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Abstract
Metasurface has extraordinary capability in the wavefront manipulation of electromagnetic waves, which provides an effective method for meta-holographic technology. However, holographic technology mostly focuses on the generation of the single-plane image, which lacks a systematic design method to generate, store, and reconstruct multi-plane holographic images. In this paper, the Pancharatnam-Berry phase meta-atom is designed as electromagnetic controller with the characteristics of the full phase range and high reflection amplitude. Different from the single-plane holography method, a novel multi-plane retrieval algorithm is proposed for the computation of the phase distribution. The metasurface, containing only 24 × 24 (30 × 30) elements, can produce high-quality single-(double-) plane image(s) with fewer elements. Meanwhile, the implementation of the compressed sensing approach stores almost all the holographic image information under a 25% compression ratio and reconstructs the image by the compressed data. The experimental measurements of the samples are consistent with the theoretical and simulated results. This systematic scheme provides an innovative and effective way for designing miniaturized meta-devices to generate high-quality images, which relate to practical applications including high-density data storage, information security, and imaging.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Holography, which was first discovered by Gabor in 1948 [1], has become a practical and promising approach to recording the complex amplitude information of the object. As an outstanding three-dimensional (3D) imaging technology, traditional holograms can be obtained by the interference of the light scattered from the target object with a coherent incident beam. However, this method requires a physical object and a highly temporal-spatial coherent light source [2]. The computer-generated holography (CGH) can solve these issues and inject new vitality into the holographic technique [3,4]. The CGH image is generated by calculating the amplitude-only, phase-only, or complex amplitude distribution into diffractive element arrangement, among which the most convenient method is phase-only modulation [5]. However, the phase manipulation relies on the light propagation over long distances inside the material to achieve the desired phase accumulation for wavefront shaping, resulting in large area and thickness of optical units compared to the wavelength [6]. Under the influence of large size of diffractive optical elements, most of the optical holography images have either low resolution or narrow field of view.
Metasurfaces, possessing ultrathin and planar characteristics, are consisted of sub-wavelength metallic or dielectric meta-atoms with appropriate structure and orientation. The arrangement of metasurface is guided by the encoding amplitude and/or phase profile, resulting in a powerful ability to arbitrarily regulate the intensity, phase, polarization state, and propagation direction of electromagnetic (EM) beams. Owing to their flexible manipulation, they have been actively designed to realize innovative devices in the optical and microwave field, including ultrathin planar lenses [7–9], integer and fractional vortex beam generators [10–12], anomalous reflectors [13,14], and arbitrary meta-hologram generators [15–32].
In contrast to the conventional bulky holographic devices by propagation length accumulation, the metasurfaces are utilizing the EM responses of meta-elements with proper geometric structures and orientation angles. The first important advantage of the metasurface is realizing the low absorption loss and high conversion efficiency in the microwave region. Next, the sub-wavelength characteristic of the meta-atom enables the development of holographic images with high resolution and small cross crosstalk. Moreover, it is simple to fabricate the metasurface by using the printed circuit board technique on the millimeter scale. Finally, the design flexibility of the metasurface is the most crucial consideration, which can realize numerous combinations of different degrees of freedom and multiple independent propagation channels. The expected amplitude, phase, and polarized state of EM waves can be obtained by elaborately modifying the geometry of the meta-atom. The metasurface with these properties and advantages functions as a potent device for reshaping EM wavefront, enabling the development of microwave holographic imaging technology and a variety of related applications including imaging [19], data storage [20,21], and information encryption [22].
