Aperiodic Sunflower-Like Metasurface for Diffusive Scattering and RCS Reduction

This letter presents the design of aperiodic sunflower-like metasurface for circularly polarized (CP) wave diffusion and radar cross-section (RCS) reduction using Pancharatnam–Berry (PB) meta-atoms. The distribution of the PB meta-atoms across the metasurface aperture is nonuniform and has a distribution inspired by sunflower seeds, i.e., an outwardly logarithmic spiral lattice with no transitional periodicity. The proposed metasurface has 600 PB meta-atoms of subwavelength size of 5 mm ≈ 0.33λ20GHz and exhibits a randomly chosen diffusive reflection phase between 0° and 360°. Both simulated and experimental results demonstrate that the proposed sunflower-like metasurface can efficiently diffuse the backscattered energy into numerous directions when normally illuminated by a CP wave with RCS reduction >7 between 16 and 23.8 GHz. Furthermore, the low-level diffuse scattering can be preserved under oblique incidence up to 60°. As a result of using this PB concept, the polarization sensitivity of the proposed metasurface is released, and this is highly desired in applications when the polarization of the incoming wave is unknown.


I. INTRODUCTION
M ANIPULATION of electromagnetic (EM) waves using metasurfaces has been a hot topic in recent years [1]- [7]. EM wave diffusion and radar cross-section (RCS) reduction is one of the applications of metasurface [8]- [11]. Metasurfaces are the 2-D version or counterparts of metamaterials, which are usually constituted by an array of periodic or nonperiodic subwavelength metallic or dielectric resonators [12], [13]. In [2]- [7], a chessboard-and checkerboard-like metasurfaces for RCS reduction were proposed using two kinds of meta-atoms exhibiting a 180°± 25°phase difference between their absolute reflection phases. However, such kinds of surfaces suffer from strong scattering in certain directions and degraded scattering characteristics under oblique incidence. In [1], a modified chessboard was proposed, and each quadrant of the conventional chessboard was replaced by a small-size 1 bit reflectarray exhibiting an optimized diffusive 1 bit quantized phase distribution Manuscript  to achieve nearly uniform diffusive scattering under both normal and oblique incidences of EM waves. In [9] and [10], the scattering characteristics of metasurfaces exhibiting concave and convex reflection phases were investigated for RCS reduction for linearly polarized waves. Furthermore, a coding metasurface was introduced in [14] and [15], in which the coding particles (unit cells) were arranged according to a certain coding sequence to achieve low-level backscattering and potentially any other desired functions [16]- [19]. In [1]- [19], metasurfaces were designed by placing meta-atoms and scatterers in rectangular periodic grids (framework). Important questions include whether this periodic arrangement is always the best option and whether it is possible to design metasurfaces with aperiodic distribution of meta-atoms to achieve elegant diffusion characteristics for circularly polarized (CP) waves. In this letter, the design of aperiodic sunflower-like metasurfaces for CP wave diffusion and RCS reduction using Pancharatnam-Berry (PB) meta-atoms is presented. The distribution of the PB meta-atoms across the metasurface aperture is nonuniform and has a sunflower-seed-inspired distribution, i.e., outwardly logarithmic spiral lattice of no transitional periodicity. All PB meta-atoms exhibit a randomly chosen diffusive reflection phase between 0°and 360°. Both simulated and experimental results demonstrate that the proposed sunflower-like metasurface can efficiently diffuse the backscattered energy with RCS reduction of a metallic plate.

