Cusp Phased Metasurfaces for Wideband RCS Reduction Under Broad Angles of Incidence

This article presents an efficient and effective design approach of the phase distribution calculation across metasurface for significant radar cross section (RCS) reduction of a circular polarization (CP) and liner polarization (LP) radar waves. The RCS reduction using the proposed design approach is achieved by imposing a novel cusp phase mask (which is usually used to generate 3D self-accelerating and self-healing cusp beams) at each geometric phased anisotropic unit cell composing the proposed cusp phased metasurface. By solving the cusp phase formula using MATLAB, it is found that the cusp phase mask required to achieve more than 10 dB of RCS reduction over a wide frequency band can be calculated without the need of significant lengthy optimizations or huge computer resources. The ability of such cusp phase mask metasurfaces to achieve significant backward scattering and RCS reduction has been rigorously investigated by means of simulations and measurements. When illuminated by a far-field radar CP or LP plane wave, the proposed cusp phased metasurface realizes more than 10 dB of RCS reduction from 10.9 to 26 GHz, corresponding to a fractional bandwidth of FBW = 81.8%. The 10 dB RCS reduction bandwidth of the cusp metasurface is maintained under both normal and wide angular incidence up to 75o. The proposed cusp metasurfaces have potential applications to make objects stealthy where the incidence radar signal has an unknown frequency, polarization, or angle of incidence.


I. INTRODUCTION
M ETASURFACES have gained significant importance in the optical community due to their unique and versatile properties.Metasurfaces enable the manipulation of light (and EM waves) at the subwavelength scale, allowing for precise control of its properties, such as phase, amplitude, and polarization.This level of control is not achievable with traditional optical components.In recent years and due to their unique ability in manipulating electromagnetic (EM) waves, metasurfaces have been applied for stealth applications by minimizing the radar cross section (RCS) of targets and preventing them from being detected by monostatic and bistatic radar sensors [1], [2], [3], [4], [5], [6], [7], [8].A metasurface is a 2D array of scatterers called unit cells distributed periodically along the x-and y-axes and the RCS reduction performance of the metasurface is a summation of the destructive scattering characteristics of all unit cells [9], [10], [11], [12], [13], [14].Despite all the advantages of chessboard metasurfaces, the strong reflections in their far-field RCS patterns toward the diagonals in the space in front of the target severely limits their application for bistatic RCS reduction [15], [16], [17], [18], [19], [20].In addition, the RCS reduction performance is typically severely degraded under oblique incidence [21], [22], [23].Random coding metasurfaces can solve the drawbacks associated with chessboard metasurfaces, however they require the use of an optimum random phase mask across the metasurface aperture, which is not an easy task [24], [25], [26], [27], [28].
The non-existence of a formula for direct calculation of the random coding phase mask to achieve more than 10 dB of RCS reduction is a serious drawback of coding metasurfaces.To find the optimum random phase mask, a series of repetitive optimizations should be implemented using complicated and time-consuming optimization algorithms with very high-performance computer resources [24], [29], [30].The design process gets more complicated when multibit (3-bits or higher) random phase masks need to be calculated or computationally larger surfaces need to be designed.
In this article, an efficient design approach for calculating the phase mask across the metasurfaces aperture without the need of lengthy optimizations or huge computer resources is presented.To the author's best knowledge, the cusp phase mask formula has been only used in the literature to generate a 3D self-accelerating and self-healing cusp beam [31], [32], [33].The RCS reduction performance of the cusp phase mask has never been explored for RCS reduction.By solving the cusp phase formula using MATLAB, it is found that the cusp phase mask required to achieve more than 10 dB of RCS reduction over a wide frequency band can be calculated directly without going through repetitive optimizations or using complicated optimization algorithms such as genetic algorithms (GA) or particle swarm optimizations (PSO).The proposed cusp phased metasurface realizes a remarkable diffusion performance compared to random coding metasurfaces, including more than 10 dB of RCS reduction from 10.9 to 26 GHz, with fractional bandwidth of FBW = 81.8%under both normal and wide oblique incidence up to 75 o .