Focus on holographic technology in the microwave region, phase-only metasurface is a convenient device to manipulate the EM wavefront for near-field pattern construction. A number of metasurfaces are proposed to utilize multi-level phase modulation for intensity image shaping under linearly-polarized (LP) or circularly-polarized (CP) EM excitations. Based on the transmission-type metasurface, a linear polarization multiplexing hologram has been designed for the creation of clear patterns [23]. Pancharatnam-Berry (P-B) phase metasurface has been utilized to fulfill multi-focus imaging under CP excitation [24]. To overcome the limitation of polarization of incident wave, a polarization-free coding metasurface has been designed to realize helicity-switched holograms [25]. The bidirectional Janus metasurface has been designed to generate holograhpic images in the reflection and transmission channels simultaneously [26,27]. EM reconfigurable coding-metasurface has been designed to modulate the dynamic intensity field distributions by switching the element phase between $0^\circ$ and $180^\circ$ [28]. Huygens’ metasurface are proposed as hardware processor to perform analog optical computations for the EM signal and image [29,30]. However, most conventional meta-devices require a large effective area to contain more meta-atoms to achieve high-quality single-plane holographic image or multi-focus pattern. A 3D meta-hologram has been developed to produce multiple letter/figure-shaped images with varying focal lengths at different interfaces, but signal loss and interference occur due to the presence of the probe, which is situated between the horn antenna and the reflected metasurface [31]. Moreover, image post-processing and storage remain important issues, and compressed sensing technology has been utilized to process holographic images and achieved great performance in the terahertz frequency band [32]. This technology could be introduced into the microwave band for holography image storage.
In this article, a broadband bowtie-shaped meta-atom is designed to realize the high conversion efficiency (over 90%) covering the bandwidth from 7.43 to 19.06 GHz, carrying the property of the continuous $360^\circ$ coverage. Inspired by numerous CGH algorithms, a novel retrieval method is proposed to calculate the phase profile of the metasurface for high-quality holographic imaging. We design P-B phase metasurfaces to produce three single-plane images (“X”, “M”, and “U”) and dual-plane images (“X”, and “U”) at 13 GHz, which are composed of $24\times 24$ and $30\times 30$ meta-atoms, respectively. The LCP spherical beam obliquely irradiates on the reflection-type plate, which avoids the probe being between the feed antenna and the metasurface, so that the probe does not interfere with the signal propagation during signal detection, as demonstrated in Fig. 1. Each square element in the metasurface is regarded as a spherical wave source to radiate the EM waves, and the scattering element obtains different P-B phases by rotating the bowtie structure. By superimposing the EM waves radiated by the element, a desired holographic image can be created on the observation interface. Besides, compressed sensing is implemented to maintain almost all the image information under a small compression and it is utilized to reconstruct the original holographic image. The experimental validation of the fabricated samples exhibits good agreement between the measured and simulated results, and the measured imaging efficiency for these samples is as high as 74.40%, 67.22%, and 63.50%.
Fig. 1. Schematic diagram depicts that the proposed holographic meta-device is utilized for projecting the holographic images. The compressed sensing is utilized to store and reconstruct the images in the computer or receiving device.
2. Design theory of proposed meta-atom
2.1 Spin-to-orbital angular momentum conversion
The Jones Matrix Calculus is an effective method to determine the relationship between the input and output EM waves for an arbitrary meta-atom. The reflected EM field can be calculated by substituting the reflection coefficients and incident EM field into Jones matrix, and the left-hand circularly polarized (LCP) and right-hand circularly polarized (RCP) conversion coefficients can be demonstrated as [10]
