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Fourier Convolution Operation on Metasurface-Based Hologram in Microwave Region

Fourier Convolution Operation on Metasurface-Based Hologram in Microwave Region hv photonics Communication Fourier Convolution Operation on Metasurface-Based Hologram in Microwave Region 1 1 1 , 2 1 3 , 1 Shuai Yang , Chunsheng Guan , Xumin Ding , Kuang Zhang , Shah Nawaz Burokur * and Qun Wu Department of Microwave Engineering, Harbin Institute of Technology, Harbin 150001, China; yanghaa@hit.edu.cn (S.Y.); guanchunsheng@stu.hit.edu.cn (C.G.); xuminding@hit.edu.cn (X.D.); zhangkuang@hit.edu.cn (K.Z.); qwu@hit.edu.cn (Q.W.) Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China LEME, UPL, Univ Paris Nanterre, F92410 Ville d’Avray, France * Correspondence: sburokur@parisnanterre.fr Abstract: In this paper, a 0.1 -thick 1-bit coding metasurface is proposed to achieve a polarization- insensitive hologram under oblique incidence, utilizing compact ground-backed patch unit cells. Fourier convolution theory in a digital signal processing system is added to the hologram calculation of the improved weighted Gerchberg–Saxton (GSW) algorithm to achieve control of the scattered pattern in the microwave region. As a proof of concept, a prototype operating at 15 GHz is designed to verify the validity of our proposed approach. The measured performances show good imaging quality under different incident polarizations, providing potential applications in imaging processing and information storage. Keywords: metasurface; polarization-insensitive; hologram 1. Introduction Citation: Yang, S.; Guan, C.; Ding, X.; Zhang, K.; Burokur, S.N.; Wu, Q. Metasurfaces, the two-dimensional (2D) version of metamaterials, are composed of Fourier Convolution Operation on arrays of artificial scatters, known as meta-atoms, with designed geometries and orientation Metasurface-Based Hologram in angles, which allow one to control the main characteristics of the scattered wave such as Microwave Region. Photonics 2021, 8, amplitude, phase and polarization [1,2]. Due to the extraordinary capability of tailoring 174. https://doi.org/10.3390/ wavefronts and low loss, low cost and low profile characteristics, metasurfaces have been photonics8060174 extensively exploited in practical devices, such as retroreflectors [3], cloaking devices [4], orbital angular momentum (OAM) generators [5], flat lenses [6], and holograms [7–10], to Received: 23 April 2021 name a few. Recently, the concept of coding metasurface has attracted much attention, in Accepted: 19 May 2021 which the phase or amplitude response of the metasurface is characterized by N-bit digital Published: 21 May 2021 coding particles rather than continuous electromagnetic (EM) parameters. For example, using the simplest 1-bit coding of the binary coding scheme, elements of the reflective Publisher’s Note: MDPI stays neutral metasurface are “0” and “1”, corresponding to phase response 0 and , respectively. Elec- with regard to jurisdictional claims in tromagnetic waves can be manipulated in a simple and effective way by designing the published maps and institutional affil- encoding sequence of digital meta-atoms, which has many applications in beam form- iations. ing [11], diffuse scattering [12], energy radiations control [13] and complex wavefront shaping [14]. Holography is one of the most promising imaging techniques [15]. Tradi- tional holograms can be generated by the interference of a reference beam and the scattered beam from the real object or calculated by using numerical computation [16,17]. Compared Copyright: © 2021 by the authors. with traditional holograms, the emergence of metasurfaces has further promoted the de- Licensee MDPI, Basel, Switzerland. velopment of computational holographic imaging by providing unprecedented spatial This article is an open access article resolution, and high-precision reconstructed images. By introducing a reconstruction distributed under the terms and algorithm such as Gerchberg–Saxton (GS) [18], computer-generated holograms can be de- conditions of the Creative Commons signed using engineered sub-wavelength elementary atoms with well-tailored amplitude Attribution (CC BY) license (https:// and phase responses, and digital elementary holography can be generated by coding the creativecommons.org/licenses/by/ holographic information of the object pattern [7,8]. Compared with traditional geometric 4.0/). Photonics 2021, 8, 174. https://doi.org/10.3390/photonics8060174 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 174 2 of 9 optics, the spatial resolution and imaging rate of metasurface holographic imaging are significantly improved. Due to the precise control of EM waves, holographic metasurface also finds applications in short-range communication systems, detection, data storage, and information processing [19–21] in the microwave regime. Efficiency is one of the most important challenges in metasurface design. Due to basic limitations and inherent ohmic losses, the efficiency of a single-layer transmissive metasurface is often fairly low, and has been shown to be only of the order of a few percent of magnitude at most [2]. Some high-efficiency transmissive metasurfaces, for instance, dielectric metasurfaces [22], Huygens’ metasurfaces [23], multilayered metasurfaces and meta-transmitarrays [24,25], have been studied to improve the efficiency. However, these designs necessitate a minimum finite thickness, significant manufacturing complexities and frequency dispersions. Reflective metasurfaces provide a solution for high-efficiency and ultrathin metasurface design and have been demonstrated in various applications such as antennas [26–29], holograms [30,31], waveplates [32] and metamirrors [33,34]. However, the feeding source of reflective metasurfaces is usually in the path of the reflected signal, which affects the performances of the metasurfaces. Recently, we proposed the coding metasurface approach for enhanced quality holo- graphic imaging by discretizing the phase distribution calculated by a GSW algorithm to different bit levels [7,8]. In this paper, a reflective 1-bit coding metasurface is proposed for polarization-insensitive hologram under oblique incidence of 60 in the microwave region, as illustrated in Figure 1a. The proposed metasurface is composed of subwavelength patch elements, which can provide a 180 phase shift for dual linearly polarized incidences. By designing the size of the patch elements, we find the meta-atoms of the binary element codes “0” and “1” to construct a 1-bit coding element hologram. A modified GSW algo- rithm is used to calculate the original interfacial phase distribution. Then, by applying Fourier convolution operations on the hologram, the direction of the scattered pattern can be steered to the desired direction. Experimental verification performed on a fabricated prototype is qualitatively consistent with theoretical predictions and numerical simulations, Photonics 2021, 8, x FOR PEER REVIEW 3 of 9 demonstrating both the feasibility of the approach and the high imaging quality of the proposed 1-bit polarization-insensitive coding element hologram. Figure 1. Cont. Figure 1. (a) Schematic demonstration of the proposed 1-bit polarization-insensitive metasurface- based hologram under oblique incidence. (b) 3D topological structure of the unit cell. (c,d) Reflec- tion phase response of the meta-atom under TM and TE polarization as functions of Px and Py, respectively. (e,f) Reflection coefficients of the binary meta-atoms as a function of frequency under TM and TE polarization, respectively. 2. Design of the Coding Elements Figure 1a shows the schematic diagram of a hologram of arbitrary polarization at a large incidence angle of 60°. By introducing Fourier convolution operation on the metasurface, the scattering pattern of the hologram can be steered as desired. For the con- venience of measurement, the hologram is designed to scatter in the normal direction here. Figure 1b shows the geometry and parameters of the coding particles. The F4BM300 dielectric substrate with thickness t = 2 mm, relative permittivity εr = 3 and tan δ = 0.0015 is used. A ground-backed patch meta-atom is exploited as the coding particle due to its good performance in polarization isolation and fabrication tolerance requirements. The perfect electric conductor (PEC) boundary condition is considered for the metal parts in simulations. Numerical simulations are performed using the commercial software CST Microwave Studio. Under the incidence of TM wave, the phase response of the meta-atom varies with the length Px of the patch along the x-direction, as shown in Figure 2c. It can Photonics 2021, 8, x FOR PEER REVIEW 3 of 9 Photonics 2021, 8, 174 3 of 9 Figure 1. (a) Schematic demonstration of the proposed 1-bit polarization-insensitive metasurface- Figure 1. (a) Schematic demonstration of the proposed 1-bit polarization-insensitive metasurface- based ho based hologram logram un under der obliq oblique ue incid incidence. ence. (b) 3D t (b) 3D opolog topological ical stru str ctu uctur re ofe the u of the nit unit cellcell. . (c,d( ) Ref c,d)lReflection ec- tion phase response of the meta-atom under TM and TE polarization as functions of Px and Py, phase response of the meta-atom under TM and TE polarization as functions of P and P , respectively. x y respectively. (e,f) Reflection coefficients of the binary meta-atoms as a function of frequency under (e,f) Reflection coefficients of the binary meta-atoms as a function of frequency under TM and TE TM and TE polarization, respectively. polarization, respectively. 