Realization of Single-Layer Fourier Phased Metasurfaces for Wideband RCS Reduction

An efficient and fast strategy to design and realize single-layer Fourier phased metasurfaces for wideband radar cross-section (RCS) reduction when illuminated by a circular polarization (CP) plane wave is proposed in this letter. The scattering phase (between 0° and 360°) required at each unit cell of the proposed metasurfaces was computed using the Fourier phase formula in which the focal length (F) is inversely proportional to the phase distribution. Pancharatnam–Berry (PB) phase theory was applied with unit cells of subwavelength periodicity to further enhance the scattering and RCS reduction characteristics. The proposed wideband Fourier phased metasurface has a square shape and contains 30 × 30 PB unit cells with subwavelength periodicity of 5 mm ≈ 0.26λ16 GHz. Both simulation and measured results show that the proposed Fourier phased metasurfaces can achieve more than 10 dB of RCS reduction under normal incidence of CP plane wave regardless of the value of F. Under oblique incidence, more than 10 dB of RCS reduction was maintained for incident angles up to 60°. In addition, the single-layer Fourier phased metasurface features wideband 10 dB RCS reduction bandwidth from 10 to 24 GHz with a thickness of only 2 mm. This resulted in an 82.3% fractional bandwidth of RCS reduction, which is higher than the other designs reported in the literature. The proposed design strategy provides a promising way to design and realize metasurfaces for wideband and stable RCS reduction performance without the need to use a computationally complex and/or time-consuming and slow running optimization algorithm.


I. INTRODUCTION
M ETASURFACES are a 2-D engineered surface, which can be used to manipulate the phase, magnitude, and polarization of the incident electromagnetic wave (EM-wave) and, therefore, achieve extraordinary functionalities, such as polarization conversion [1], [2], [3], [4], [5], beam steering [6], beam focusing [7], [8], and cloaking [9], [10]. Radar cross section (RCS) and diffusion of EM waves are one of the important functions of the metasurface and have been a hot topic over the past decade [11], [12], [13], [14], [15]. Chessboard and checkerboard metasurfaces are among the first metasurfaces' designs for RCS reduction [16], [17], [18], [19]. Even though they have good boresight RCS reduction characteristics, their scattering patterns have strong reflection in some directions. In addition, the scattering characteristics of the chessboard and checkerboard metasurfaces are degraded severely under oblique incidence of EM plane wave. To overcome the drawbacks associated with chessboard and checkerboard metasurfaces, coding metasurfaces was proposed in [20] to realize diffusive scattering and to provide an extraordinary freedom for manipulating EM waves. However, the diffused scattering of the coding metasurface cannot be ensured without using a complicated and time-consuming algorithm for massive optimizations (sometimes prohibitive) to find the optimum 1-bit, 2-bit, or multibit phase distribution, which necessitates plenty of computational computer resources [21], [22]. In addition, ensuring wideband RCS reduction under wide angles of incidence is not an easy task. Moreover, timeconsuming algorithms are quite complicated for layman users to design coding metasurfaces as plenty of specialized knowledge in those complicated optimization algorithms are required. In addition, the absence of a design formula that can be used to achieve the optimum phase distribution required for more than 10 dB RCS reduction that make the design and realization of metasurface is much harder [23], [24], [25], [26], [27].
Fourier phase formula has been used recently to design a metalens for EM-wave focusing and for beam scanning [28], [29], [30]. To the authors' best knowledge, the scattering performance and RCS reduction of metasurfaces designed using Fourier phase distribution have never been explored before. This letter presents an efficient technique based on 2-D Fourier phase formula and Pancharatnam-Berry (PB) theory to design diffusive metasurfaces with wideband RCS reduction under both normal and oblique incidence of EM plane wave. The proposed technique makes the design process more efficient less time-consuming and without the need to use complicated optimization algorithms to find the optimum phase distribution.