in which $r_{uu}$, $r_{vv}$, $r_{ll}$ and $r_{rr}$ represent the co-polarized reflection coefficients under the $u-$polarized, $v-$polarized, LCP and RCP state excitations. And $r_{vu}$, $r_{uv}$, $r_{rl}$ and $r_{lr}$ indicate the cross-polarized reflection coefficients under the $u-$polarized, $v-$polarized, LCP and RCP state excitations. The rotation angle $\theta$ of the meta-atom is adopted to regulate the reflected phase of LCP and RCP waves, and it is capable of realizing continuous response phase manipulation for covering the range from $0^\circ$ to $360^\circ$. To simplify the conversion coefficient equations, the bowtie-shaped structure is selected as the scattering element for realizing $r_{uv}=r_{vu}=0$ in Fig. 1, which must possess the property of the mirror-symmetry along the $u-$ and $v-$directions. Then, there are only two terms ($r_{uu}=A_{uu} e^{j\varphi _{uu}}$ and $r_{vv}=A_{vv}e^{j\varphi _{vv}}$) left in the conversion coefficient equations. Since the metal ground covers the rear of the meta-atom, the incident EM waves are entirely reflected, and the associated intensities $A_{uu}$ and $A_{vv}$ satisfy the formula $A_{uu}=A_{vv}=1$. For the purpose of obtaining high circularly co-polarized conversion amplitude $A_{ll} \approx A_{rr} \approx 1$, $r_{uu}$ and $r_{vv}$ should adhere to the regulations of having the same amplitude $A_{uu}=A_{vv}=1$ and the reflected phase difference $\varphi _{diff} = \varphi _{uu} - \varphi _{vv} \approx \pi$.2.2 Optimization of bowtie-shaped meta-atom
The P-B phase meta-atom, since it has a continuous phase manipulation function, is proposed for designing the LCP/RCP coding metasurface in Fig. 1. The metallic bowtie-shaped patch printed on a ground-covered dielectric plate is exploited as the scattering element owing to its advantages of mirror-symmetric structure, ultrathin profile, and easy fabrication. The dielectric slab is chosen as substrate with thickness $h = 3.00$ mm and dielectric constant $\varepsilon _r = 3.2$. The lattice of the square element is $p = 8.00$ mm and the other geometrical parameters are related to the bowtie-shaped patch. In our design, the length $L$ and width $W$ related to the metallic patch are set as $6.75$ mm and $3.30$ mm, and parameters $L_h$ and $W_h$ represent the half length of $L$ and $W$, respectively. The initial setting of the remaining parameters ($sl_1, sw_1, sl_2, sw_2$) is illustrated in the center block diagram of Fig. 2. The $u-$ and $v-$polarized co-polarization reflection coefficients of the element can be controlled by changing the four triangle gaps in the patch. In order to analyze the influence of the gaps on the reflection phase curves, one of the variables in the triangle gaps is changed separately while other parameters remain constant.
Fig. 2. The setting of parameters about gaps is depicted in the center block. Simulation results of $\varphi _{uu}$, $\varphi _{vv}$, and $\varphi _{diff}=\varphi _{uu}-\varphi {vv}$ are simulated according to the separate modifies of parameters $sl_1$, $sw_1$, $sl_2$, and $sw_2$.
According to transmission line theory, the meta-atom can be equivalent to the circuit model as a series circuit with the inductance and the capacitance in Fig. 1. Then, the reflection phase curves ($\varphi _{uu}$, $\varphi _{vv}$, $\varphi _{diff}$) are simulated and illustrated in Fig. 2. As the value of $sl_1$ and $sl_2$ changes, this mainly affects the inductance $L_u$ and the capacitance $C_u$, which eventually affects the $u-$direction reflection phase $\varphi _{uu}$ as shown in Figs. 2(a) and (c). The parameters $sw_1$ and $sw_2$ govern the gap of the patch in the $v-$direction, causing the inductance $L_v$ and the capacitance $C_v$ to change, which primarily affect the change of reflection phase $\varphi _{vv}$ in Figs. 2(b) and (d). When only the parameter $sl_1$ is changed, the phase difference $\varphi _{diff}$ shifts upward in the whole operating band with the increase of the parameter $sl_1$. A similar phenomenon appears when the parameter $sw_1$ is modified, and the law of these two parameters can be utilized for overall adjustment of the phase difference. However, with an increase of the geometric parameter $sl_2$ or $sw_2$, the phase difference $\varphi _{diff}$ tends to shift downward in the working band. The increase of $sw_2$ mainly reduces the phase difference within $6 - 12$ GHz, while the alteration of $sl_2$ primarily affects that in $12 - 20$ GHz. Inspired by the influence of the aforementioned behaviors, fine-tuning of the reflection phase curves can be accomplished by independently controlling the parameters $sl_2$ and $sw_2$, to achieve $\varphi _{diff} \approx \pi$ in the entire frequency band.