2. Design of the Coding Elements 2. Design of the Coding Elements Figure 1a shows the schematic diagram of a hologram of arbitrary polarization at a Figure 1a shows the schematic diagram of a hologram of arbitrary polarization at large incidence angle of 60°. By  introducing Fourier convolution operation on the a large incidence angle of 60 . By introducing Fourier convolution operation on the metasurface, the scattering pattern of the hologram can be steered as desired. For the con- metasurface, the scattering pattern of the hologram can be steered as desired. For the venience of measurement, the hologram is designed to scatter in the normal direction convenience of measurement, the hologram is designed to scatter in the normal direction here. Figure 1b shows the geometry and parameters of the coding particles. The F4BM300 here. Figure 1b shows the geometry and parameters of the coding particles. The F4BM300 Photonics 2021, 8, x FOR PEER REVIEW dielectric substrate with thickness t = 2 mm, relative permittivity εr = 3 and tan δ = 0.0014 of 5 9 dielectric substrate with thickness t = 2 mm, relative permittivity # = 3 and tan d = 0.0015 is used. A ground-backed patch meta-atom is exploited as the coding particle due to its is used. A ground-backed patch meta-atom is exploited as the coding particle due to its good performance in polarization isolation and fabrication tolerance requirements. The good performance in polarization isolation and fabrication tolerance requirements. The perfect electric conductor (PEC) boundary condition is considered for the metal parts in perfect electric conductor (PEC) boundary condition is considered for the metal parts in simulations. Numerical simulations are performed using the commercial software CST also be observed that the length simulations. Numerical Py of the pa simulations tch along are y performed -direction using has l theit commer tle infl cial uen softwar ce on t e CST he Microwave Studio. Under the incidence of TM wave, the phase response of the meta-atom Microwave Studio. Under the incidence of TM wave, the phase response of the meta-atom phase response. The reflection phase coverage approaches 210° for TM incidences by var- varies with the length Px of the patch along the x-direction, as shown in Figure 2c. It can varies with the length P of the patch along the x-direction, as shown in Figure 2c. It can ying the length Px. Similarly, a reflection phase coverage of 310° is obtained by varying also be observed that the length P of the patch along y-direction has little influence on the length Py. The phase the phase coverage response. s un The de rr dual eflectionline phase arcoverage ly polarized approaches incidences ar 210 for TM incidences e efficient by varying the length P . Similarly, a reflection phase coverage of 310 is obtained by varying to achieve a 180° phase shift for the unit cell design. A bare unit cell (without metal patch the length P . The phase coverages under dual linearly polarized incidences are efficient to element) is utilized here to operate  as code “0” to simplify the design process and also to achieve a 180 phase shift for the unit cell design. A bare unit cell (without metal patch reduce the coupling e element) ffect between adj is utilized hera ecent un to operate it cells as code . To “0” satisfy th to simplify e 180° the design phas process e shift and be- also to reduce the coupling effect between adjacent unit cells. To satisfy the 180 phase shift tween code “0” and code “1” under dual linearly polarized incidences, the parameters of between code “0” and code “1” under dual linearly polarized incidences, the parameters unit cell code “1” is optimized to be Px = 5.2 mm and Py = 3.4 mm. of unit cell code “1” is optimized to be P = 5.2 mm and P = 3.4 mm. x y Figure 2. (a) Phase distribution of the original hologram. (b) Gradient phase distribution. (c) Phase distribution of hologram in normal direction. (d) 1-bit coding map. Figure 2. (a) Phase distribution of the original hologram. (b) Gradient phase distribution. (c) Phase distribution of hologram in normal direction. (d) 1-bit coding map. Figure 1e,f shows the reflection responses of the binary unit cells under TM and TE incidences as a function of frequency. For the dual linear polarizations, a phase difference of 180° is achieved at 15 GHz, providing the freedom to have the same phase shift in both TE and TM polarizations sharing the same aperture. The reflection amplitudes can also be nearly uniform under the different polarizations, as shown in Figure 1e,f. Since arbitrary polarizations can be decomposed into TE and TM polarizations, the same hologram for any polarization can be obtained from the metasurface. 3. Design of the Coding Meta-Hologram The modified GSW algorithm is used to retrieve the required theoretical phase profile [2]. The method consists in selecting ideal point sources as virtual sources and placing them at pre-designed hotspots. Considering that there are N hotspots located at (xn, yn, zn) (n = 1 to N), the phase delay at the position of each coding element ϕ (xm, ym, zm) (m = 1 to M) can be retrieved by superposing the electromagnetic field generated by all the virtual sources described by Green’s function. Accordingly, the reconstructed electric field is con- verged to the predesigned hotspots. In order to keep uniform intensity distribution among hotspots, a weight factor wn is introduced to reduce intensity difference among the N hotspots. An iterative procedure between the holography imaging and meta-hologram is proposed to obtain the uniform intensity profile of the target image as follows: ikr pp −1 wE nn φ =arg( )  (1) p −1 n =1 np −+ ikr iφ mm E = (2) m =1 p −1  n pp −1 n =1 (3) ww = nn p −1 NE Photonics 2021, 8, 174 4 of 9 Figure 1e,f shows the reflection responses of the binary unit cells under TM and TE incidences as a function of frequency. For the dual linear polarizations, a phase difference of 180 is achieved at 15 GHz, providing the freedom to have the same phase shift in both TE and TM polarizations sharing the same aperture. The reflection amplitudes can also be nearly uniform under the different polarizations, as shown in Figure 1e,f. Since arbitrary polarizations can be decomposed into TE and TM polarizations, the same hologram for any polarization can be obtained from the metasurface. 3. Design of the Coding Meta-Hologram The modified GSW algorithm is used to retrieve the required theoretical phase pro- file [2]. The method consists in selecting ideal point sources as virtual sources and placing them at pre-designed hotspots. Considering that there are N hotspots located at (x , y , n n z ) (n = 1 to N), the phase delay at the position of each coding element f (x , y , z ) n m m m (m = 1 to M) can be retrieved by superposing the electromagnetic field generated by all the virtual sources described by Green’s function. Accordingly, the reconstructed electric field is converged to the predesigned hotspots. In order to keep uniform intensity distribution among hotspots, a weight factor w is introduced to reduce intensity difference among the N hotspots. An iterative procedure between the holography imaging and meta-hologram is proposed to obtain the uniform intensity profile of the target image as follows: p p1 ikr e w E p n n f = arg( ) (1) m å p1 n=1 ikr +if m m E = (2) n å m=1 p1 p p1 n=1 w = w (3) n n p1 N E th where f is defined as the phase shift of the m (m = 1 to M) coding element and E m n th n denotes the electric field intensity of the n (n = 1 to N) hotspots. r is the distance between th th th m coding element and n hotspot and superscript p represents the p iterative step. According to Equations (1) and (3), the weight factor w is adjusted step by step until the