, 0, 0, 90, 90, 90, 90] (unit: degree). The current distributions of the meta-atom are shown in Fig. 2(a) and 2(b) under the LCP and RCP incidences at 7.5 GHz, respectively. It could be observed that the surface current is bounded by the circular ring with a strong current response on the DCSRR and no exciting current on the MJCR at 7.5 GHz, indicating the well isolation between the resonators. The simulated reflected co-polarized phases and amplitudes of the 8 engineered meta-atoms are plotted in Fig. 2(c) and 2(d), respectively. It could be observed that the 8 meta-atoms could cover the 360° phase with a step interval of 45° and maintain high reflection efficiency (average over 0.9) at 7.5 GHz. Moreover, Figs. 2(e) and 2(f) shows the geometric phases and amplitudes by rotating one of the 8 DCSRR from 0 to 180°, where the geometric phase is twice of the rotation angle of DCSRR with an unchanged amplitude. Therefore, the suitable phase modulation for circular-polarized multiplexing could be realized by the 3-bit propagation phase and uniformly changing geometric phase according to Table 1.
Fig. 2. (a), (b) The current distributions of the dual-band polarization-controlled multiplexing meta-atom at 7.5 GHz under LCP and RCP incidences. (c), (d) The 3-bit reflected co-polarized propagation phase and corresponding amplitude profiles of the meta-atoms with θ = 0 under LCP or RCP incidence. (e), (f) The PB phase and amplitude profiles of the meta-atom by varying θ. (g) The current distribution of the meta-atom at 13 GHz under x-polarized incidence. (h), (i) The 2-bit propagation phase and corresponding amplitude profiles of the meta-atoms under x-polarized incidence.
Furthermore, the 2-bit independent phase modulations for y-LP and x-LP at 13 GHz can be obtained by tuning the size parameters of [l1, l2] and [l3, l4], respectively, which are optimized to be [l1] ([l3]) = [4.5, 4, 5.5, 4.5] and [l2] ([l4]) = [1.8, 1.4, 2.6, 2.2] (unit: mm). As a showcase, Fig. 2(g) plots the instantaneously surface current distribution on the metallic layer of the meta-atom at 13 GHz while illuminated by an x-LP wave. It can be seen that the surface current flows along the y-direction branches, and has little response in the x-direction branches, implying that the x-LP and y-LP controls are well isolated and regulated only by the y- and x-direction branches of the MJCR, respectively. In addition, the DCSRR has not excited surface current, demonstrating the little coupling between the DCSRR and MJCR. Figures 2(h) and 2(i) demonstrate the reflected phase and amplitude profiles of the meta-atoms under x-polarized incidence, where the meta-atoms obtain 2-bit phase coverage maintaining amplitudes of more than 0.9.
3. Results and discussion
Based on the 2-bit dual-band polarization-controlled multiplexing meta-atom, a four-channel joint-polarization-frequency-selected multifunctional encryption meta-hologram is designed, which could reconstruct the incident wave as different holographic images on a preset plane through the co-selection of both frequency and polarization.
Holography is one of the most attractive imaging techniques to enable recoding and reconstruction of the full information of a preset target image. In the conventional optical holography, light illuminates a target object and interferes the scattered light with the reference light to record the object’s information. Instead, the computer-generated hologram (CGH) could directly obtain the information of target, demonstrating low-cost and fast design process. Thus, the CGH has attracted great interest since its emergence. Theoretically, the phase profile of the meta-hologram generated by CGH could be expressed as the following [52]:
The designed four-channel joint-polarization-frequency-selected encryption meta-hologram is first numerically verified via MATLAB, where each meta-atom is treated as an ideal point source and the electric field in the space could be obtained by the field superposition formula according to Green’s function. Figures 4(a), 4(b) and Figs. 4(c), 4(d) illustrate the calculated intensities on the XY plane with z = 200 mm at 7.5 GHz and 13 GHz, respectively, where the letters ‘U’, ‘S’, ‘T’, ‘C’ are reproduced clearly. Then the four-channel meta-hologram is simulated by CST. In the array simulation, LCP, RCP, x-LP and y-LP horn antennas irradiate the meta-hologram at a distance of 600 mm, and the co-polarized intensities of the electric field on the imaging plane at 7.5 and 13 GHz are recorded, as shown in Figs. 4(e)–4(h). It can be observed from Fig. 4(e) (4(f)/4(g)/4(h)) that the letter ‘U’ (‘S’/‘T’/‘C’) is reconstructed while choosing the LCP wave at 7.5 GHz (RCP wave at 7.5 GHz / x-LP wave at 13 GHz / y-LP wave at 13 GHz) as the incidence, which indicates that the information is encrypted by both the frequency and the polarization of incidence and scatter waves. Moreover, the simulated results are in very good agreement with the calculated ones, and the discrepancies between them could be caused by the antenna deviating from the phase center point and the non-ideal edge diffraction of the metasurface.
Fig. 3. (a)-(h) The target images of ‘U’, ‘S’, ‘T’, ‘C’ and the corresponding phase distributions at 7.5 and 13 GHz. (i)-(l) The phase compensation at 7.5 and 13 GHz. (m)-(p) The digitized total phases of the four-channel meta-hologram at 7.5 and 13 GHz.