In the optimization process of the meta-atom, the geometrical parameters start from the aforementioned state 1 ($sl_1=0.5L, sw_1=0.5W_h, sl_2=0.5L_h, sw_2=0.5W$), as illustrated in Fig. 3(a). By observing the phase difference $\varphi _{diff}$ in Fig. 3(b), it can be determined that the phase difference of the meta-atom fulfills $\varphi _{diff} \approx 120^\circ$ throughout the whole frequency range. For achieving high CP co-polarization conversion efficiency, the phase difference should satisfy the regulation of $\varphi _{diff} \approx 180^\circ$, so the whole phase difference curve $\varphi _{diff}$ needs to be shifted up within $6 - 20$ GHz. Firstly, $sl_1$ and $sw_1$ are increased to make the phase difference move upward, to approach the goal $180^\circ$. The meta-atom is optimized into state 2 during this step, as shown in Fig. 3(a). Next, the phase difference is adjusted to meet the goal in state 3 by reducing $sl_2$ and $sw_2$. The optimum parameters of meta-atom are listed in Table 1.
Fig. 3. (a) Schematic diagram shows three classical states of the meta-atom on the optimization route. (b) The phase difference $\varphi _{diff}$ of three meta-atom states, and the reflected amplitude and phase of state 3 under linearly polarized (LP) excitation. (c) The co-polarized amplitude and conversion efficiency of state 3 under LCP excitation. (d) The reflected amplitude and phase of meta-atom state 3 of varied orientation angles $\theta$.
Table 1. The parameters of meta-atom (Unit:mm)
After completing the optimization process, the EM response behavior of the meta-atom state 3 is calculated under LCP excitation as illustrated in Fig. 3(b). Within a wide frequency bandwidth, both the reflection amplitude of $u-$polarized and $v-$polarized state are almost equal to 1, with approximately $180^\circ$ phase difference. The conversion efficiency ($\eta =2|(r_{xx}-r_{yy})/2|^2/[|r_{xx}|^2+|r_{xy}|^2+|r_{yx}|^2+|r_{yy}|^2]$) is calculated to measure the conversion performance of the meta-atom as demonstrated in Fig. 3(c), which describes the ratio between co-polarized conversion energy and total reflected energy. The designed high-performance meta-atom remains co-polarization reflection $r_{ll}$ greater than 0.95 and conversion efficiency higher than 0.90 within a wide bandwidth covering from 7.43 to 19.06 GHz (relative bandwidth is 87.7%). It is significant to find that the phase responses are paralleled as desired and the co-polarization reflection amplitudes are all greater than 0.90 inside the entire working bandwidth for varied orientation angles $\theta$ in Fig. 3(d). Hence, the design bowtie-shaped meta-atom (state 3) can be used as the superior candidate for the generation of the holographic image in the microwave region.
3. Design scheme of letter-shaped meta-hologram
3.1 Modified weighted Gerchberg-Saxton algorithm
The next assignment is to calculate the phase distribution profile of the metasurface for producing the specific holographic image on the observation interface. Various retrieval methods are proposed to seek the optimum coding phase profile required for freely controlling the intensity distribution, which include direct search algorithm [33], Fienup Fourier algorithm [34], and Gerchberg-Saxton (GS) algorithm [35]. The weighted Gerchberg-Saxton (GSW) algorithm [36] is an improved version of GS algorithm with an iteration weight factor, and it has a better performance in the meta-hologram design for precise energy distribution than GS method. The original GSW algorithm is utilizing Fraunhofer diffraction or Green function as the propagation formula in other literatures [37,38]. But the Rayleigh-Sommerfeld (R-S) diffraction theory [15] is a better choice to describe the EM radiation behavior in the microwave region, which can be applied in the modified GSW algorithm.
The diagram schematically shows that the metasurface generates the multi-plane holographic images on the observation plane by reflecting the feeding beam in Fig. 1. First, we only focus on the generation of single-plane holography imaging. The metasurface is composed of N square meta-atoms following the orthogonal lattice distribution. In addition, $E_n$ ($\varphi _n$) represents the complex amplitude (abrupt phase accumulation) of the $n^{th}$ meta-atoms under the normal excitation. Above the metasurface at the distance of the focal length, the observation plane is segmented into a grid with various focal points, and the focal point is defined as the yellow square allocated the electric energy. The intensity $E_m$ at $m^{th}$ focal point is derived from the superposition of the EM waves reflected by N square scattering elements. On the one hand, to realize the meta-hologram with high imaging efficiency, the sum of intensity $\sum ^M_{m=1} |E_m|$ needs to be maximized. On the other hand, the intensity of the electric field at the $m^{th}$ spot should close to the predefined $s_m$, which can utilize the weight matrix $[w_m]$ for reducing the error between $E_m$ and $s_m$. Since it is impossible to obtain an explicit relation between $E_m$ and $\varphi _n$, the best coding phase $\varphi _n$ of the metasurface is calculated through the iteration procedure. In the end, the issue about the generation of holographic images is evolved into the computation of weight factor $w_m$ and phase shift $\varphi _n$.