II. GEOMETRIC PHASE ANISOTROPIC UNIT CELL DESIGN
The unit cell of the proposed cusp metasurface is presented in Fig. 1(a), which shows the front, side, and 3D views.The unit cell is formed by a metallic resonator etched on RO4003C dielectric slab which has ε r = 3.55, thickness h = 2.03 mm and a loss tangent of 0.0027.The lower side of the unit cell was fully covered by solid ground metallic layer.The metallic layers of the resonator and the ground layer are made up of a copper with a thickness of t = 0.018 mm and conductivity of 5.96×10 7 S/m.Electromagnetic simulation software CST Microwave Studio was used to access the reflection and scattering behavior of the proposed unit cell.In the simulations, periodic boundary conditions were applied to the four sides of the unit cell in the xy-plane, while a Floquet port was used in the z-direction to excite the waves.The optimal geometrical dimensions of the unit cells are P = 4 mm, L =2.2 mm, R = 1.1 mm, w = 0.4 mm.The simulated co-polarization (co-pol) and crosspolarization (cross-pol) reflection coefficients of the unit cell are shown in Fig. 1(b) and a strong co-polarization reflection close to 0 dB is achieved from 10.9 to 25.8 GHz.Over this frequency range, the cross-polarization reflection is significantly suppressed when Fig. 1(b) is examined, it is observed that three resonances occur at 12 GHz, 17.7 GHz, As can be seen, the geometric phase which is the reflection phase of the co-pol component, and the unit cell rotation angle (ψ) are linearly related as φ geometric = φ co-pol = ±2ψ.The 0 o ≤ φ co-pol ≤ 360 o is achieved when rotating the unit cell around its center point by 0 o ≤ φ co-pol ≤ 180 o .Thus, the proposed cusp metasurface will be composed of several identical unit cells with different orientations to modulate the required cusp phase mask.

III. CUSP PHASED METASURFACES DESIGN AND RESULTS
The key design step of the proposed cusp metasurfaces is the calculation of the cusp phase mask across the metasurface aperture.In the literature, cusp phase masks were used to generate cusp beams which are one type of complex structured beams with unique multiple selfaccelerating channels [31], [32], [33].Here the RCS reduction performance of a cusp phased metasurface is investigated.The proposed cusp metasurface is constructed by arranging 50 × 50 anisotropic geometric phased unit cells in the xy-plane and occupies a square area of 250 × 250 mm 2 .Through the coordinate transformation, equation ( 1) is the general expression of the cusp phase mask formula in the Cartesian coordinate system.
In equation ( 1), φ cusp (x c , y c ) is the cusp phase to be imposed at each geometric unit cell across the metasurface aperture, x c and y c are the coordinates of the unit cell with respect to the center of the metasurface in the xy-plane, C is a constant scaling number, B represents the initial phase over all unit cells of the cubic phase mask, and the polynomial order M is an integer represents the modulation index of the cubic phase mask.For the cusp metasurfaces in this work, the constants in equation (1) were chosen as C =1000, B = π /2 and both constants will affect the maximum phase range.The parameter that significantly affects the cusp phase patterns is the modulation index (M).The effect of M on the cusp phase masks was examined carefully to get full understanding of the importance of this parameter in the design approach.Using a MATLAB code based on equation (1), four cusp phase masks with M = 1,2,3, and 4 were calculated, see Fig. 2. As can be seen, M has an outstanding impact on  the cusp phase distribution across the metasurface aperture.To understand the impact of M on the RCS reduction and backscattering diffusion, four metasurfaces were designed based on the cusp phase masks presented in Fig. 2. For the sake of brevity, the layouts of only two metasurfaces when M = 1 and 3 are shown in Fig. 3 and the unit cell in Section II were rotated according to the relation φ geometric = φ cusp = 2ψ.CST Microwave Studio was used to compute the 3D farfield RCS patterns of the four metasurfaces and the results are shown in Fig. 4. As can be seen in Fig. 4, the PEC plate reflects the incident waves similar to a mirror and in such a manner that the angle of incidence is equal to the angle of reflection according to Snell's law of reflection.When M =1, the cusp metasurface has failed to efficiently diffuse the backscattered energy in all directions in the space in front of the metasurface.As can be seen, a dense scattering was considered around the boresight direction.When M = 2, the reflected pattern has a flat and intense reflection around the boresight direction.It can be concluded that both cusp phase masks with M = 1 and 2 cannot efficiently reduce the backscattering and such scattering patterns are not effective for RCS reduction.
When M = 3 and 4, the amplitude and distribution of the scattering patterns have been changed completely and the backscattered patterns were severely diffused in all directions in the space in front of the cusp metasurfaces.Such kinds of scattering patterns (M = 3 and M = 4) are of  great importance for RCS reduction.The far-field scattering patterns of four cusp metasurfaces were further investigated by looking at the 2D field distribution of the reflected waves, see Fig. 5.For M = 1, the reflected waves were intensively confined around the boresight direction and when M = 2 a square shape beam of constant amplitude is achieved.When M = 3 and 4 the reflected waves have been severely diffused with a clear RCS reduction.The simulated RCS reduction curves from 10 GHz to 28 GHz under normal incidence of CP plane wave are shown in Fig. 6 and shows that the four metasurfaces achieved more than 10 dB of RCS reduction.However, based on the results in Fig. 4, Fig. 5, and Fig. 6 one can conclude that the M = 3 cusp metasurface achieved the best RCS reduction performance in terms of scattering patterns shape and RCS reduction amplitude and will be further investigated in the rest of this article.The 3D scattering patterns of the  M = 3 cusp metasurface under normal incidence are shown in Fig. 7 at various frequencies and it can be seen that a low-amplitude diffused scattering is dominant for all frequencies from 11 GHz to 26 GHz.In a real-world radar application, the angle of the incoming radar waves and polarization is unknown.The RCS reduction of the M = 3 metasurface was analyzed using CST Microwave Studio under the illumination of both CP and linearly polarized (LP) plane waves, as illustrated in Fig. 8.The M = 3 metasurface exhibited a substantial RCS reduction, consistently exceeding 10 dB across the frequency range from 10 to 26 GHz for both CP and LP incident waves.The findings presented in Fig. 8   and uniform diffused scattering patterns under wide angular incidence of CP plane wave up to 75 o from 11 GHz to 26 GHz.Here, it is worth mentioning that the excellent RCSR bandwidth of the presented cusp metasurfaces under normal and oblique incidence is a consequence of using both a geometric phase unit cell with wideband reflection characteristics and the nature cusp phase mask.In other words, the phase mask plays a vital role (in addition to the PB meta-atom) in achieving excellent RCSR characteristics.

