Wideband Radar-Cross-Section Reduction Using Parabolic Phased Metasurfaces

This letter presents a fast and efficient metasurface design approach without using time-consuming optimization algorithms, for wide-angle low scattering applications and wideband radar-cross-section (RCS) reduction. Using ray-tracing theory and by engineering the proposed metasurfaces to exhibit a diffusive parabolic phase distribution across its aperture at frequencies other than the center frequency (f = 18 GHz), significantly diffused backscattering is guaranteed by redirecting the reflected energies over all directions over a wide range of frequencies. Based on the proposed approach, the scattering behavior of metasurfaces with parabolic phase distributions from 1f to 20f was carefully investigated. Numerical and experimental results both demonstrated that a metasurface of phase profile at 5f is extremely powerful in distributing the scattering energy more uniformly than a metasurface of 1f phase profile. The designed metasurfaces using the proposed approach achieved more than 10 dB monostatic/bistatic RCS reduction over a wideband frequency range from 12 to 24 GHz (66.7%) and even for off-normal incidence up to 60°. The proposed approach can overcome the inherent challenges of ensuring wide scattering angle over wideband frequencies of conventional chessboard and coding metasurfaces in the literature.

, genetic algorithms [10], or neural networks [21] to achieve the optimum amplitude/phase distribution or coding sequences. This process is intensive time-consuming and will cost lots of computing resources to reach the desired RCS reduction level, and it is not an easy task. Parabolic phase distribution is extensively used in the literature to design high-gain antennas, such as focusing lenses [22] and reflectarrays [23], [24], [25]. As shown in [26], [27], [28], and [29], metasurfaces with parabolic phase distribution across their apertures can be used for both monostatic and bistatic RCS reduction due to their intrinsic diffusive scattering features. However, it was shown in [26], [27], [28], and [29] that a full parabolic phased metasurface has some drawbacks, such as narrow bandwidth and scattering patterns of narrow scattering angles. To overcome these drawbacks, the researchers in [26] have divided the metasurface into a number of subarrays to exhibit nonsimilar parabolic phase profiles and distributed randomly across the metasurface aperture. In [29], the metasurface was divided into four subarrays exhibiting hybrid-phase constructed by combining the focusing parabolic phase with 1-D linear phase gradients. In [28], a chessboard-like phase profile was combined with parabolic phased subarrays of random focal lengths by each unit cell.
In this letter, a fast and efficient approach to design full parabolic phased metasurfaces is proposed. The designed metasurfaces can achieve diffused scattering patterns of wide scattering angles for both monostatic and bistatic RCS regardless of polarization and under wide range incident angle up to 60 • . The proposed approach does not require dividing the metasurface into small subarrays or combining two types of phase profiles as in the literature. There is no need to use complicated timeconsuming optimization algorithms. The phase distribution can be obtained directly using the modified parabolic phase formula presented in this work.

II. UNIT CELL DESIGN
The geometry (top and side views) of the wideband reflective anisotropic unit cell is shown in Fig. 1(a) and (b) with R = 0.7 mm, W = 0.2 mm, M = 2.61 mm, and P = 5 mm. The dimensions were optimized carefully such that it has wideband reflection properties. The anisotropic unit cell was designed and optimized based on Pancharatnam-Berry (PB) phase theory in which when a circularly polarized (CP) plane wave illuminates the unit cell, the magnitude of the cross-polarized (cross-pol) reflection component will be low, and a strong copolarized (co-pol) reflection will dominate [30], [31], [32], [33]. The reflection characteristics of the PB unit cell were simulated using frequency-domain solver of CST Microwave Studio [34] with appropriate boundary conditions. As shown in Fig. 1(c), the unit cell has a very strong copol reflection close to 0 dB and low-level cross-polarized components of less than −18 dB from 12 to 24 GHz. In addition, as stated by PB phase theory [30], [31], [32], [33], [35], the reflection phase (ϕ r ) of the copolarized reflection component is related to the resonator rotation angle (ψ) as ϕ r = ±2ψ, "+" and "−" signs denote the left and right CP waves, respectively. As can be seen in Fig. 1(d), the simulated reflection phase response of the unit cell when illuminated by CP wave is almost linear and precisely twice the rotation angle (ψ) value.