least mean square error between the target and the reconstructed image becomes less than a predesigned threshold. Based on the modified GSW retrieval algorithm, the theoretical phase distribution can be obtained, as shown in Figure 2a. As a property of the Fourier transform, the convolution theorem can be described: FFT f (t)g(t) , f (w) g(w) (4) The arguments t and w in Equation (1) can be replaced by x and sinq, respectively, leading to the following equation [35]: FFT f (x )g(x ) , f (sin q) g(sin q) (5) l l where x = x/l is the electrical length, and q is the angle with respect to the normal direc- tion. Equation (2) can be simplified when the item g (x ) becomes a Dirac-delta function: FFT jx sin q l 0 E(x )e , E(sin q) d(sin q sin q ) l 0 (6) = E(sin q sin q ) where x sinq describes the gradient phase along a determined direction. Equation (3) l 0 jx sin q l 0 shows that by introducing a gradient phase of e , the scattering pattern E (sinq ) can 0 Photonics 2021, 8, 174 5 of 9 be deviated from its original direction by the quantity sinq in the angular coordinate. Such a process can be regarded as superposing an additional phase distribution to the original one, reducing computational complexity for optimizing the scattering patterns. Based on the scattering pattern shift principle, the hologram can be arbitrarily rotated around the normal axis by the convolution operation. Since the incidence angle is designed to be 60 here, a gradient phase distribution shown in Figure 2b is added to the original hologram to steer the scattering pattern to the normal direction. Then, the obtained phase distribution in Figure 2c is discretized to 0 and  values. Therefore, the phase information can be described by the 1-bit coding map shown in Figure 2d. Then, the 1-bit coding hologram can be constructed based on the obtained coding map. 4. Results and Discussion To demonstrate the proposed 1-bit polarization-insensitive hologram, a metasurface is designed at 15 GHz and simulated to project a “square” image with four corner hotspots, as illustrated in Figure 1a. The metasurface is composed of 41  41 meta-atoms with the size of 235.75 mm  235.75 mm. The metasurface is fabricated using the conventional printed circuit board (PCB) technique where copper is used for the metal parts. The imaging plane here is designed to be 4 away from the metasurface. The metasurface is illuminated by TM, TE, left-hand circularly polarized (LHCP) and right-hand circularly polarized (RHCP) waves under an oblique incidence angle of 60 . Figure 3a,b, respectively, present the intensity distribution of the simulated reflected electric field in the imaging plane under TM and TE incident waves illumination. Under LHCP and RHCP wave incidences, the simulated reflected electric field strength of the cross-polarized component is shown in Figure 3c,e. The simulation results are consistent with the theoretical design, showing good imaging quality. It should be noted that a small part of incident CP wave is transformed into its co-polarized component in the reflected field, as shown in Figure 3d,f, since the Photonics 2021, 8, x FOR PEER REVIEW 6 of 9 reflection phases for TM and TE incidences are not identical, as previously presented in Figure 1e,f. Figure 3. Simulated reflected electric field intensity distributions (a,b) under TM and TE incidence, Figure 3. Simulated reflected electric field intensity distributions (a,b) under TM and TE incidence, respectively. (c,d) Cross- and co-polarized component under LHCP incidence, respectively. (e,f) respectively. (c,d) Cross- and co-polarized component under LHCP incidence, respectively. (e,f) Cross- and Cross- and co- co-polarized polarized com component ponent u under nder RHCP inci RHCP incidence, dence, respe respectively ctively.. In order to experimentally verify the performances of the proposed polarization-in- sensitive hologram, a sample is fabricated and depicted by the photograph shown in the inset of Figure 4a. The schematic diagram of the near-field scanning system exploited to measure the electric field distribution is illustrated in Figure 4a, and the measurements are carried out in a microwave anechoic chamber. The feeding source, which is a dual- polarized broadband horn antenna, is placed far away enough from the metasurface to launch quasi-plane waves (TM, TE, LHCP and RHCP as required) at an oblique incidence angle of 60°. The feeding horn antenna is connected to one port of a vector network ana- lyzer (VNA) and fixed at the angle of 60°. A field-sensing probe is used to measure both the amplitude and the phase of the electric field. From the measured data of the electric field along the x- and y-axes, the LHCP and RHCP components are calculated as: EE=−()iE LHCP x y (7) EE=+()iE RHCP x y where Ex and Ey is the electric field along x- and y-axis, respectively. ELHCP and ERHCP is the electric field of the LHCP and RHCP component, respectively. Figure 4b–g depicts the measured results, showing good qualitative agreement with the simulated ones presented in Figure 3a–f. The imaging efficiency, which refers to the proportion of the total incident energy concentrated in the preset focus, is calculated as the energy in the preset focus referenced to the total reflected energy on the measured plane [7,8]. The imaging efficiency is calculated to be 37.3% and 40.3% for TM and TE incidence, respectively. It should be noted that a higher bit level of coding elements can reduce the phase discretization and improve the performance of the metasurface, as it has been demonstrated in a previous work [7]. However, here, the 1-bit coding level is used as a good tradeoff between design complexity and imaging performance. As discussed above, since the reflection phases for TM and TE incidences are not identical, some of the incident CP wave is transformed into its co-polarized component in the reflected field, as Photonics 2021, 8, 174 6 of 9 In order to experimentally verify the performances of the proposed polarization- insensitive hologram, a sample is fabricated and depicted by the photograph shown in the inset of Figure 4a. The schematic diagram of the near-field scanning system exploited to measure the electric field distribution is illustrated in Figure 4a, and the measurements are carried out in a microwave anechoic chamber. The feeding source, which is a dual- polarized broadband horn antenna, is placed far away enough from the metasurface to Photonics 2021, 8, x FOR PEER REVIEW 7 of 9 launch quasi-plane waves (TM, TE, LHCP and RHCP as required) at an oblique incidence angle of 60 . The feeding horn antenna is connected to one port of a vector network analyzer (VNA) and fixed at the angle of 60 . A field-sensing probe is used to measure both shown in Figure 4e,g. The ratio of the co-polarized component on the measured plane to the amplitude and the phase of the electric field. From the measured data of the electric the total reflected energy is measured to be 39.6% and 35.4% for LHCP and RHCP inci- field along the x- and y-axes, the LHCP and RHCP components are calculated as: dence, respectively. The imaging efficiency of the cross- and co-polarized component is E = (E iE ) measured to be 18.4% and 11.7% for LHCP incidence, and 19.9% and 7.5% for RHCP inci- LHCP x y (7) dence. The signal-to-noise ratio (SNR) is used p to describe the ratio between the peak in- E = (E + iE ) RHCP x y tensity in the image and the standard deviation of the background noise [7,8], which is calculated to be 15.7, 14.1, 13.9, 12.9, 13.4 and 11.6 for the measured results shown in Fig- where E and E is the electric field along x- and y-axis, respectively. E and E is x y LHCP RHCP ure 4b–g, the electric respectively. field of the LHCP and RHCP component, respectively. Figure 4. (a) Schematic diagram of the experimental setup used to measure the electric field distri- Figure 4. (a) Schematic diagram of the experimental setup used to measure the electric field distri- bution. A photograph of the fabricated sample is shown in the inset. (b,c) Measured reflected field bution. A photograph of the fabricated sample is shown in the inset. (b,c) Measured reflected field intensity distribution under TM and TE incidence, respectively. (d,e) Measured reflected electric intensity distribution under TM and TE incidence, respectively. (d,e) Measured reflected electric intensity distribution of the cross- and co-polarized component under LHCP incidence, respec- intensity distribution of the cross- and co-polarized component under LHCP incidence, respectively. tively. (f,g) Measured reflected electric intensity distribution of the cross- and co-polarized compo- (f,g) Measured reflected electric intensity distribution