II. PB UNIT CELL DESIGN AND RESULTS
In order to design a metasurface with a wideband characteristic, a unit cell with a wideband reflection characteristic is required. The configuration of the proposed PB unit cell in this study is shown in Fig. 1(a). The unit cell consists of a dielectric substrate (ε r = 4.4 and h = 2 mm) sandwiched between two copper layers.
The thickness of the copper layer was set as t = 0.018 mm. The upper copper layer is composed of the resonator, as shown in Fig. 1(a), with a full metal ground plane (bottom layer). The PB unit cell periodicity was selected as P = 5 mm, which is equivalent to 0.26λ o at 16 GHz. The optimized physical parameters of the unit cell are L = 1.6 mm, M = 3 mm, G = 0.5 mm, w = 0.2 mm, and R = 0.8 mm. The reflection characteristics of the PB unit cell were achieved using CST Microwave Studio with unit cell boundary conditions along both ±x and ±y directions. Excitation ports were assigned in the ±z directions. The simulated magnitudes of the copolarized (co-pol) and cross-polarized (cross-pol) reflected components under circularly polarized (CP) plane wave excitation are shown in Fig. 1(b). The magnitude of the co-pol component is close to 0 dB, which means a very high level of reflection. On the other hand, the magnitude of the cross-pol component is kept less than −11 dB over a wide frequency band from 10.2 to 23.6 GHz (fractional bandwidth (FBW) = 79.3%) and reached more than −50 dB at resonance frequencies. In addition, it can be noted that the unit cell has three resonance frequencies at 11.1, 15.6, and 21.4 GHz as a result of the parallel and antiparallel current distributions according to Faraday's law [31]. Based on the reflection component results and according to PB phase theory [32], the reflection phase (φ co-pol ) of the co-pol component will be a function to the rotation angle (β) of the copper resonator and related to each other as φ co-pol = ±2 β. The "+" and "−" denote the right-hand circular polarization and left-hand circular polarization incident waves. When β (rotation angle) gradually increased from 0°to 180°, the φ co-pol range is between ±180°o ver the frequency band from 10 to 24 GHz. Thus, any desired reflection phase value across the proposed metasurface aperture can be achieved by rotating the unit cell to the desired angle. The key motivation of using a wideband PB unit cell is to make the Fourier metasurface insensitive the polarization of the incident wave (over a wide frequency band), which is highly needed for the radar stealth applications when the polarization of the incoming EM plane wave is usually unknown.