III. PARABOLIC PHASED METASURFACES DESIGN
The metasurfaces designed using only full parabolic phase profiles across their apertures suffer from narrow RCS reduction bandwidth and narrow scattering angle [26], [27], [28], [29]. In this work, an efficient and fast design approach is proposed based on adding the parameter N (N = 1, 2, 3, 4, 5, …) to the original parabolic phase equation and the modified formula becomes the following equation: In (1), X cell and Y cell are the coordinates of the PB unit cell in the xy-plane across the metasurface aperture, F is the focal length, c is the speed of light in vacuum, and f is the design frequency. The parameter Nf (N is an integer) in (1) means that the modified parabolic phase distribution will be a multiplier of the base frequency. In this work, a metasurface consisting of 30 × 30 PB unit cells with D = 150 mm, F = 0.9D was used and the 2-D phase distribution have been investigated when N = 1, 5, 10, 15 at f = 18 GHz. The 2-D phase distribution maps of metasurfaces at N = 1, 5, 10, and 15 are shown in Fig. 2. As can been in Fig. 2, the parameter N strongly affects the 2-D phase distribution profile across the metasurfaces, and the resultant phase profiles are completely different from the classical parabolic phase profile. Advantages of this approach include the following.
1) The phase distribution maps in this work were obtained directly without any complex or time-consuming algorithms, such as particle swarm optimization (PSO) or genetic aalgorithm (GA) [10], [20]. 2) Without dividing the metasurface into number of subarrays [26] and without designing each subarray separately. 3) Without adding any additional phase terms to the original parabolic phase formula [29]. 4) Without using different F/D values across the metasurface aperture for each unit cell. The required phase compensation at each PB unit cell was achieved via rotating the metallic resonator to the desired angle based on the data in Fig. 1(d) and four metasurfaces were designed, as shown in Fig. 3.
First, a detailed study on the relation between N and the scattering angles in the half plane in front of the metasurfaces was conducted for 1 ≤ N ≤ 20, as shown in Fig. 4(a). As can be seen, the scattering angle of the classical full parabolic phased metasurface (N = 1) is about 28 • , so it fails to diffuse the EM wave over a wide scattering angle. When the value of N increases, the scattering angle gets wider until N reaches 5, which shows the widest scattering angle of 169 • . The reason for that is the phase distribution when N = 5 has the best phase cancelation (destructive phase) compared with the other values of N.
For N > 5, the scattering angle is almost stable between 110 • and 135 • . The 10 dB RCS reduction bandwidth and maximum   Fig. 4(b) and normalized to the RCS of an equalsized copper plate. It was found that all the four metasurfaces can achieve more than 10 dB RCS reduction over a wide frequency band from 12 to 24 GHz, yielding a fractional bandwidth of 66.7%. However, it was also found that the maximum RCS reduction levels are a function of N, for instance, when N = 1, the maximum RCS reduction level is around 15.2 dB, but it reaches 24.3 dB, 19 dB, and 20.5 dB when N = 5, 10, and 15, respectively. Simulated 3-D scattering patterns of the parabolic phased metasurfaces when illuminated by CP plane wave with different values of N are presented in Fig. 5. It is noticed that when N = 1, the 3-D far-field scattering pattern has a narrow scattering angle and distributed around the boresight direction, and it was not distributed uniformly in front of the metasurface, which confirms the results in Fig. 4(a). However, when N = 5, 10, or 15, the shape and level of the backscattered patterns have been changed and the reflected energies are significantly diffused in more uniform fashion with much wider scattering angles, as shown in Fig. 5(b)-(d).
As the N = 5 metasurface has the best diffusion characteristics in terms of scattering angle and maximum RCS reduction levels, as shown in Fig. 4, its scattering performances under oblique and off-normal incidences were investigated carefully. The simulated results when the angle of incidence (θ inc ) increased gradually from 15°to 60°in steps of 15°are shown in Fig. 6. Wide-angle backward diffusion with more than 10 dB RCS reduction was still preserved over the whole frequency band at angles up to 60°for the N = 5 metasurface. As can be seen in Fig. 6, for a bare perfect electrical conductor (PEC) plate under oblique incidence, the  reflection obeys Snell's law of reflection with equal angles of incidence and reflection. The scattering characteristics of N = 5 metasurface were further investigated by computing the RCS reduction amplitude in various incident planes for different angles of incidence (θ inc ). A sketch showing the angles of incidence and the planes considered in this letter are shown in Fig. 7(a). The RCS reduction curves were computed when the θ inc increased from 15°to 60°in φ inc = 0°, 45°, and 90°planes, as shown in Fig. 7(b)-(d). It can be seen that RCS reduction is always more than 10 dB for all angles of incidence in all planes and frequencies.