The first task is to determine the initial setting in the iteration procedure, which primarily consists of two parts: one is to set the focal phase $\varphi _m^0$ on the observation surface, and another is to set the weight factor $w_m^0$. Based on the modified GSW algorithm, the initial setting is written as
Next, the amplitude of each focal spot is set to 1 to form the uniform letter shape in this paper. The complex amplitude of every source spot is put into the R-S diffraction function to derive the electric energy distribution of the near-field observation plane under the LCP plane excitation. The results of abrupt phase $\varphi _n$, weight factor $w_m$, and focal intensity $E_m$ in the iteration step are calculated as
The previous single-plane GSW R-S method can achieve a clear image in the monolayer holography application, but it has the limitation of high noise and low resolution in multi-plane holography imaging due to the inhomogeneity of imaging intensity in different planes, which is displayed in Fig. S1 (see Supplement 1). For solving this problem, a layer factor $f_{lx, (lx=1,2,\ldots )}$ is introduced to adjust the intensity of different planes and retrieve the complex amplitude of the metasurface plane. In our multi-plane GSW R-S method, the Eqs. (6), (7), (11), and (12) are replaced by
For evaluating the image quality quantitatively, imaging efficiency and root-mean-square error (RMSE) are employed to describe the intensity regulation ability of the metasurface. Imaging efficiency, defined as the proportion of energy in the hologram ($I_{energy}$) to the total energy on the measured plane ($I_{plane}$), is utilized to evaluate the capacity to regulate EM fields [39]. The RMSE is adopted to measure the difference between the focal intensity of the holographic image and the pre-determined $s_m$ [38]. When the RMSE and imaging efficiency reach the set threshold, or when the number of iterations exceeds the limitation, the coding phase profile is output as the result and the iterative calculation is stopped.
Imaging efficiency (IE) is calculated as
Practically, the RMSE ($\sigma$) is described as
3.2 Generation of letter-shaped images
In this work, each metasurface is composed of $24 \times 24$ bowtie-shaped meta-atoms with appropriate rotation angles for the generation of the single-plane image, which is far less than the number of elements used in other designs in Table 2, covering the area about $192 \times 192$ mm$^2$. Based on the previous single-plane GSW algorithm, the coding phase profile $\varphi _n$ of the metasurface is calculated for projecting the corresponding letter-shaped holographic image with a specific focal length, which includes “X”, “M” and “U” shapes. By constructing the metasurface using phase map $\varphi _n$, it has potential application for holographic imaging within the operating bandwidth of 7.43-19.06 GHz, as shown in Fig. S2 (see Supplement 1). However, the feed needs to be placed at a large distance directly above the metasurface, and the probe obstructs the propagation of EM waves. To avoid blocking EM waves of the feeding source, the scattering elements are excited by a helical antenna tilted in $45^\circ$. An abrupt phase shift term needs to be superimposed to convert the spherical wave into a plane wave, which limits the metasurface to operate in a narrow band with a center frequency selecting from 7.43-19.06 GHz range. The total phase accumulation equation is written as
Table 2. The comparision of different metasurfaces for holograms.