II. PB META-ATOM DESIGN
The geometry of the proposed anisotropic subwavelength PB meta-atom is presented in Fig. 1(a) and (b) and consists of a copper resonator of dumbbell-shape etched on the upper side of a dielectric spacer (ε r = 4.4 and h = 2 mm) and backed by copper ground; the thickness of the copper film is 0.018 mm. The frequency-domain solver of the CST Microwave Studio has been used to obtain the reflection characteristics of the unit cell via conducting a series of EM numerical simulations [20], [21]. For the purpose of achieving high-efficiency PB meta-atoms, the dimensions of the metallic resonator have been optimized, and final dimensions of the anisotropic PB meta-atom are W = 0.3, P = 5, and R = 0.6 (all in millimeters). When the proposed PB meta-atom was illuminated by a CP wave, it has a high copolarization (co-pol) reflection and very low crosspolarization (cross-pol) reflection, as can be seen in Fig. 1(c). The reflection phase of this PB meta-atom when illuminated by x-or y-polarized waves, respectively, is presented in Fig. 1

(d).
As can be seen, the reflection phase is continuous, and there is about 180°± 27°phase difference between x-and y-polarized reflections between 14.1 and 23.3 GHz. According to the PB phase theory [8], [22], if the unit cell has a high reflection magnitude under LP wave illumination with around 180°reflection 1536-1225 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information. phase difference between orthogonal linearly x-and y-polarized incidences, then when the unit cell is illuminated by a CP wave, the cross-pol reflection will be significantly reduced, leading to high co-pol reflection. In addition, the co-pol reflection phase (ϕ) can be expressed as ϕ = ±2ψ, where the polarization signs "-" and "+" correspond to left-hand circularly polarized (LHCP) and right-hand circularly polarized (RHCP) incident waves, respectively, and ψ is the rotation angle of the dumbbell-shape metallic resonator. Based on the angular rotation of the copper resonator, a 360°co-pol reflection phase is achieved, as shown in Fig. 1(e), when the angular rotation angle increased gradually from 0°to 180°.

III. SUNFLOWER-LIKE CP METASURFACE DESIGN
The PB meta-atoms of the proposed sunflower-like CP metasurface should be arranged in similar way to the seeds of a sunflower in nature, as shown in Fig. 2(a). In other words, realizing a logarithmic spiral lattice, the position of each PB meta-atom in the xy plane can be found as follows: (1) which is the Cartesian form of the polar equations in [24]- [26]. In (1), τ is the spiral golden ratio, S is the spacing between the centers of any two adjacent meta-atoms, and n is the number of meta-atom on the metasurface aperture (n = 1, …., N, where N is the total number of meta-atoms). Using MATLAB code, the positions of the PB meta-atoms were calculated using (1), as shown in Fig. 2(b), for S = 5 mm, τ = ( √ 5 + 1)/2, and N = 600. As can be seen, in such an aperiodic distribution, the meta-atoms are not too far from each other and at the same time not overlapping.
The required diffusive reflection phase at each unit cell should be calculated such that the backscattered energy will be distributed in a nearly uniform shape in the half space in front of the sunflower-like CP metasurface. A random diffusive phase (DP) between 0°and 360°was introduced for each PB meta-atom of the metasurface by rotating the metallic resonators by a certain angle (ψ) based on the PB formula DP = 2ψ.
The random phase distribution of the whole sunflower metasurface was generated by a random function produced by MATLAB. Three different random phase distribution maps are shown in Fig. 3 and named as SFM#1, SFM#2, and SFM#3, respectively. It is important here to mention that each phase distribution map leads to different phase distributions  and different scattering patterns. Based on the phase distribution maps, three diffusive metasurfaces are designed, as shown in Fig. 4, and the metasurfaces have ultrathin thickness of 0.12λ. The time solver of CST Microwave Studio was used to obtain the diffusion characteristics of these metasurfaces. The 3-D far-field scattering patterns of the three sunflower-like metasurfaces under normal illumination of CP plane wave are presented in Fig. 5. The scattering patterns of all three sunflower-like metasurfaces have diffuse-like  scattering patterns at all frequencies, and it is very obvious that the specular reflection wavefront has been destroyed, which is intrinsically different from that of an equal-sized perfect electrically conducting (PEC) plate in Fig. 5(d), for which the specular reflection according to Snell's law of reflection is dominated. As a result of the phase change across the metasurface aperture and the aperiodic distribution of PB meta-atoms, the incident wave is reflected in countless directions (angles) in the whole half space in front of the three metasurfaces. It was observed that the sunflower-like metasurface (SFM#3) in Fig. 5(c) had the lowest scattering levels and exhibited much more uniform scattering patterns. The scattering patterns of SFM#3 at various frequencies are presented in Fig. 6, which shows that a low-level diffused scattering pattern dominates compared with those of equal-sized PEC plates at the same frequencies, for which a single-beam specular reflection is dominated. To better understand the scattering characteristics of SFM#3, the 2-D backscattered field distribution is presented in Fig. 7, and as can be seen, the backscattered field is diffused and distributed on the half space in front of SFM#3, which is not the case for a PEC plate, in which the backscattered field is very strong in the boresight direction for all phi angles. The diffuse scattering characteristics of SFM#3 under oblique incidence of CP wave are also investigated, and the results are presented in Fig. 8. Here, three cases are considered when the incident angle (θ inc ) is 30°, 45°, and 60°. As can be seen, even under the illumination of oblique CP wave, the sunflower metasurface still efficiently diffuse the incident CP wave.

