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A Four-leaf Clover-shaped Coding Metasurface For Ultra-wideband Diffusion-like Scattering
DOI: 10.12000/JR21061
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Abstract: In this paper, a novel four-leaf clover-shaped coding metasurface is proposed and applied to achieve an ultra-wideband diffusion-like scattering. The proposed metasurface element has rotational symmetry; hence, it produces similar reflection characteristics for both x- and y-polarized waves. To realize a 1-bit coding metasurface, two elements are chosen that have a phase difference of 180°±37° from 15.5 to 40.5 GHz. An optimization algorithm is applied to get the best arrangement of unit cells in the array to attain the wideband RCS reduction. The four-leaf clover-shaped metasurface can attain more than 10 dB RCS reduction from 15.5 to 26.5 GHz and 30.5 to 40.5 GHz. A prototype of the proposed design is fabricated, and an experiment is carried out to validate the performance of the metasurface. The proposed concept of four-leaf clover-shaped coding metasurface is an effective solution for wideband RCS reduction applications.摘要: 该文提出了一种结构新颖的四叶草形编码超表面，并利用该超表面实现了超宽带漫散射。所提出的编码超表面具有旋转对称性，它对x极化和y极化波产生相似的反射特性。为了实现1比特编码超表面，该文设计了在15.5～40.5 GHz的频率范围内且相位差为180°±37°的两个超表面单元。采用优化算法得到阵列中单元的最佳排列，从而实现了宽带RCS的缩减。四叶草形编码超表面可以在15.5～26.5 GHz和30.5～40.5 GHz这两个频带内实现10 dB的RCS缩减。该文加工了该编码超表面并与仿真结果进行了比较，从而有效验证了所设计的四叶草形编码超表面可以在宽频带内实现RCS的缩减。
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1. Introduction
Metasurfaces have attracted attention in recent years due to their unique characteristic to manipulate wavefronts. Metasurfaces can realize the fascinating applications that are non-existent in natural materials by introducing abrupt changes in phase, amplitude, and polarization of the incident ElectroMagnetic (EM) at subwavelength.
The metasurfaces are more advantageous than the 3D metamaterials for various applications because of their less thickness, easy fabrication, and low complexity. In the last decade, metasurfaces have been applied to realize many fascinating applications including beam manipulation[1], subwavelength focusing[2] electromagnetic cloak[3], holography[4], and perfect absorber[5]. The concept of coding and programmable metasurface is introduced recently, which characterizes meta-atom as a digital bit with a value of “0” or “1”. In the case of coding metasurface, “0” and “1” represent two types of elements with a reflection phase of 0° and 180°, respectively[6]. By arranging the two kinds of elements in the two-dimensional plane, a digital metasurface is realized to control the electromagnetic waves.
Several designs of the Artificial Magnetic Conductor (AMC) have been presented in the literature for RCS reduction application[7]. A chessboard-like configuration of AMC and Perfect Electric Conductor (PEC) is used to realize RCS reduction by using the principle of opposite phase cancellation to minimize the specular reflection[8]. The major limitation chessboard-like configuration of PEC and AMC is the bandwidth limitation of AMC. Outside the operating frequency of AMC, it behaves as a PEC and the phase cancellation condition is not satisfied anymore. To overcome this limitation, two AMC structures are designed which resonate at different frequencies[9]. Such kind of chessboard-like configuration based on two kinds of AMC structures can be used to realize wideband RCS reduction. A wideband polarization rotation reflective surface based on the AMC is presented that can achieve a Polarization Conversation Ratio (PCR) of 96% and the proposed design is applied to realize wideband RCS reduction[10].
In the last decade, coding metasurfaces have attracted significant attention, and have been applied to realize numerous applications including beam manipulation, diffusion-like scattering, and absorption. A chaos-based metasurface is presented to achieve the wideband RCS reduction based on the relation of the phase distribution of coding metasurface and spatiotemporal chaos patterns[11]. A broadband RCS reduction is demonstrated by careful arrangements of unit cells to produce the diffusion-like scattering which distributes the scattering energy in many directions and minimizes the specular reflection of incident EM waves[12].