The single-plane electric field intensity distributions of theoretical and simulated results are depicted in Fig. 4 (left box). It should be noted that the observation surface is 350 mm above the metasurface with an area $500 \times 500$ mm$^2$. The simulation results under the ideal LCP plane wave or spherical wave excitations agree well with the theoretical calculations, and the highlighted patterns of them are obviously consistent with the letters “X”, “M”, and “U”. The simulated results under the ideal LCP plane wave incidence are like a copy of the theoretical patterns with perfect uniform intensity distributions. However, the uniformity of the intensity field in the simulation results under the spherical wave is worse than that in Fig. 4(e-g), because of the nonideal LCP excitation and the error in converting a spherical wave into a plane wave. Since the bowtie-shaped element has opposite phase response for LCP and RCP incidence, the elaborate LCP holographic phase map becomes disordered under the excitation of RCP wave. Under the simultaneous incidence of LCP and RCP waves, the metasurface can generate the letter-shaped LCP patterns (“X”, “M”, and “U”) and the chaotic RCP patterns, as illustrated in Figs. S5 and S6 (see Supplement 1). When the working frequency deviates from 13 GHz, the phase map of the metasurface superimposes the phase difference caused by space EM wave transmission, thus making the holographic image deform and deviate from the preset position, as demonstrated in Fig. S7 (see Supplement 1).
Fig. 4. (a-d) Theoretical calculation, (e-h) simulated calculation under the ideal LCP plane wave (PW) excitation, and (i-l) simulated calculation under the LCP spherical wave (SW) excitation of single-plane/double-plane letter-shaped intensity distributions.
To verify the performance of the multi-plane modified GSW R-S method, double-plane images (“X” and “U”) are designed in different focal lengths by using the metasurface with $30\times 30$ meta-atoms, and the comparison of unit quantity with other designs is illustrated in Table 2. The projecting intensity shapes in different planes of theoretical and simulated results are shown in Fig. 4 (right box). The obtained results are exactly consistent with the distribution properties in single-plane images, which validate the practicability and correctness of the proposed multi-plane method. The EM field reflected by the metasurface scatters and changes continuously along the propagation path. The depth of holographic image “X”/“U” is 200/360 mm range from 290/570 to 490/930 mm, as displayed in Figs. S8 and S9 (see Supplement 1). In the middle of two planes with focal length of 490 and 570 mm, the field intensity distribution is relatively confusing and cannot be well distinguished from “X” and “U”. Moreover, this method can be further applied to triple-plane holographic imaging application, as demonstrated in Fig. S10 (see Supplement 1).
3.3 Storage and reconstruction of letter-shaped images
According to compressed sensing theory, the target image can be recorded practically all of the image information under a small compression, in which the target image must have sparsity or be transformed into a sparse matrix through a specific basis. Compressed sensing theory consists mostly of two types of reconstruction algorithms. One method is based on greedy algorithms that demand sparse signal as an input, but it faces with issue about that the input matrix and its sparsity are often unknown. Another method is based on a convex optimization technique, which typically delivers more accurate responses at the expense of increased computing complexity. Basis pursuit is adopted for meta-hologram reconstruction by using L1 minimization in this paper [42], which is a high-performance image storage and reconstruction scheme for a two-dimensional (2D) input signal. It has a low computation time, great reconstruction quality, and supports various measurement matrices and multiple constrain regulations.
In this work, we choose the Gausse random matrix as an observation matrix, which is composed of elements with a value of 0 or 1. A row of the Gausse random matrix can be extracted and transformed into a $n \times n$ 2D matrix, which is employed as a mask filter. Then, we record amplitude $y_i$ at 13 GHz corresponding to each mask filter. Next, all the measured $y_i$ are arranged into a one-dimensional column vector $Y$, the related equation can be represented as
where $Y$ is a column vector of $M \times 1$ that restores the compressed data, H is a $M \times N$ ($N=n^2$) Gausse matrix, and $x$ is a row vector of $N \times 1$ that holds the reconstruction information. The method of holographic image reconstruction is solving the above equation for $x$ with the given $Y$ and reshaping the solution $x$ into a 2D square matrix. Therefore, it is only necessary to store the compressed data $Y$ in the whole system.The reconstruction effect with under-sampling is checked on the simulated results in Fig. 4(i-l), and compressed holographic images are obtained by post-processing the original energy distribution pattern. In Fig. 5, it shows the holography images reconstructed via basis pursuit at $z = 350 (650)$ mm imaging plane under different compression ratios (CR). The reconstructed image gradually becomes indistinct at the center and edge of the letter-shaped intensity pattern when CR is reduced. The Person correlation coefficient between each compressed image and simulation image is calculated to estimated the compression performance, which is defined as the following equation [32]
Fig. 5. Reconstruction effect of three letter-shaped holographic image with different compression rate. The reconstructed images (a-d) under 75% compression; (e-h) under 50% compression; (i-l) under 25% compression.
