A Four-leaf Clover-shaped Coding Metasurface For Ultra-wideband Diffusion-like Scattering

YASIR Saifullah YANG Guomin XU Feng

(Key Laboratory for Information Science of Electromagnetic Waves,Fudan University, Shanghai 200433, China)

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 bothx-andy-polarized waves.To realize a1-bit coding metasurface,two elements are chosen that have a phase difference of180°±37°from15.5to40.5GHz.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 than10dB RCS reduction from15.5 to26.5GHz and30.5to40.5GHz.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.

Key words:Coding metasurface;Water cycle algorithm;Radar Cross-Section(RCS);Diffusion-like scattering;Four-leaf clover

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 the3D 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 metaatom 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 of0°and180°,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)of96%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 of180°±37°from15.5to40.5GHz.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 clovershaped 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 is5×5×1.5mm3and the four-leaf clover-shaped resonator having a thickness of0.035mm is printed on F4B substrate with relative permittivity of2.65and a loss tangent of0.001.The unit cell can be used for polarization-insensitive application as it produces the same response forx-andy-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 a1-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.

Fig.1 The schematic of proposed unit cell

For 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 thex-andy-axis whereas the Floquet port is employed along thez-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 of180°is achieved from15.5to40.5GHz,while the value of simulated magnitude is around–0.2dB.

Fig.2 Simulation results of reflection phase and magnitude

3 Optimized Array Design for Diffusionlike 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 diffusionlike scattering.

If thePandQare the numbers of elements along thex-andy-axis,respectively,then the scattering pattern for theP×Qarray is given by

where EP is the element pattern,θis the is elevation angle,φis the azimuth angle.The array factor AF can be expressed as

whereu=sinθcosφ,v=sinθsinφ,the size of the unit cell isd,PandQare the number of unit cells along thex-andy-axis.The phase of coding metasurface element jΦ(m,n)is the most important factor.For a1-bit coding metasurface,the phase of the individual coding element could be0°or180°.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.

Fig.3 Flow chart of water cycle algorithm

To achieve the optimum diffusion-like scattering,the fitness function is given by

The2D and3D 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 for100iterations with a population size of100.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 of40×40unit cells with a super-cell size of4×4is designed,whereas the coding matrix is10×10.

Fig.4 Simulation results of the four-leaf clover-based coding metasurface

Fig.5 Convergence characteristics of proposed WCA algorithm

Fig.6 Optimized arrangement of element‘0’and element‘1’obtained from MATLAB to form the coding matrix

The array simulations were performed using CST Microwave Studio and simulation results are shown in Fig.7.The far-field simulation results of the proposed1-bit optimized coding metasurface and PEC at16.5GHz,23.5GHz,and39.5GHz,and the results are shown in Fig.7.The proposed metasurface has the RCS of1.21dBsm,3.41dBsm,and7.26dBsm at16.5GHz,23.5 GHz,and39.5GHz,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.At16.5GHz,23.5GHz,and39.5 GHz,the RCS reduction of16.8dBsm,17.6 dBsm,and18dBsm is achieved as compared to the same size of PEC.

Fig.7 The3D 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 from15.5to40.5GHz and the results are shown in Fig.8.An ultra-wideband RCS reduction of10dB is attained from 15.5to26.5GHz and30.5to40.5GHz under normal incidence as compared with a copper sheet of the same size.

Fig.8 The RCS of proposed coding metasurface and PEC

4 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.

Fig.9 The fabricated sample of four-leaf clover-shaped coding metasurface

To 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 Kaband horn antennas are used for measurement to cover the bandwidth from15.5to40.5GHz.The sample is placed in the far-field of the antenna and far-field condition is given by

Fig.10 Experimental setup in an anechoic chamber

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 10dB is achieved for normal incidence from15.5 to26.5GHz and30.5to40.5GHz,whereas more than6dB RCS reduction is observed from26.5to 30.5GHz.

Fig.11 Comparison of simulation and measurement results

However,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)of80%with a thickness of0.13λ0that makes the proposed design wideband with less thickness.As compared with binary optimization algorithm which can only be applied for1-bit metasurface,here,we have introduced DWCA which can be extended towards multi-bit metasurface designs.

5 Conclusion

A novel four-leaf clover-shaped coding metasurface is designed and applied to achieve an ultrawideband diffusion-like scattering.By optimization the dimension of the four-leaf clover,two elements are selected with a phase difference of 180°±37°from15.5to40.5GHz.An optimization algorithm is applied to get the best arrangement of unit cells to attain the ultra-wideband RCS reduction.More than10dB RCS reduction is obtained from15.5to26.5GHz and30.5to 40.5GHz as compared with a copper sheet of the same size.Furthermore,the RCS reduction of more than6dB is realized from26.5to30.5GHz.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.