of the cross- and co-polarized component nent under RHCP incidence, respectively. under RHCP incidence, respectively. To further validate the performances of the metasurface when deviating from the Figure 4b–g depicts the measured results, showing good qualitative agreement with preset conditions, the results obtained at different focal distances and incidence angles are the simulated ones presented in Figure 3a–f. The imaging efficiency, which refers to the shown and discussed. Under oblique incidence different from 60°, the simulated results proportion of the total incident energy concentrated in the preset focus, is calculated as under y-polarized incidence for 50° and 70° incidence are shown in Figure 5, where it can the energy in the preset focus referenced to the total reflected energy on the measured b plane e clea[r7ly ,8 ob ]. The served imaging that th efe p ficiency ropose isd calculated metasurface to can be 37.3% still ach and ieve re 40.3% ason forab TM le p and erfor- TE mance. The incidence, rsimulation results espectively. It should at diffe be noted rent fo that cal distances of a higher bit level 60 mm of, 70 coding mm, elements 90 mm acan nd 10 reduce 0 mmthe arephase also pdiscr resent etization ed in Fiand gure impr 6. When ove the the foc performance al distance d of the evmetasurface, iates from the des as it has ig- nated v been demonstrated alue, the image in quality a previous decre work ases, owin [7]. However g to the, chang here, the e of1-bit phase coding delay on t levelhis e foc used al pla as n ae. good tradeoff between design complexity and imaging performance. As discussed above, since the reflection phases for TM and TE incidences are not identical, some of the incident CP wave is transformed into its co-polarized component in the reflected field, as shown in Figure 4e,g. The ratio of the co-polarized component on the measured plane to the total reflected energy is measured to be 39.6% and 35.4% for LHCP and RHCP Figure 5. Simulated reflected electric intensity distributions under y-polarized incidence at differ- ent oblique incidence angles: (a) 50°. (b) 70°. Photonics 2021, 8, x FOR PEER REVIEW 7 of 9 shown in Figure 4e,g. The ratio of the co-polarized component on the measured plane to the total reflected energy is measured to be 39.6% and 35.4% for LHCP and RHCP inci- dence, respectively. The imaging efficiency of the cross- and co-polarized component is measured to be 18.4% and 11.7% for LHCP incidence, and 19.9% and 7.5% for RHCP inci- dence. The signal-to-noise ratio (SNR) is used to describe the ratio between the peak in- tensity in the image and the standard deviation of the background noise [7,8], which is calculated to be 15.7, 14.1, 13.9, 12.9, 13.4 and 11.6 for the measured results shown in Fig- ure 4b–g, respectively. Photonics 2021, 8, 174 7 of 9 Figure 4. (a) Schematic diagram of the experimental setup used to measure the electric field distri- bution. A photograph of the fabricated sample is shown in the inset. (b,c) Measured reflected field intensity distribution under TM and TE incidence, respectively. (d,e) Measured reflected electric incidence, respectively. The imaging efficiency of the cross- and co-polarized component intensity distribution of the cross- and co-polarized component under LHCP incidence, respec- is measured to be 18.4% and 11.7% for LHCP incidence, and 19.9% and 7.5% for RHCP tively. (f,g) Measured reflected electric intensity distribution of the cross- and co-polarized compo- incidence. The signal-to-noise ratio (SNR) is used to describe the ratio between the peak nent under RHCP incidence, respectively. intensity in the image and the standard deviation of the background noise [7,8], which is calculated to be 15.7, 14.1, 13.9, 12.9, 13.4 and 11.6 for the measured results shown in To further validate the performances of the metasurface when deviating from the Figure 4b–g, respectively. preset conditions, the results obtained at different focal distances and incidence angles are To further validate the performances of the metasurface when deviating from the shown and discussed. Under oblique incidence different from 60°, the simulated results preset conditions, the results obtained at different focal distances and incidence angles are under y-polarized incidence for 50° and 70° incidence are shown in Fig  ure 5, where it can shown and discussed. Under oblique incidence different from 60 , the simulated results be clearly observed that the proposed metasurface can still achieve reasonable perfor- under y-polarized incidence for 50 and 70 incidence are shown in Figure 5, where it can mance. The simulation results at different focal distances of 60 mm, 70 mm, 90 mm and be clearly observed that the proposed metasurface can still achieve reasonable performance. 100 mm are also presented in Figure 6. When the focal distance deviates from the desig- The simulation results at different focal distances of 60 mm, 70 mm, 90 mm and 100 mm nated value, the image quality decreases, owing to the change of phase delay on the focal are also presented in Figure 6. When the focal distance deviates from the designated value, plane. the image quality decreases, owing to the change of phase delay on the focal plane. Photonics 2021, 8, x FOR PEER REVIEW 8 of 9 Figure 5. Simulated reflected electric intensity distributions under y-polarized incidence at different Figure 5. Simulated reflected electric intensity distributions under y-polarized incidence at differ- oblique incidence angles: (a) 50 . (b) 70 . ent oblique incidence angles: (a) 50°. (b) 70°. Figure 6. Simulated reflected electric intensity distributions under y-polarized incidence at different Figure 6. Simulated reflected electric intensity distributions under y-polarized incidence at differ- distances: (a) 60 mm. (b) 70 mm. (c) 90 mm. (d) 100 mm. ent distances: (a) 60 mm. (b) 70 mm. (c) 90 mm. (d) 100 mm. 5. Conclusions 5. Conclusions In conclusion, a polarization-insensitive 1-bit metasurface is designed and validated In conclusion, a polarization-insensitive 1-bit metasurface is designed and validated for imaging hologram under oblique incidence in the microwave region. It is also demon- for imaging hologram under oblique incidence in the microwave region. It is also demon- strated that the scattering direction of the hologram can be steered as desired by simply strated that the scattering direction of the hologram can be steered as desired by simply adding a gradient phase distribution based on the Fourier convolution theory. For the adding a gradient phase distribution based on the Fourier convolution theory. For the arbitrarily considered linear and circular polarized waves, the experimental measure- arbitrarily considered linear and circular polarized waves, the experimental measure- ments performed on a fabricated prototype highlight good imaging quality. The proposed ments performed on a fabricated prototype highlight good imaging quality. The proposed ultra-thin polarization-insensitive 1-bit metasurface-based hologram may pave the way to ultra-thin polarization-insensitive 1-bit metasurface-based hologram may pave the way potential applications in imaging processing and information storage. to potential applications in imaging processing and information storage. Author Contributions: Conceptualization, S.Y. and X.D.; methodology, S.Y.; software, S.Y. and C.G.; Author Contributions: Conceptualization, S.Y. and X.D.; methodology, S.Y.; software, S.Y. and writing—original draft preparation, S.Y. and C.G.; writing—review and editing, X.D., K.Z. and C.G.; writing—original draft preparation, S.Y. and C.G.; writing—review and editing, X.D., K.Z. S.N.B.; supervision, X.D. and Q.W.; funding acquisition, X.D. All authors have read and agreed to the and S.N.B.; supervision, X.D. and Q.W.; funding acquisition, X.D. All authors have read and agreed published version of the manuscript. to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant Funding: This research was funded by the National Natural Science Foundation of China, grant number 61701141 and the Open project of State Key Laboratory of Millimeter Waves, grant num- number 61701141 and the Open project of State Key Laboratory of Millimeter Waves, grant number ber K202001. K202001. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on reasonable request from the corresponding author. Conflicts of Interest: The authors declare no conflict of interest. References 1. Yu, N.; Genevet, P.; Kats, M.A.; Aieta, F.; Tetienne, J.P.; Capasso, F.; Gaburro, Z. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. 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Fourier Convolution Operation on Metasurface-Based Hologram in Microwave Region