4. Experimental validation
For the purpose of verifying the proposed systematic design process, the metasurface sample for single-plane (double-plane) holographic imaging has been designed and fabricated at 13 GHz in Fig. 6(a), which is composed of $24 \times 24$ ($30 \times 30$) scattering elements. To generate holographic images with uniform energy distribution on the observation interface, the LCP helical antenna is used to irradiate a spherical wave on the metasurface. A foam box is used to assemble the feed antenna and metasurface, which has a very small impact on the propagation of EM waves. The meta-device is placed on the wooden holder in front of the near-field planar scanning system. The photographs of the antenna and metasurface are shown in Fig. 6(a), which also demonstrates the enlarged views of them at the end of the arrow.
Fig. 6. (a) Photographys of the assembly and measure environment of the fabricated metasurface and helical antenna. (b-c) The measured results of the generated holographic images. (d-g) The reconstructed holographic images with different compressed rates.
In our experimental setting, the metasurface’s center is aligned with the origin point of the scanning coordinate system, and the scanning observation plane is parallel to the metasurface plane. The experimental observation plane is set to 350 (650) mm above the metasurface, covering an area of $500 \times 500$ mm$^2$. The waveguide probe moves freely in the $xoy$ plane with a step length of 3.33 mm, allowing for the accurate measurement of the amplitude distribution of the reflected waves at a specific position. After completing the near-field detection of the reflected EM wave in the anechoic chamber, Figs. 6(b) and (c) demonstrate the measure intensity patterns are consistent with the simulated images in Figs. 4(i) and (l). It is worth noting that the tiny discrepancy between the simulation and experimental results could be a consequence of fabrication, assembly, and alignment issues in the meta-device.
The imaging efficiencies of the measured images in Figs. 6(b) and (c) are calculated to be 74.40%, 67.22%, and 63.50%, respectively. These values closely match the imaging efficiencies of the simulated results (80.13%, 75.80%, and 73.48%), which indicates a high degree of accuracy in holographic imaging generation. As shown in Table 2, the comparison results illustrate that our retrieve algorithm and design scheme have high performance in the holographic field, including a small number of units and high imaging efficiency. The proposed design method realizes these two advantages for the following reasons: (1) The selected PB phase units can obtain continuous regulation 360$^\circ$ phase, which is different from other designs that discretized the phase into 1-bit, 2-bit, and 3-bit coding levels. Selecting the phase map of single-plane letter “X” as an example, the imaging efficiency continuously improves as the coding level increases in Fig. S11 (see Supplement 1). (2) Compared to Green’s function used in other works, the selected R-S diffraction theory is a better choice to describe the EM field generated by the meta-atom, which is shown in Fig. S11(d) (see Supplement 1).
In order to validate that compressed sensing technology can effectively preserve images, 50% and 25% CRs are selected to compress and store the generated holographic images. The reconstructed images preserve more than 93% image information under 50% and 25% CRs in Figs. 6(d-g), and this technique can be applied to most image compression saves.
5. Conclusion
In this paper, we combine computer-generated holography and compressed sensing technology for generation and reconstruction of images. Firstly, a broadband bowtie-shaped meta-atom is proposed with the characteristics of full phase coverage and high co-polarized conversion efficiency. Next, a multi-plane GSW R-S algorithm is derived for the phase distribution of single- or double-plane letter-shaped images. With the guidance of phase profiles, the metasurfaces are composed of $24 \times 24$ ($30 \times 30$) meta-atoms with appropriate orientation angles, which has fewer element quantity than the metasurfaces in other literatures. Finally, the letter-shaped holographic images are compressed under a small ratio to record almost all the image information. For verifying the correctness of our design procedure, two meta-devices are fabricated for experimental measurement, and the experimental result agrees well with the simulated result. It provides this systematic method in holographic technology to implement various applications, including data storage, information encryption, and imaging.
Funding
National Natural Science Foundation of China (62071403).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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