Since there could be countless arrangements based on the random combinations of digital elements, there is a requirement to find the optimal configuration of unit cells. Genetic algorithm[13-15] and Particle Swarm optimization[16-18] have been used in literature to optimize array factors to get the optimum arrangement of unit cells for better diffusion-like-scattering. A Particle Swarm Optimization (PSO) algorithm is applied to the array factor to find the optimum arrangements of unit cells[19]. A fast design method is proposed for wideband metasurface design by using a non-linear fitting method instead of the Pancharatnam-Berry (PB) phase, and the genetic algorithm is applied for array optimization[20].
In this paper, we proposed a novel four-leaf clover-shaped coding metasurface and applied it to realize an ultra-wideband diffusion-like scattering. By optimization the dimension of leaf, two elements are designed which have a phase difference of 180°±37° from 15.5 to 40.5 GHz. An optimization algorithm is applied to get the best arrangement of unit cells to achieve the wideband diffusion-like scattering. The simulation and experimental results agree well and hence the proposed design can be used for wideband RCS reduction applications.
2. Design of Metasurface Unit Cell
The schematic model of the four-leaf clover-shaped coding metasurface unit cell is shown in Fig. 1. The unit element is a sandwich structure with the four-leaf clover-shaped metallic pattern as a resonator, the middle dielectric material as a spacer, and the bottom metallic layer as ground. The size of the unit cell is 5×5×1.5 mm3 and the four-leaf clover-shaped resonator having a thickness of 0.035 mm is printed on F4B substrate with relative permittivity of 2.65 and a loss tangent of 0.001. The unit cell can be used for polarization-insensitive application as it produces the same response for x- and y-polarizations because of the rotational symmetry of the unit cell. Two different sizes of four-leaf clovers are designed to represent the two digital states of a 1-bit coding metasurface. By changing the size of four-leaf clovers, the phase response of metasurface unit cells changes. To achieve the phase difference of 180°±37° between the two types of unit cells, the dimensions of the four-leaf clover are optimized.
Figure 1. The schematic of proposed unit cellFor full-wave simulations, CST Microwave Studio with frequency-domain solver is used to simulate the proposed unit cell. The periodic boundary conditions are applied along the x- and y-axis whereas the Floquet port is employed along the z-axis. The simulation results for phase and magnitude responses are shown in Fig. 2 (a) and Fig. 2(b), respectively. The simulated phase response shows that a phase difference of 180° is achieved from 15.5 to 40.5 GHz, while the value of simulated magnitude is around –0.2 dB.
Figure 2. Simulation results of reflection phase and magnitude3. Optimized Array Design for Diffusion-like Scattering
Once the four-leaf clover-shaped metasurface unit element is designed, the two digital elements are arranged on a two-dimensional plane to realize the metasurface to control electromagnetic waves. To realize the diffusion-like scattering, the element “0” and element “1” can be arranged in a random wave. There could be countless random arrangements of digital elements, hence, we applied an optimization algorithm to find the optimized arrangement of unit cells for better diffusion-like scattering.
If the P and Q are the numbers of elements along the x- and y-axis, respectively, then the scattering pattern for the P×Q array is given by
E(θ,φ)=EP(θ,φ)⋅AF(θ,φ) (1) where EP is the element pattern, θ is the is elevation angle,
φ is the azimuth angle. The array factor AF can be expressed asAF(θ,φ)=P∑p=1Q∑q=1exp{jkd[(p−12)⋅u+(q−12)⋅v]+jΦ(p,q)} (2) where
u=sinθcosφ ,v=sinθsinφ , the size of the unit cell is d, P and Q are the number of unit cells along the x- and y-axis. The phase of coding metasurface elementjΦ(m,n) is the most important factor. For a 1-bit coding metasurface, the phase of the individual coding element could be 0° or 180°. The array is designed by careful placement of element “0” and element “1” to realize a better diffusion-like scattering. The Water Cycle Algorithm (WCA) is used to obtain the optimum arrangement of element “0” and element “1”. The water cycle algorithm offers better solutions than other optimizers in terms of efficiency and the number of function evaluations[21]. The flow chart of the water cycle algorithm is presented in Fig. 3.