IV. FABRICATION AND MEASUREMENTS
For experimental verification of the proposed CP sunflowerlike metasurface, SFM#3 was fabricated using the standard printed circuit board process, as shown in Fig. 9(a). The reflection measurements were performed inside an anechoic chamber to reduce the reflections and interferences from the surroundings. The measurement setup is shown in Fig. 9(b). In the measurement setup, a pair of horn antenna serving as a transmitter (T x ) and a receiver (R x ) are connected to a vector network analyzer (VNA) via coaxial cables. The distance between the horn antennas and the SFM#3 under test was chosen carefully according to the far-field formula in [27]. To avoid unwanted reflections from nearby objects, the time gating function of the VNA was used. The simulated and measured RCS curves of both SFM#3 and a bare copper plate are presented in Fig. 9(c). Greater than 7 reduction was achieved across the band from 16 to 23.8 GHz with approximately 18 dB reduction around 20 GHz. The small deviation between the measured and simulated RCS results in Fig. 9(c) can be attributed to the misalignment of the horn antennas and the metasurfaces inside the anechoic chamber during the measurements, the fabrication error, and the uncertainty of the dielectric permittivity of the substrate at this frequency.
It is well known that the conventional chessboard metasurface suffers from strong scattering in certain directions and degraded scattering characteristics under oblique incidence. The modified chessboard structure in [1] consisted of four reflectarrays and using 1 bit quantized parabolic reflection phase. In other words, only two phase states (0°and 180°) were used. Also, in [1], the unit cells have been distributed periodically in rectangular grids. Compared to those chessboard metasurfaces in the literature, the proposed SFM#3 has a countless number of random PB phase states between 0°and 360°and an aperiodic distribution of PB meta-atoms across its aperture. Compared to the RCS patterns in [1], it has been noticed that for the proposed surface, the backscattered energy is severely diffused and distributed in a more uniform fashion in front of SFM#3, as shown in Fig. 5. Furthermore, the proposed sunflower-like metasurface has a lower RCS scattering levels under oblique incidence compared to the modified chessboard in [1].

V. CONCLUSION
In summary, the proposed aperiodic SFM#3 uses PB metaatoms, and the distribution of the 600 PB meta-atoms across the metasurface aperture is nonuniform and has a sunflowerseed-like distribution with random reflection phase. Both simulated and experimental results demonstrated that the proposed sunflower-like metasurface can efficiently diffuse the backscattered energy into numerous directions when normally illuminated by a CP wave. The RCS reduction was greater than 7 across the frequency range 16-23.8 GHz. Furthermore, the low-level diffuse scattering is preserved under oblique incidence up to 60°.