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hv photonics Communication Fourier Convolution Operation on Metasurface-Based Hologram in Microwave Region 1 1 1 , 2 1 3 , 1 Shuai Yang , Chunsheng Guan , Xumin Ding , Kuang Zhang , Shah Nawaz Burokur * and Qun Wu Department of Microwave Engineering, Harbin Institute of Technology, Harbin 150001, China; yanghaa@hit.edu.cn (S.Y.); guanchunsheng@stu.hit.edu.cn (C.G.); xuminding@hit.edu.cn (X.D.); zhangkuang@hit.edu.cn (K.Z.); qwu@hit.edu.cn (Q.W.) Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China LEME, UPL, Univ Paris Nanterre, F92410 Ville d’Avray, France * Correspondence: sburokur@parisnanterre.fr Abstract: In this paper, a 0.1 -thick 1-bit coding metasurface is proposed to achieve a polarization- insensitive hologram under oblique incidence, utilizing compact ground-backed patch unit cells. Fourier convolution theory in a digital signal processing system is added to the hologram calculation of the improved weighted Gerchberg–Saxton (GSW) algorithm to achieve control of the scattered pattern in the microwave region. As a proof of concept, a prototype operating at 15 GHz is designed to verify the validity of our proposed approach. The measured performances show good imaging quality under different incident polarizations, providing potential applications in imaging processing and information storage. Keywords: metasurface; polarization-insensitive; hologram 1. Introduction Citation: Yang, S.; Guan, C.; Ding, X.; Zhang, K.; Burokur, S.N.; Wu, Q. Metasurfaces, the two-dimensional (2D) version of metamaterials, are composed of Fourier Convolution Operation on arrays of artificial scatters, known as meta-atoms, with designed geometries and orientation Metasurface-Based Hologram in angles, which allow one to control the main characteristics of the scattered wave such as Microwave Region. Photonics 2021, 8, amplitude, phase and polarization [1,2]. Due to the extraordinary capability of tailoring 174. https://doi.org/10.3390/ wavefronts and low loss, low cost and low profile characteristics, metasurfaces have been photonics8060174 extensively exploited in practical devices, such as retroreflectors [3], cloaking devices [4], orbital angular momentum (OAM) generators [5], flat lenses [6], and holograms [7–10], to Received: 23 April 2021 name a few. Recently, the concept of coding metasurface has attracted much attention, in Accepted: 19 May 2021 which the phase or amplitude response of the metasurface is characterized by N-bit digital Published: 21 May 2021 coding particles rather than continuous electromagnetic (EM) parameters. For example, using the simplest 1-bit coding of the binary coding scheme, elements of the reflective Publisher’s Note: MDPI stays neutral metasurface are “0” and “1”, corresponding to phase response 0 and , respectively. Elec- with regard to jurisdictional claims in tromagnetic waves can be manipulated in a simple and effective way by designing the published maps and institutional affil- encoding sequence of digital meta-atoms, which has many applications in beam form- iations. ing [11], diffuse scattering [12], energy radiations control [13] and complex wavefront shaping [14]. Holography is one of the most promising imaging techniques [15]. Tradi- tional holograms can be generated by the interference of a reference beam and the scattered beam from the real object or calculated by using numerical computation [16,17]. Compared Copyright: © 2021 by the authors. with traditional holograms, the emergence of metasurfaces has further promoted the de- Licensee MDPI, Basel, Switzerland. velopment of computational holographic imaging by providing unprecedented spatial This article is an open access article resolution, and high-precision reconstructed images. By introducing a reconstruction distributed under the terms and algorithm such as Gerchberg–Saxton (GS) [18], computer-generated holograms can be de- conditions of the Creative Commons signed using engineered sub-wavelength elementary atoms with well-tailored amplitude Attribution (CC BY) license (https:// and phase responses, and digital elementary holography can be generated by coding the creativecommons.org/licenses/by/ holographic information of the object pattern [7,8]. Compared with traditional geometric 4.0/). Photonics 2021, 8, 174. https://doi.org/10.3390/photonics8060174 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 174 2 of 9 optics, the spatial resolution and imaging rate of metasurface holographic imaging are significantly improved. Due to the precise control of EM waves, holographic metasurface also finds applications in short-range communication systems, detection, data storage, and information processing [19–21] in the microwave regime. Efficiency is one of the most important challenges in metasurface design. Due to basic limitations and inherent ohmic losses, the efficiency of a single-layer transmissive metasurface is often fairly low, and has been shown to be only of the order of a few percent of magnitude at most [2]. Some high-efficiency transmissive metasurfaces, for instance, dielectric metasurfaces [22], Huygens’ metasurfaces [23], multilayered metasurfaces and meta-transmitarrays [24,25], have been studied to improve the efficiency. However, these designs necessitate a minimum finite thickness, significant manufacturing complexities and frequency dispersions. Reflective metasurfaces provide a solution for high-efficiency and ultrathin metasurface design and have been demonstrated in various applications such as antennas [26–29], holograms [30,31], waveplates [32] and metamirrors [33,34]. However, the feeding source of reflective metasurfaces is usually in the path of the reflected signal, which affects the performances of the metasurfaces. Recently, we proposed the coding metasurface approach for enhanced quality holo- graphic imaging by discretizing the phase distribution calculated by a GSW algorithm to different bit levels [7,8]. In this paper, a reflective 1-bit coding metasurface is proposed for polarization-insensitive hologram under oblique incidence of 60 in the microwave region, as illustrated in Figure 1a. The proposed metasurface is composed of subwavelength patch elements, which can provide a 180 phase shift for dual linearly polarized incidences. By designing the size of the patch elements, we find the meta-atoms of the binary element codes “0” and “1” to construct a 1-bit coding element hologram. A modified GSW algo- rithm is used to calculate the original interfacial phase distribution. Then, by applying Fourier convolution operations on the hologram, the direction of the scattered pattern can be steered to the desired direction. Experimental verification performed on a fabricated prototype is qualitatively consistent with theoretical predictions and numerical simulations, Photonics 2021, 8, x FOR PEER REVIEW 3 of 9 demonstrating both the feasibility of the approach and the high imaging quality of the proposed 1-bit polarization-insensitive coding element hologram. Figure 1. Cont. Figure 1. (a) Schematic demonstration of the proposed 1-bit polarization-insensitive metasurface- based hologram under oblique incidence. (b) 3D topological structure of the unit cell. (c,d) Reflec- tion phase response of the meta-atom under TM and TE polarization as functions of Px and Py, respectively. (e,f) Reflection coefficients of the binary meta-atoms as a function of frequency under TM and TE polarization, respectively. 2. Design of the Coding Elements Figure 1a shows the schematic diagram of a hologram of arbitrary polarization at a large incidence angle of 60°. By introducing Fourier convolution operation on the metasurface, the scattering pattern of the hologram can be steered as desired. For the con- venience of measurement, the hologram is designed to scatter in the normal direction here. Figure 1b shows the geometry and parameters of the coding particles. The F4BM300 dielectric substrate with thickness t = 2 mm, relative permittivity εr = 3 and tan δ = 0.0015 is used. A ground-backed patch meta-atom is exploited as the coding particle due to its good performance in polarization isolation and fabrication tolerance requirements. The perfect electric conductor (PEC) boundary condition is considered for the metal parts in simulations. Numerical simulations are performed using the commercial software CST Microwave Studio. Under the incidence of TM wave, the phase response of the meta-atom varies with the length Px of the patch along the x-direction, as shown in Figure 2c. It can Photonics 2021, 8, x FOR PEER REVIEW 3 of 9 Photonics 2021, 8, 174 3 of 9 Figure 1. (a) Schematic demonstration of the proposed 1-bit polarization-insensitive metasurface- Figure 1. (a) Schematic demonstration of the proposed 1-bit polarization-insensitive metasurface- based ho based hologram logram un under der obliq oblique ue incid incidence. ence. (b) 3D t (b) 3D opolog topological ical stru str ctu uctur re ofe the u of the nit unit cellcell. . (c,d( ) Ref c,d)lReflection ec- tion phase response of the meta-atom under TM and TE polarization as functions of Px and Py, phase response of the meta-atom under TM and TE polarization as functions of P and P , respectively. x y respectively. (e,f) Reflection coefficients of the binary meta-atoms as a function of frequency under (e,f) Reflection coefficients of the binary meta-atoms as a function of frequency under TM and TE TM and TE polarization, respectively. polarization, respectively. 