IV. CURVED PARABOLIC PHASED METASURFACES
The scattering characteristics of the proposed metasurface (N = 5) when integrated on curved surfaces have been investigated. As the cylindrical structure is typically involved in the bodies of various moving platforms, the conformal integration of the proposed metasurface (N = 5) into a cylindrical platform skin was investigated for various radii. The side view of the curved metasurface with the incident and reflected beams is shown in Fig. 8(a)-(c), and the radii of cylinder were chosen as 45, 60, and 75 mm, respectively. The proposed metasurface has wide scattering angles when applied to the curved surfaces with more than 10 dB of RCS reduction for all radii (30,45,60, and 75 mm), as shown in Fig. 8(d). The RCS reduction characteristics of the curved metasurfaces were further investigated under oblique incidence of EM plane wave. The proposed N = 5 metasurface preserved more than 10 dB of RCS reduction when attached to a  cylindrical surface under oblique incidence of EM plane wave, as shown in Fig. 9. As can be seen, the RCS reduction was always greater than 10 dB for all metasurfaces from 12 to 24 GHz even though the unit cells across the curved metasurface will have a different oblique incidence. This is because the RCS reduction of the metasurface is a summation of the responses of all unit cells, which are still able to produce a destructive interference.

V. FABRICATION AND MEASUREMENTS
For experimental verification, N = 1 and N = 5 metasurfaces were fabricated using PCB technology, as shown in Fig. 10(a). The RCS measurements were conducted inside a microwave anechoic chamber to reduce the unwanted reflections from the surroundings, see the experimental setup in Fig. 10(b). The metasurfaces were placed on a foam platform in front of the horn antennas, and the distance R was chosen carefully to satisfy the far-field region requirements [36]. Due to the limited experimental resources, only monostatic RCS reduction was performed, and the results are presented in Fig. 10(c). As can be seen in Fig. 10(c), backscattered reflection suppression and RCS reduction are observed from 12 to 24 GHz and the N = 5 metasurface has the lowest reflection levels compared with the N  = 1 metasurface and the copper plate. The proposed metasurface (N = 5) was compared with metasurfaces (chessboard, coding, random, and pixelated) found in the literature, and the results of the comparison are presented in Table I. The comparison shows that the proposed metasurface, which were designed based on the proposed technique, achieved wider RCS reduction bandwidth under wider angle of incidence up to 60°.

VI. CONCLUSION
In summary, an efficient design approach is presented with the following advantages.
1) The phase distribution maps were obtained directly without any complex or time-consuming algorithms, such as PSO or GA. 2) Without dividing the metasurface into number of subarrays. 3) Without adding any additional phase term (profile) to the original parabolic phase formula. 4) Without using different F/D values for each part (subarray) or unit cell across the metasurface aperture. The designed metasurfaces achieved wider RCS reduction bandwidth (66.7%) compared with those designs in the literature (chessboard, coding, random, and pixelated) under wider angle of incidence up to 60°. Strongly diffused patterns were achieved for both planal and curved metasurfaces from 12 to 24 GHz.