Figure 3. Flow chart of water cycle algorithmTo achieve the optimum diffusion-like scattering, the fitness function is given by
fitness=min(AFmax) (3) The 2D and 3D scattering pattern of the four-leaf clover-shaped coding metasurface is demonstrated in Fig. 4 (a) and Fig. 4(b), respectively. The water algorithm is applied for 100 iterations with a population size of 100. The convergence characteristics of the algorithm are presented in Fig. 5. For the minimum array factor, the corresponding arrangement of element “0” and element “1” are shown in the coding matrix in Fig. 6. The final array is designed based on the optimized coding matrix to achieve optimum RCS reduction. An array of 40×40 unit cells with a super-cell size of 4×4 is designed, whereas the coding matrix is 10×10.
Figure 4. Simulation results of the four-leaf clover-based coding metasurface
Figure 5. Convergence characteristics of proposed WCA algorithm
Figure 6. Optimized arrangement of element ‘0’ and element ‘1’ obtained from MATLAB to form the coding matrixThe array simulations were performed using CST Microwave Studio and simulation results are shown in Fig. 7. The far-field simulation results of the proposed 1-bit optimized coding metasurface and PEC at 16.5 GHz, 23.5 GHz, and 39.5 GHz, and the results are shown in Fig. 7. The proposed metasurface has the RCS of 1.21 dBsm, 3.41 dBsm, and 7.26 dBsm at 16.5 GHz, 23.5 GHz, and 39.5 GHz, respectively. An optimized arrangement of the metasurface unit cells is used to realize the diffusion-like scattering. The reflected wave from the metasurface is dispersed in several directions and hence, the specular reflection is reduced. At 16.5 GHz, 23.5 GHz, and 39.5 GHz, the RCS reduction of 16.8 dBsm, 17.6 dBsm, and 18 dBsm is achieved as compared to the same size of PEC.
Figure 7. The 3D scattering patterns of the four-leaf clover-shaped coding metasurface (left column) and the PEC (right column)To verify the concept efficiency proposed metasurface, the RCS of the proposed design is compared with PEC from 15.5 to 40.5 GHz and the results are shown in Fig. 8. An ultra-wideband RCS reduction of 10 dB is attained from 15.5 to 26.5 GHz and 30.5 to 40.5 GHz under normal incidence as compared with a copper sheet of the same size.
Figure 8. The RCS of proposed coding metasurface and PEC4. Results and Discussions
The Printed Circuit Board (PCB) technology is used to fabricate the prototype of four-leaf clover-shaped coding metasurface and the sample is as presented in Fig. 9.
Figure 9. The fabricated sample of four-leaf clover-shaped coding metasurfaceTo analyze the performance of the proposed metasurface, the measurement of the fabricated sample was carried out in the anechoic chamber and the measurement setup is demonstrated in Fig. 10. The experimental setup consists of a vector network analyzer (Agilent N5227A), horn antennas, and a fabricated prototype of the proposed metasurface. Three sets of Ku-, K-, and Ka-band horn antennas are used for measurement to cover the bandwidth from 15.5 to 40.5 GHz. The sample is placed in the far-field of the antenna and far-field condition is given by
Figure 10. Experimental setup in an anechoic chamberR>2D2λmin (4) To verify the performance, the measured RCS of the proposed metasurface is compared with the simulated RCS of metasurface and PEC as depicted in Fig. 11. The RCS reduction of 10 dB is achieved for normal incidence from 15.5 to 26.5 GHz and 30.5 to 40.5 GHz, whereas more than 6 dB RCS reduction is observed from 26.5 to 30.5 GHz.