2. Design of the Coding Elements 2. Design of the Coding Elements Figure 1a shows the schematic diagram of a hologram of arbitrary polarization at a Figure 1a shows the schematic diagram of a hologram of arbitrary polarization at large incidence angle of 60°. By  introducing Fourier convolution operation on the a large incidence angle of 60 . By introducing Fourier convolution operation on the metasurface, the scattering pattern of the hologram can be steered as desired. For the con- metasurface, the scattering pattern of the hologram can be steered as desired. For the venience of measurement, the hologram is designed to scatter in the normal direction convenience of measurement, the hologram is designed to scatter in the normal direction here. Figure 1b shows the geometry and parameters of the coding particles. The F4BM300 here. Figure 1b shows the geometry and parameters of the coding particles. The F4BM300 Photonics 2021, 8, x FOR PEER REVIEW dielectric substrate with thickness t = 2 mm, relative permittivity εr = 3 and tan δ = 0.0014 of 5 9 dielectric substrate with thickness t = 2 mm, relative permittivity # = 3 and tan d = 0.0015 is used. A ground-backed patch meta-atom is exploited as the coding particle due to its is used. A ground-backed patch meta-atom is exploited as the coding particle due to its good performance in polarization isolation and fabrication tolerance requirements. The good performance in polarization isolation and fabrication tolerance requirements. The perfect electric conductor (PEC) boundary condition is considered for the metal parts in perfect electric conductor (PEC) boundary condition is considered for the metal parts in simulations. Numerical simulations are performed using the commercial software CST also be observed that the length simulations. Numerical Py of the pa simulations tch along are y performed -direction using has l theit commer tle infl cial uen softwar ce on t e CST he Microwave Studio. Under the incidence of TM wave, the phase response of the meta-atom Microwave Studio. Under the incidence of TM wave, the phase response of the meta-atom phase response. The reflection phase coverage approaches 210° for TM incidences by var- varies with the length Px of the patch along the x-direction, as shown in Figure 2c. It can varies with the length P of the patch along the x-direction, as shown in Figure 2c. It can ying the length Px. Similarly, a reflection phase coverage of 310° is obtained by varying also be observed that the length P of the patch along y-direction has little influence on the length Py. The phase the phase coverage response. s un The de rr dual eflectionline phase arcoverage ly polarized approaches incidences ar 210 for TM incidences e efficient by varying the length P . Similarly, a reflection phase coverage of 310 is obtained by varying to achieve a 180° phase shift for the unit cell design. A bare unit cell (without metal patch the length P . The phase coverages under dual linearly polarized incidences are efficient to element) is utilized here to operate  as code “0” to simplify the design process and also to achieve a 180 phase shift for the unit cell design. A bare unit cell (without metal patch reduce the coupling e element) ffect between adj is utilized hera ecent un to operate it cells as code . To “0” satisfy th to simplify e 180° the design phas process e shift and be- also to reduce the coupling effect between adjacent unit cells. To satisfy the 180 phase shift tween code “0” and code “1” under dual linearly polarized incidences, the parameters of between code “0” and code “1” under dual linearly polarized incidences, the parameters unit cell code “1” is optimized to be Px = 5.2 mm and Py = 3.4 mm. of unit cell code “1” is optimized to be P = 5.2 mm and P = 3.4 mm. x y Figure 2. (a) Phase distribution of the original hologram. (b) Gradient phase distribution. (c) Phase distribution of hologram in normal direction. (d) 1-bit coding map. Figure 2. (a) Phase distribution of the original hologram. (b) Gradient phase distribution. (c) Phase distribution of hologram in normal direction. (d) 1-bit coding map. Figure 1e,f shows the reflection responses of the binary unit cells under TM and TE incidences as a function of frequency. For the dual linear polarizations, a phase difference of 180° is achieved at 15 GHz, providing the freedom to have the same phase shift in both TE and TM polarizations sharing the same aperture. The reflection amplitudes can also be nearly uniform under the different polarizations, as shown in Figure 1e,f. Since arbitrary polarizations can be decomposed into TE and TM polarizations, the same hologram for any polarization can be obtained from the metasurface. 3. Design of the Coding Meta-Hologram The modified GSW algorithm is used to retrieve the required theoretical phase profile [2]. The method consists in selecting ideal point sources as virtual sources and placing them at pre-designed hotspots. Considering that there are N hotspots located at (xn, yn, zn) (n = 1 to N), the phase delay at the position of each coding element ϕ (xm, ym, zm) (m = 1 to M) can be retrieved by superposing the electromagnetic field generated by all the virtual sources described by Green’s function. Accordingly, the reconstructed electric field is con- verged to the predesigned hotspots. In order to keep uniform intensity distribution among hotspots, a weight factor wn is introduced to reduce intensity difference among the N hotspots. An iterative procedure between the holography imaging and meta-hologram is proposed to obtain the uniform intensity profile of the target image as follows: ikr pp −1 wE nn φ =arg( )  (1) p −1 n =1 np −+ ikr iφ mm E = (2) m =1 p −1  n pp −1 n =1 (3) ww = nn p −1 NE Photonics 2021, 8, 174 4 of 9 Figure 1e,f shows the reflection responses of the binary unit cells under TM and TE incidences as a function of frequency. For the dual linear polarizations, a phase difference of 180 is achieved at 15 GHz, providing the freedom to have the same phase shift in both TE and TM polarizations sharing the same aperture. The reflection amplitudes can also be nearly uniform under the different polarizations, as shown in Figure 1e,f. Since arbitrary polarizations can be decomposed into TE and TM polarizations, the same hologram for any polarization can be obtained from the metasurface. 3. Design of the Coding Meta-Hologram The modified GSW algorithm is used to retrieve the required theoretical phase pro- file [2]. The method consists in selecting ideal point sources as virtual sources and placing them at pre-designed hotspots. Considering that there are N hotspots located at (x , y , n n z ) (n = 1 to N), the phase delay at the position of each coding element f (x , y , z ) n m m m (m = 1 to M) can be retrieved by superposing the electromagnetic field generated by all the virtual sources described by Green’s function. Accordingly, the reconstructed electric field is converged to the predesigned hotspots. In order to keep uniform intensity distribution among hotspots, a weight factor w is introduced to reduce intensity difference among the N hotspots. An iterative procedure between the holography imaging and meta-hologram is proposed to obtain the uniform intensity profile of the target image as follows: p p1 ikr e w E p n n f = arg( ) (1) m å p1 n=1 ikr +if m m E = (2) n å m=1 p1 p p1 n=1 w = w (3) n n p1 N E th where f is defined as the phase shift of the m (m = 1 to M) coding element and E m n th n denotes the electric field intensity of the n (n = 1 to N) hotspots. r is the distance between th th th m coding element and n hotspot and superscript p represents the p iterative step. According to Equations (1) and (3), the weight factor w is adjusted step by step until the least mean square error between the target and the reconstructed image becomes less than a predesigned threshold. Based on the modified GSW