Fig. 4. (a), (b) The calculated intensities on the XY plane with z = 200 mm at 7.5 GHz. (c), (d) The calculated intensities on the imaging plane at 13 GHz. (e), (f) The simulated co-polarized intensities of electric field on the imaging plane at 7.5 GHz under LCP and RCP incidence. (g), (h) The simulated co-polarized intensities of electric field on the imaging plane at 13 GHz under x- and y-LP incidence.
In order to further verify the holographic algorithm, the designed four-channel encryption meta-hologram has been fabricated and measured. The top view of the fabricated sample is shown in Fig. 5(a), which consists of 31 × 31 meta-atoms with an area of 347.2 × 347.2 mm2. The inset image is a magnified view of a small part of the sample. Besides, Fig. 5(b) demonstrates the schematic of the experimental setup, where a dual-circularly polarized horn antenna (LB-SJ-60180-P03, 6-16 GHz) and a LP horn antenna (HD-60180DRHA10S, 6-18 GHz) are employed as the transmitters and placed at a distance of 600 mm away from the meta-hologram, which irradiate the LCP, RCP, x-LP and y-LP spherical wave to the meta-hologram. The same type of LP horn antenna is used as a receiver to record the reflected x-LP and y-LP fields, which could be converted to the LCP and RCP fields by the calculation of EL/R = Ex ± jEy. A Vector Network Analyzer (VNA) is adopted during the measurement. Figures 5(c)-5(f) plot the measured 2D intensity distributions of the LCP and RCP reflected waves with z = 200 mm under the LCP or RCP incidence at 7.5 GHz. It can be observed that when illuminating the LCP and RCP incidences, the co-polarized components of the reflected waves are reconstructed to form the patterns of ‘U’ and ‘S’, respectively, as shown in Figs. 5(c) and 5(e). Additionally, the cross-polarized components display a haphazard diffuse scattering, as plotted in Figs. 5(d) and 5(f). Similar conclusions could be drawn for the LP incidence at 13 GHz, as plotted in Figs. 5(g)-5(j), where the letters ‘T’ and ‘C’ (diffuse scattering) are observed clearly for co-polarized (cross-polarized) waves on the imaging plane. The experiment results indicate that the information of every channel is only available if one chooses the correct frequency and the polarization of both the incidence and the recorded EM wave, demonstrating the encryption characteristics of the meta-hologram. The measured results exhibit more noise than the simulated ones, which could be caused by the fabrication tolerance, alignment, and the receiver blockage, which could be improved by adding a deflection factor to the meta-holograms so that the incident wave is irradiated from the surface at an oblique incidence. Furthermore, the x- and y-LP electric fields detected by the receiver do not exactly coincide with each other, which leads to the degradation of the imaging quality for circular polarization at 7.5 GHz.
Fig. 5. (a) The top views of the fabricated sample for the proposed four-channel meta-holograms. (b) Schematic of the experimental setup. (c), (d) The measured intensities of LCP/RCP electric field under a normal LCP incidence on the XY planes with z = 200 mm at 7.5 GHz. (e), (f) The measured intensities of RCP/LCP electric field under a normal RCP incidence at 7.5 GHz. (g), (h) The measured intensities of x-LP/y-LP electric field under a normal x-LP incidence at 13 GHz. (i), (j) The measured intensities of y-LP/x-LP electric field under a normal y-LP incidence at 13 GHz. The scanning step is 5 mm on the XY plane.
4. Conclusion
In summary, we have proposed a new type of single-layer reflective metasurface to achieve four-channel operation for both CP and LP incidences. Based on the unique design of the single-cell patterned metallic layer, the coupling between DCSRR and MJCR is greatly suppressed, and thus the two resonators work only in their corresponding frequency bands. Through tuning the sizes of DCSRR, 3-bit propagation phase and continuous geometric phase could be obtained at 7.5 GHz, which could enable 2-bit circular polarization multiplexing. Besides, the MJCR achieves the 2-bit linear polarization multiplexing at 13 GHz via modifying two orthogonal metal branches, which achieves polarization-controlled multiplexing in each of the two frequencies and a four-channel operating mode. As a demonstration example, a four-channel joint-polarization-frequency-selected multifunctional encryption meta-hologram is studied to display holographic images. Only when the frequency and polarization of the both incident wave and detected wave are correctly selected, the information of the corresponding channel could be decrypted, where the letters ‘U’/‘S’ for LCP/RCP at 7.5 GHz and ‘T’/‘C’ for x-LP/y-LP at 13 GHz could be reconstructed. Moreover, the experimental results agree very well with the numerical predictions and full-wave simulations. The proposed manipulation of multiple DOFs obtained by the dual-band polarization-controlled metasurface provides a new route for multi-channel meta-device and could be implemented in various wireless systems.
Funding
Fundamental Research Funds for Central Universities; National Natural Science Foundation of China (61775060, 62171186).
Acknowledgments
The authors would like to thank Information Science Laboratory Center of USTC 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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