IV. FABRICATION AND MEASUREMENTS
For a further validation of the proposed design, the M = 3 cusp metasurface was fabricated using PCB technology as displayed in Fig. 10(a).The reflection measurement setup shown in Fig. 10(b) which consists of two identical horn antennas connected to a vector network analyzer via flexible coaxial cables.The fabricated M = 3 cusp metasurface was placed on a plastic holder in front of the horn antennas.The distance between the horn antennas and the metasurface under test was chosen carefully according to the farfield formula to avoid the near-field effects.The T x horn transmitted the wave and the R x horn antenna collected the reflected waves.The reflection from a bare copper plate was measured as well for calibration and normalization purposes.The measured and simulated RCS reduction curves from 11 GHz to 26 GHz are shown in Fig. 10(c).Significant RCS reduction from 10.9 GHz to 26 GHz was achieved with more than 10 dB of RCS reduction.The simulated and measured results have good agreement.However, some discrepancies can be seen at some frequencies, which are attributed to the misalignment of the horn antennas and the metasurface under test, uncertainty of the dielectric constant at this frequency band as it was given at 10 GHz by the manufacturer, and the fabrication tolerance of the metasurface.

V. COMPARISON AND RESULTS DISCUSSION
The proposed M = 3 cusp phased metasurface was compared with various RCS reduction designs in the literature.The [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [47] [48] [46] results of the comparison are listed in Table 1.As can be seen, compared to well-known design approaches in the literature such as chessboard, coding, phase-gradient, Alvarez phased, modulated metasurface, hybrid phase, and parabolic phased metasurfaces.The proposed cusp phased metasurface shows a far better RCS reduction performance.Particularly, a wider RCS reduction fractional bandwidth (FBW) of 81.8% which is wider than the FBW of metasurfaces designed with other techniques.In addition, the M = 3 cusp phased metasurface has a wide angular stability under offnormal incidence and maintained excellent RCS reduction performance up to 75 o incidence angles.Furthermore, using the geometric phase theory in the design of the M = 3 cusp phased metasurface will minimize its sensitivity to the polarization of the incoming radar waves and this is very important in real-world application when the polarization of the incident radar wave is unknown.The M = 3 cusp metasurface has the similar RCS reduction performance when illuminated by RHCP and LHCP plane waves.Thus, the proposed approach is simple to implement, and very powerful for achieving low-level backscattering and RCS reduction over the desired frequency band.Furthermore, it can be seen in the literature that some chessboard (sometimes also called checkerboard) or random coding metasurface designs in the literature may show a wider RCS reduction bandwidth, however, such designs failed to maintain the same RCS reduction bandwidth under both normal and oblique incidences, for example see [24] and [35].On the other hand, with the presented design the wideband RCS reduction bandwidth has been maintained for both normal and oblique incidence.
Metasurfaces have become a transformative technology in the microwave and optical communities due to their ability to manipulate light in ways that were previously unattainable.The design approach in this article is very effective in EM wave diffusion at the presented frequency band (10.9 -26 GHz), and it can be extended to other frequency bands such as THz range and optical frequencies.Both the choice of materials and fabrication techniques are crucial and plays a pivotal role in determining the performance of metasurfaces at optical properties.Different materials exhibit different responses to light at various wavelengths, and the selection of materials can significantly impact the metasurfaces functionality, efficiency, and bandwidth.At THz or optical frequencies, the metasurfaces typically consist of subwavelength