retrieval algorithm, the theoretical phase distribution can be obtained, as shown in Figure 2a. As a property of the Fourier transform, the convolution theorem can be described: FFT f (t)g(t) , f (w) g(w) (4) The arguments t and w in Equation (1) can be replaced by x and sinq, respectively, leading to the following equation [35]: FFT f (x )g(x ) , f (sin q) g(sin q) (5) l l where x = x/l is the electrical length, and q is the angle with respect to the normal direc- tion. Equation (2) can be simplified when the item g (x ) becomes a Dirac-delta function: FFT jx sin q l 0 E(x )e , E(sin q) d(sin q sin q ) l 0 (6) = E(sin q sin q ) where x sinq describes the gradient phase along a determined direction. Equation (3) l 0 jx sin q l 0 shows that by introducing a gradient phase of e , the scattering pattern E (sinq ) can 0 Photonics 2021, 8, 174 5 of 9 be deviated from its original direction by the quantity sinq in the angular coordinate. Such a process can be regarded as superposing an additional phase distribution to the original one, reducing computational complexity for optimizing the scattering patterns. Based on the scattering pattern shift principle, the hologram can be arbitrarily rotated around the normal axis by the convolution operation. Since the incidence angle is designed to be 60 here, a gradient phase distribution shown in Figure 2b is added to the original hologram to steer the scattering pattern to the normal direction. Then, the obtained phase distribution in Figure 2c is discretized to 0 and  values. Therefore, the phase information can be described by the 1-bit coding map shown in Figure 2d. Then, the 1-bit coding hologram can be constructed based on the obtained coding map. 4. Results and Discussion To demonstrate the proposed 1-bit polarization-insensitive hologram, a metasurface is designed at 15 GHz and simulated to project a “square” image with four corner hotspots, as illustrated in Figure 1a. The metasurface is composed of 41  41 meta-atoms with the size of 235.75 mm  235.75 mm. The metasurface is fabricated using the conventional printed circuit board (PCB) technique where copper is used for the metal parts. The imaging plane here is designed to be 4 away from the metasurface. The metasurface is illuminated by TM, TE, left-hand circularly polarized (LHCP) and right-hand circularly polarized (RHCP) waves under an oblique incidence angle of 60 . Figure 3a,b, respectively, present the intensity distribution of the simulated reflected electric field in the imaging plane under TM and TE incident waves illumination. Under LHCP and RHCP wave incidences, the simulated reflected electric field strength of the cross-polarized component is shown in Figure 3c,e. The simulation results are consistent with the theoretical design, showing good imaging quality. It should be noted that a small part of incident CP wave is transformed into its co-polarized component in the reflected field, as shown in Figure 3d,f, since the Photonics 2021, 8, x FOR PEER REVIEW 6 of 9 reflection phases for TM and TE incidences are not identical, as previously presented in Figure 1e,f. Figure 3. Simulated reflected electric field intensity distributions (a,b) under TM and TE incidence, Figure 3. Simulated reflected electric field intensity distributions (a,b) under TM and TE incidence, respectively. (c,d) Cross- and co-polarized component under LHCP incidence, respectively. (e,f) respectively. (c,d) Cross- and co-polarized component under LHCP incidence, respectively. (e,f) Cross- and Cross- and co- co-polarized polarized com component ponent u under nder RHCP inci RHCP incidence, dence, respe respectively ctively.. In order to experimentally verify the performances of the proposed polarization-in- sensitive hologram, a sample is fabricated and depicted by the photograph shown in the inset of Figure 4a. The schematic diagram of the near-field scanning system exploited to measure the electric field distribution is illustrated in Figure 4a, and the measurements are carried out in a microwave anechoic chamber. The feeding source, which is a dual- polarized broadband horn antenna, is placed far away enough from the metasurface to launch quasi-plane waves (TM, TE, LHCP and RHCP as required) at an oblique incidence angle of 60°. The feeding horn antenna is connected to one port of a vector network ana- lyzer (VNA) and fixed at the angle of 60°. A field-sensing probe is used to measure both the amplitude and the phase of the electric field. From the measured data of the electric field along the x- and y-axes, the LHCP and RHCP components are calculated as: EE=−()iE LHCP x y (7) EE=+()iE RHCP x y where Ex and Ey is the electric field along x- and y-axis, respectively. ELHCP and ERHCP is the electric field of the LHCP and RHCP component, respectively. Figure 4b–g depicts the measured results, showing good qualitative agreement with the simulated ones presented in Figure 3a–f. The imaging efficiency, which refers to the proportion of the total incident energy concentrated in the preset focus, is calculated as the energy in the preset focus referenced to the total reflected energy on the measured plane [7,8]. The imaging efficiency is calculated to be 37.3% and 40.3% for TM and TE incidence, respectively. It should be noted that a higher bit level of coding elements can reduce the phase discretization and improve the performance of the metasurface, as it has been demonstrated in a previous work [7]. However, here, the 1-bit coding level is used as a good tradeoff between design complexity and imaging performance. As discussed above, since the reflection phases for TM and TE incidences are not identical, some of the incident CP wave is transformed into its co-polarized component in the reflected field, as Photonics 2021, 8, 174 6 of 9 In order to experimentally verify the performances of the proposed polarization- insensitive hologram, a sample is fabricated and depicted by the photograph shown in the inset of Figure 4a. The schematic diagram of the near-field scanning system exploited to measure the electric field distribution is illustrated in Figure 4a, and the measurements are carried out in a microwave anechoic chamber. The feeding source, which is a dual- polarized broadband horn antenna, is placed far away enough from the metasurface to Photonics 2021, 8, x FOR PEER REVIEW 7 of 9 launch quasi-plane waves (TM, TE, LHCP and RHCP as required) at an oblique incidence angle of 60 . The feeding horn antenna is connected to one port of a vector network analyzer (VNA) and fixed at the angle of 60 . A field-sensing probe is used to measure both shown in Figure 4e,g. The ratio of the co-polarized component on the measured plane to the amplitude and the phase of the electric field. From the measured data of the electric the total reflected energy is measured to be 39.6% and 35.4% for LHCP and RHCP inci- field along the x- and y-axes, the LHCP and RHCP components are calculated as: dence, respectively. The imaging efficiency of the cross- and co-polarized component is E = (E iE ) measured to be 18.4% and 11.7% for LHCP incidence, and 19.9% and 7.5% for RHCP inci- LHCP x y (7) dence. The signal-to-noise ratio (SNR) is used p to describe the ratio between the peak in- E = (E + iE ) RHCP x y tensity in the image and the standard deviation of the background noise [7,8], which is calculated to be 15.7, 14.1, 13.9, 12.9, 13.4 and 11.6 for the measured results shown in Fig- where E and E is the electric field along x- and y-axis, respectively. E and E is x y LHCP RHCP ure 4b–g, the electric respectively. field of the LHCP and RHCP component, respectively. Figure 4. (a) Schematic diagram of the experimental setup used to measure the electric field distri- Figure 4. (a) Schematic diagram of the experimental setup used to measure the electric field distri- bution. A photograph of the fabricated sample is shown in the inset. (b,c) Measured reflected field bution. A photograph of the fabricated sample is shown in the inset. (b,c) Measured reflected field intensity distribution under TM and TE incidence, respectively. (d,e) Measured reflected electric intensity distribution under TM and TE incidence, respectively. (d,e) Measured reflected electric intensity distribution of the cross- and co-polarized component under LHCP incidence, respec- intensity distribution of the cross- and co-polarized component under LHCP incidence, respectively. tively. (f,g) Measured reflected electric intensity distribution of the cross- and co-polarized compo- (f,g) Measured reflected electric intensity distribution of the cross- and co-polarized component nent under RHCP incidence, respectively. under RHCP incidence, respectively. To further validate the