Figure 11. Comparison of simulation and measurement resultsHowever, the small difference between the simulation and measurement results is mainly caused by fabrication error and measurement tolerance. To highlight the advantages of the proposed research, a comparison of this study is drawn with literature and presented in Tab. 1. The proposed four-leaf clover-shaped coding metasurface has Fractional BandWidth (FBW) of 80% with a thickness of 0.13λ0 that makes the proposed design wideband with less thickness. As compared with binary optimization algorithm which can only be applied for 1-bit metasurface, here, we have introduced DWCA which can be extended towards multi-bit metasurface designs.
Table 1. Comparison of our work with earlier worksRef. Freq. band (GHz) σR (dB) Metasurface arrangement Thickness FBW (%) [22] 11.60～18.65 10 Random 0.15λ0 46 [23] 9.9～19.8 10 Random 0.15λ0 66 [24] 8～18 10 Random 0.13λ0 77 [25] 7.2～15.6 10 Random 0.12λ0 73 [26] 12.2～23.4 10 Spiral coding 0.12λ0 62 [27] 5.57～7.37 10 Ergodic 0.06λ0 28 [28] 5.8～12.2 10 GA 0.14λ0 77 [29] 6.94～9.23 10 GA 0.05λ0 28 [20] 12～24 10 GA 0.12λ0 66 [30] 8～15 10 Random 0.10λ0 0.47 This work 15.5～26.5, 30.5～40.5 10 WCA 0.13λ0 80 λ0 is the free-space wavelength corresponding to the center frequency of the operation bandwidth.
FBW: The fractional bandwidth FBW= (fH – fL)/fc, fc = (fH + fL) /2
σR: RCS reduction| Show Table
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5. Conclusion
A novel four-leaf clover-shaped coding metasurface is designed and applied to achieve an ultra-wideband diffusion-like scattering. By optimization the dimension of the four-leaf clover, two elements are selected with a phase difference of 180°±37° from 15.5 to 40.5 GHz. An optimization algorithm is applied to get the best arrangement of unit cells to attain the ultra-wideband RCS reduction. More than 10 dB RCS reduction is obtained from 15.5 to 26.5 GHz and 30.5 to 40.5 GHz as compared with a copper sheet of the same size. Furthermore, the RCS reduction of more than 6 dB is realized from 26.5 to 30.5 GHz. The proposed design is verified through simulation and experiment. Therefore, the proposed concept of four-leaf clover-shaped coding metasurface is an effective solution for wideband RCS reduction applications.
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Figure 6. Optimized arrangement of element ‘0’ and element ‘1’ obtained from MATLAB to form the coding matrix
Figure 7. The 3D scattering patterns of the four-leaf clover-shaped coding metasurface (left column) and the PEC (right column)
Table 1. Comparison of our work with earlier works
Ref. Freq. band (GHz) σR (dB) Metasurface arrangement Thickness FBW (%) [22] 11.60～18.65 10 Random 0.15λ0 46 [23] 9.9～19.8 10 Random 0.15λ0 66 [24] 8～18 10 Random 0.13λ0 77 [25] 7.2～15.6 10 Random 0.12λ0 73 [26] 12.2～23.4 10 Spiral coding 0.12λ0 62 [27] 5.57～7.37 10 Ergodic 0.06λ0 28 [28] 5.8～12.2 10 GA 0.14λ0 77 [29] 6.94～9.23 10 GA 0.05λ0 28 [20] 12～24 10 GA 0.12λ0 66 [30] 8～15 10 Random 0.10λ0 0.47 This work 15.5～26.5, 30.5～40.5 10 WCA 0.13λ0 80 λ0 is the free-space wavelength corresponding to the center frequency of the operation bandwidth.
FBW: The fractional bandwidth FBW= (fH – fL)/fc, fc = (fH + fL) /2
σR: RCS reduction
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