nanostructures, and their precise fabrication demands advanced nanofabrication techniques other than using the low-cost PCB technology.The importance of the presented cusp phase mask is equation ( 1), the formula used for the cusp phase calculations, which is not a function of frequency.In other words, the cusp phase mask is not free space wavelength (λ) dependent, and the cusp phase formula can be used to design a metasurface diffuser at any frequency band such as THz band or higher.Furthermore, to redesign the presented metasurface at, for instance THz or optical frequencies, the unit cell periodicity should be altered and optimized to be less than λ/2 at the center of the frequency band of interest.When designing for a higher frequency, one should keep in mind that a dielectric substrate with low loss should be selected.Thus, the presented design approach is of great importance, and it is valid not only at the presented frequency band but at other frequency bands as well.It is important here to mention that EM wave diffusion plays a crucial role in understanding how light propagates through various media.The phenomenon of diffusion helps explain how light scatters and spreads as it interacts with these materials, impacting the design and performance of optical devices.

VI. CONCLUSION
In summary, in this article the design of cusp phased metasurfaces for efficient wideband RCS reduction under wide angular incidence angle is presented.The cusp phased metasurface with modulation index M = 3 achieved more than 10 dB of RCS reduction from 10.9 GHz to 26 GHz with a diffused scattering like RCS patterns which is confirmed by both simulation and measurements.The FBW of the proposed design is 81.8% which is wider than other designs in the literature.In addition, when the incident wave is off-normal to the M = 3 cusp metasurface, an excellent and stable angular RCS reduction performance is maintained when the incidence angle increased from 0 o to 75 o .Furthermore, the proposed M = 3 cusp metasurface is insensitive to the polarization of the incident wave as a result of the geometric phase theory used in the design process.The proposed design approach is efficient and uncomplicated, and it has great potential in future stealth applications.

FIGURE 1 .
FIGURE 1.(a) Illustration (front, side, and 3D views) of the anisotropic unit cell.(b) Simulated amplitudes of the co-and cross-polarized reflection coefficients of the unit cell when illuminated by a CP plane-wave.(c) The relation between the φco-pol and the rotation angle (ψ).

FIGURE 4 .
FIGURE 4. Simulated 3D far-field RCS scattering patterns of the four cusp metasurfaces with M = 1,2,3, and 4 and an equal-sized PEC plate.All cusp metasurface were normally illuminated by a CP plane-wave.

FIGURE 6 .
FIGURE 6. Simulated RCS reduction versus frequency curves of the cusp phased metasurfaces for various M values under normal CP plane-wave illumination.

FIGURE 7 .
FIGURE 7. Simulated 3D far-field RCS scattering patterns of the M = 3 cusp metasurface when normally illuminated by a CP plane-wave at various frequencies.

FIGURE 8 .
FIGURE 8. Simulated RCS reduction versus frequency curves of the M=3 cusp metasurface under normal CP and LP plane-wave illumination.
unequivocally validate the polarization insensitivity of the M = 3 metasurface.The RCS reduction performance of the M = 3 cusp metasurface under off-normal (oblique) incidence was further investigated.The angle of incidence (θ inc ) is the angle of the incoming radar waves with respect to z-axis.The simulated scattering patterns of the M = 3 cusp metasurface at various frequencies are shown in Fig. 9 for θ inc = 15 o , 45 o , and 75 o .As can be seen, the M = 3 cusp metasurface maintained an excellent RCS reduction

FIGURE 9 .
FIGURE 9. Simulated RCS scattering patterns of the M = 3 cusp metasurface when illuminated by a CP plane-wave at various frequencies and angles of incidence.

FIGURE 10 .
FIGURE 10.(a) Photograph of the fabricated M = 3 cusp metasurface with zoomed view.(b) RCS measurement setup.(c) Measured and simulated RCS reduction curves.