III. FOURIER PHASED METASURFACE DESIGN
The proposed design technique is based on using Fourier phase formula for direct calculation of the phase distribution and to design RCS reducer metasurfaces without the need to use any complicated or time-consuming algorithms. The first step in the design of the proposed Fourier phased metasurfaces is to calculate the 2-D Fourier phase using the following equation [29]: (1) In (1), k is the free-space wavenumber, F is the focal length (the distance from the focal point to the metasurface center), λ o is the free-space wavelength at 16 GHz, and X c and Y c denote the centers of the PB unit cell in the xy-plane. As can be seen in (1), the focal length F is inversely proportional to the scattering phase distribution, which is an opposite case to the conventional parabolic phase distribution in which F is directly proportional [27]. Based on (1), an in-house MATLAB script has been used to calculate the phase distribution of a 2-D Fourier metasurfaces consisting of 30 × 30 PB unit cells. To understand the effect F on the Fourier phase distribution and the scattering characteristics, four Fourier phase distributions have been calculated with the aid of (1) for F/D = 1, 0.75, 0.5, and 0.25 with D = 150 mm, as shown in Fig. 2 (only phase distributions with F/D = 1 and 0.25 are shown for brevity). Based on those Fourier phase distributions, four metasurfaces were designed (only F/D = 1 and 0.25 metasurfaces are presented for brevity), as shown in Fig. 3. To evaluate the RCS reduction performance of the Fourier phased metasurfaces, a series of full-wave simulations were conducted using the time-domain solver in CST Microwave Studio. The metasurface was placed in the xy-plane and clarification of the angles used in this work is shown in Fig. 4(a) and the simulated RCS reduction curves of the four metasurfaces are presented in Fig. 4(b) under normal incidence (θ inc = 0°). Compared with copper plates of the same size, all Fourier metasurfaces achieved more than 10 dB RCS reduction regardless of the F value over the frequency band from 10 to 24 GHz resulting in an FBW =  82.3%. The mechanism of achieving such a wide RCS reduction bandwidth is due to two reasons: first, using highly reflective unit cells of subwavelength periodicity and wideband operation; and second, Fourier phase in which F is inversely related to the phase distribution. For such a phase distribution, an incident plane wave radiated from a source placed at F will be focused. But if that plane wave is coming from a far-field region, then it will be severely diffused. To further validate the RCS reduction characteristic of the Fourier metasurfaces, the 3-D scattering patterns were computed and depicted in Fig. 5 at four different frequencies. The 3-D scattering patterns' results prove that the incident CP plane wave is severely diffused and reflected back to countless directions instead of a single directive lobe reflected in the boresight direction with a perfect electrical conductor (PEC) plate. However, it is noticed that for F/D = 1 and 0.75, the scattering patterns are narrow and not very well diffused over the whole plane in front of the metasurface. As the Fourier metasurface with F/D = 0.25 shows a better RCS reduction level and scattering pattern shape compared with other three metasurfaces (see Figs. 4 and 5), the Fourier metasurface with F/D = 0.25 will be further investigated in the rest of this letter. The Cartesian far-field scattering patterns of this metasurface were computed and presented in Fig. 6 along with those of a bare PEC plate for comparisons. It can be seen that a PEC plate has a strong reflection lobe in the boresight direction, as stated by Snell's law of reflection. However, a significant RCS reduction in the backward direction can be seen over all angles in the plane in front of the Fourier metasurface as confirmed by the 2-D scattering plots in Fig. 7(a). The backscattered energy was severely diffused and distributed on the xoy-plane in front of the metasurface and the directive lobe that appears as a red spot for the PEC plate case has been reduced. These results demonstrate  the capability of the Fourier metasurface for RCS reduction. The RCS reduction characteristics of the F/D = 0.25 Fourier phased metasurface were further investigated under oblique incidence of CP plane wave when θ inc increased from 15°to 60°, as shown in Fig. 7(b). In a PEC plate case, the angles of incidence and reflection are equal according to Snell's law of reflection and the reflected beam can be clearly seen as a red spot at θ inc = θ reflected . For the F/D = 0.25 Fourier phased metasurface, the scattered energy is severely diffused into countless angles with θ inc ࣔ θ reflected . The RCS reduction was further investigated under oblique incidence for φ inc = 0°, 45°, and 90°planes and θ inc increased from 15°to 60°and the results are presented in Fig. 8. It is noticed that the RCS reduction magnitude is always more than 10 dB for all angles. These results confirm that the presented design approach is robust and the ability of the Fourier metasurfaces using direct design formula to efficiently achieve more than 10 dB of RCS reduction without using any complicated optimization algorithms.

IV. FABRICATION AND EXPERIMENTAL RESULTS
For experimental verification, a prototype of the proposed F/D = 0.25 Fourier metasurface was fabricated using standard printed circuit board (PCB) technology. The overall dimensions of the fabricated sample are 150 mm × 150 mm, as shown in Fig. 9(a). A sketch of the measurement setup used for the RCS  reduction measurement is shown in Fig. 9(b), which consists of two identical horn antennas: one for transmitting waves and the other one for collecting the backscattered waves. The horn antennas were placed symmetrically and close to each other and, at the same time, far enough from the metasurface under test at a distance R to satisfy the far-field formula [33]. Both simulated and measured monostatic RCS results are normalized to a copper plate with the same dimensions and plotted in Fig. 9(c). It can be seen that more than 10 dB of RCS reduction was achieved from 10 to 24 GHz. A small discrepancy between the measured and simulated results was observed, which is a result of the fabrication tolerance and misalignment of the antennas during the measurements. The proposed Fourier metasurface was compared with other designs in the literature, as listed in Table I.  The Fourier phased metasurface demonstrated a wider RCS reduction bandwidth (FBW) under oblique incidence up to 60°.

V. CONCLUSION
In summary, the CP Fourier phased metasurfaces for RCS reduction are proposed in this letter. The proposed metasurfaces were designed using direct technique based on the Fourier phase formula for the calculations of the phase distribution. The proposed metasurfaces were designed without the need for any complicated or time-consuming algorithms and achieved an RCS reduction bandwidth of 82.3%, which is wider than the other metasurfaces in the literature. The RCS reduction behaviors can hold under oblique incidence of EM wave at angles up to 60°. Both simulated and measured results confirmed the excellent RCS reduction performance of the Fourier metasurfaces and the proposed design approach. The proposed design approach is very useful in applications when both monostatic and bistatic RCS reductions are required.