performances of the metasurface when deviating from the Figure 4b–g depicts the measured results, showing good qualitative agreement with preset conditions, the results obtained at different focal distances and incidence angles are the simulated ones presented in Figure 3a–f. The imaging efficiency, which refers to the shown and discussed. Under oblique incidence different from 60°, the simulated results proportion of the total incident energy concentrated in the preset focus, is calculated as under y-polarized incidence for 50° and 70° incidence are shown in Figure 5, where it can the energy in the preset focus referenced to the total reflected energy on the measured b plane e clea[r7ly ,8 ob ]. The served imaging that th efe p ficiency ropose isd calculated metasurface to can be 37.3% still ach and ieve re 40.3% ason forab TM le p and erfor- TE mance. The incidence, rsimulation results espectively. It should at diffe be noted rent fo that cal distances of a higher bit level 60 mm of, 70 coding mm, elements 90 mm acan nd 10 reduce 0 mmthe arephase also pdiscr resent etization ed in Fiand gure impr 6. When ove the the foc performance al distance d of the evmetasurface, iates from the des as it has ig- nated v been demonstrated alue, the image in quality a previous decre work ases, owin [7]. However g to the, chang here, the e of1-bit phase coding delay on t levelhis e foc used al pla as n ae. good tradeoff between design complexity and imaging performance. As discussed above, since the reflection phases for TM and TE incidences are not identical, some of the incident CP wave is transformed into its co-polarized component in the reflected field, as shown in Figure 4e,g. The ratio of the co-polarized component on the measured plane to the total reflected energy is measured to be 39.6% and 35.4% for LHCP and RHCP Figure 5. Simulated reflected electric intensity distributions under y-polarized incidence at differ- ent oblique incidence angles: (a) 50°. (b) 70°. Photonics 2021, 8, x FOR PEER REVIEW 7 of 9 shown in Figure 4e,g. The ratio of the co-polarized component on the measured plane to the total reflected energy is measured to be 39.6% and 35.4% for LHCP and RHCP inci- dence, respectively. The imaging efficiency of the cross- and co-polarized component is measured to be 18.4% and 11.7% for LHCP incidence, and 19.9% and 7.5% for RHCP inci- dence. The signal-to-noise ratio (SNR) is used to describe the ratio between the peak in- tensity in the image and the standard deviation of the background noise [7,8], which is calculated to be 15.7, 14.1, 13.9, 12.9, 13.4 and 11.6 for the measured results shown in Fig- ure 4b–g, respectively. Photonics 2021, 8, 174 7 of 9 Figure 4. (a) Schematic diagram of the experimental setup used to measure the electric field distri- bution. A photograph of the fabricated sample is shown in the inset. (b,c) Measured reflected field intensity distribution under TM and TE incidence, respectively. (d,e) Measured reflected electric incidence, respectively. The imaging efficiency of the cross- and co-polarized component intensity distribution of the cross- and co-polarized component under LHCP incidence, respec- is measured to be 18.4% and 11.7% for LHCP incidence, and 19.9% and 7.5% for RHCP tively. (f,g) Measured reflected electric intensity distribution of the cross- and co-polarized compo- incidence. The signal-to-noise ratio (SNR) is used to describe the ratio between the peak nent under RHCP incidence, respectively. intensity in the image and the standard deviation of the background noise [7,8], which is calculated to be 15.7, 14.1, 13.9, 12.9, 13.4 and 11.6 for the measured results shown in To further validate the performances of the metasurface when deviating from the Figure 4b–g, respectively. preset conditions, the results obtained at different focal distances and incidence angles are To further validate the performances of the metasurface when deviating from the shown and discussed. Under oblique incidence different from 60°, the simulated results preset conditions, the results obtained at different focal distances and incidence angles are under y-polarized incidence for 50° and 70° incidence are shown in Fig  ure 5, where it can shown and discussed. Under oblique incidence different from 60 , the simulated results be clearly observed that the proposed metasurface can still achieve reasonable perfor- under y-polarized incidence for 50 and 70 incidence are shown in Figure 5, where it can mance. The simulation results at different focal distances of 60 mm, 70 mm, 90 mm and be clearly observed that the proposed metasurface can still achieve reasonable performance. 100 mm are also presented in Figure 6. When the focal distance deviates from the desig- The simulation results at different focal distances of 60 mm, 70 mm, 90 mm and 100 mm nated value, the image quality decreases, owing to the change of phase delay on the focal are also presented in Figure 6. When the focal distance deviates from the designated value, plane. the image quality decreases, owing to the change of phase delay on the focal plane. Photonics 2021, 8, x FOR PEER REVIEW 8 of 9 Figure 5. Simulated reflected electric intensity distributions under y-polarized incidence at different Figure 5. Simulated reflected electric intensity distributions under y-polarized incidence at differ- oblique incidence angles: (a) 50 . (b) 70 . ent oblique incidence angles: (a) 50°. (b) 70°. Figure 6. Simulated reflected electric intensity distributions under y-polarized incidence at different Figure 6. Simulated reflected electric intensity distributions under y-polarized incidence at differ- distances: (a) 60 mm. (b) 70 mm. (c) 90 mm. (d) 100 mm. ent distances: (a) 60 mm. (b) 70 mm. (c) 90 mm. (d) 100 mm. 5. Conclusions 5. Conclusions In conclusion, a polarization-insensitive 1-bit metasurface is designed and validated In conclusion, a polarization-insensitive 1-bit metasurface is designed and validated for imaging hologram under oblique incidence in the microwave region. It is also demon- for imaging hologram under oblique incidence in the microwave region. It is also demon- strated that the scattering direction of the hologram can be steered as desired by simply strated that the scattering direction of the hologram can be steered as desired by simply adding a gradient phase distribution based on the Fourier convolution theory. For the adding a gradient phase distribution based on the Fourier convolution theory. For the arbitrarily considered linear and circular polarized waves, the experimental measure- arbitrarily considered linear and circular polarized waves, the experimental measure- ments performed on a fabricated prototype highlight good imaging quality. The proposed ments performed on a fabricated prototype highlight good imaging quality. The proposed ultra-thin polarization-insensitive 1-bit metasurface-based hologram may pave the way to ultra-thin polarization-insensitive 1-bit metasurface-based hologram may pave the way potential applications in imaging processing and information storage. to potential applications in imaging processing and information storage. Author Contributions: Conceptualization, S.Y. and X.D.; methodology, S.Y.; software, S.Y. and C.G.; Author Contributions: Conceptualization, S.Y. and X.D.; methodology, S.Y.; software, S.Y. and writing—original draft preparation, S.Y. and C.G.; writing—review and editing, X.D., K.Z. and C.G.; writing—original draft preparation, S.Y. and C.G.; writing—review and editing, X.D., K.Z. S.N.B.; supervision, X.D. and Q.W.; funding acquisition, X.D. All authors have read and agreed to the and S.N.B.; supervision, X.D. and Q.W.; funding acquisition, X.D. All authors have read and agreed published version of the manuscript. to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant Funding: This research was funded by the National Natural Science Foundation of China, grant number 61701141 and the Open project of State Key Laboratory of Millimeter Waves, grant num- number 61701141 and the Open project of State Key Laboratory of Millimeter Waves, grant number ber K202001. K202001. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on reasonable request from the corresponding author. Conflicts of Interest: The authors declare no conflict of interest. References 1. Yu, N.; Genevet, P.; Kats, M.A.; Aieta, F.; Tetienne, J.P.; Capasso, F.; Gaburro, Z. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. 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Journal

Photonics – Multidisciplinary Digital Publishing Institute

Published: May 21, 2021

Keywords: metasurface; polarization-insensitive; hologram

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