Ultra-wideband and large-range incident angles radar cross-section reduction by quasi-fractal polarisation conversion metasurfaces

This study proposes a quasi-fractal polarisation conversion metasur- face (PCM) for ultra-wideband radar cross-section reduction (RCSR). The simple and proposed metasurface is composed of double-heads arrowed-like unit cell beneﬁted from the second iteration Koch fractal in its arm and cut-line to broaden the bandwidth. Consequently, this PCM unit cell and its 90, 180 and 270 degrees rotated counterparts obtain destructive interference cancellation between their reﬂected waves and RCSR. The proposed metasurface demonstrates 10-dB RCSR from 7.68 to 40.87 GHz (136.73%) for normal incident waves, and more than 96.7% up to 40 degrees incident angle that veriﬁes the large range incident angle RCSR of the surface. The experimental measurement results at the normal incident angle and their comparison with simulation ones prove the idea.

Introduction: During recent decades, microstrip structures ranging from radio frequency (RF) and microwave circuits to radiation and scattering structures have come into vogue [1][2][3][4]. Nowadays, 2D surfaces composed of sub-wavelength periodic unit cells have engaged many researchers. Such 2D periodic unit cells that are called metasurfaces have some features that we may rarely find or cannot find in nature. Due to rapid developments of the radar technology, hiding from eagle eyes of radars have been considered more than before [5,6]. Although the geometrical-shaping method of the vehicles can be considered as a solution to minimise radar cross-section (RCS) by redirecting scattered waves, it imposes some constraints on the vehicle shape that is undesirable, especially in the case of flying objects in which aerodynamics property is very critical. Recently, metasurfaces have been proposed for RCS reduction (RCSR) as an effective solution. These metasurfaces can be categorised into two groups: Phase cancellation mechanism by using two different artificial magnetic conductors unit cells with 180 ± 37 degrees reflection phase differences [7][8][9][10][11], and polarisation conversion mechanism by using rotated counterparts polarisation conversion metasurfaces [12,13].
In this study, a new quasi-fractal metasurface is proposed to improve the bandwidth and their oblique incident response of polarisation conversion metasurfaces (PCMs) surface and RCSR consequently for hiding from eagle eyes of radars. The RCSR bandwidth of the proposed metasurface that is implemented on a very thin, low cost, and commercially available FR-4 substrate is higher than the early published studies such as [12,13]. In addition, 10-dB RCSR bandwidth of the surface for 40 degrees oblique incident is significantly better than the state-of-the-art studies such as [9]. The 10-dB RCSR bandwidth of the proposed PCM is from 7.68 to 40.87 GHz (136.73%) for normal incident waves and more than 96.7% and 78% for transverse electric (TE)-and transverse magnetic (TM)-polarisations, respectively, up to 40 degrees incident angle, which proves the large incident angle RCSR of the surface. Such good specifications of the proposed metasurface is a good solution and make it a candidate for RCSR in practical applications.
PCM unit cell design: The proposed unit cell consists of two stacked layers: Upper layer material that is commercially low-cost available FR-4 (ε r = 4.4, tan δ = 0.02), and lower layer material that is sandwiched between FR-4 and ground air gap as shown in Figure 1(a). The unit cell looks like as diagonal double arrows where the arrow arms and connecting line are replaced with the second iteration of Koch fractals. Using

Fig 1 (a) Top and side view of the double-heads arrow quasi-fractal polarisation conversion metasurface (PCM) unit cell
Koch fractal and circles increase the effective electrical lengths in the PCM unit cell and excite more Plasmon resonance frequencies that improve the bandwidth polarisation conversion of the unit cell accordingly.
The optimum values of the proposed unit cells are h = 2.25 mm, h 1 = 0.25 mm, W 1 = 0.41 mm, W 2 = 0.14 mm, L 1 = 2.14 mm, L 2 = 1.7 mm, and R = 0.744 mm, which are achieved by tuning that is performed with full-wave simulation software, CST Microwave Studio. The polarisation conversion concept of this unit cell is a direct consequence of anisotropy [14]. According to [13,14] and with respect to Figure 2(a), when the y-polarised incident electrical wave impinges the structure, it can be decomposed into two components along u and v axis, E u and E v . The E u component reflects out-phase, while E v is reflected in-phase from the surface. Therefore, the resulting reflected wave, E r, has 90 degrees polarisation conversion with respect to the incident waves. Engineering this process and using symmetry, one can rearrange a group of similar cells with 0, 90, 180 and 270 degrees rotations. Therefore, the backscattered waves destruct themselves and minimise the reflected energy and achieve RCSR accordingly.
The polarisation conversion efficiency of the presented unit cell can be expressed by polarisation conversion ratio (PCR) for x-to y-and yto x-polarisation as [12][13][14]: where R xx = |E xr /E xi | and R yx = |E yr /E xi | demonstrate the co-and crosspolarisations reflection ratio for x-polarised incidence wave, respectively. In a similar manner, R yy = |E yr /E yi | and R xy = |E xr /E yi | are coand cross-polarisations reflection ratio for y-polarised incident wave. Figure 3 demonstrates the co-and cross-polarisations ratio of the proposed unit cells versus frequency. As it is observed, this unit cell converts the incident x-or y-polarised wave into y-or x-polarised one, respectively, in wide bandwidth. It is worth mentioning that within the 3 dB bandwidth the polarisation conversion efficiency is more than 50% and the ultra-wideband behaviour of the structure is a direct consequence of the six resonance (Plasmon) frequencies at 7.81, 11.37, 19.5, 29.73, The proposed unit cell surface current distributions are depicted in Figure 4 for various angles of rotation (0, 90, 180 and 270 degrees) at f = 19.5 GHz, which has good PCM efficiency. As expected from previous discussions, the surface current on 0 and 180 degrees rotated cells have an opposite current component along the x-axis, while they have an in-phase current component along y-axis. Therefore, it can be concluded that one part of the reflected waves (along x) cancel out each other, while the other one (along y) are added in-phase. A similar argument can be explained for 90 and 270 degrees rotated cells. Therefore, this unit cell with its mirrors can be used for PCM RCSR in the arrangement as shown in Figure 2(b).

Design, simulation and experimental results:
The proposed quasifractal PCM surface is fabricated as shown in Figure 6. This surface consists of the proposed quasi-fractal PCM with three 90, 180, 270 degrees rotated ones arranged in 3 × 3 tiles array. The monostatic RCSR of the proposed surface for the different incident angle is shown in Figure 5 at both TE-and TM-incident polarisations, which prove more than 96.7% and 78% 10-dB RCSR bandwidth for TE-and TMpolarisations, respectively, up to 40 degrees incident angle.
The simulation results depict more than 10-dB RCSR from 7.68 to 40.87 GHz (136.73%) for the normal incident and something about (90.7%) for 40 degrees oblique incident.
The simulation results are verified for the normal incident by a simple experimental set-up for RCS measurement, and both of them have been shown for better comparison in Figure 7. The best performance of the proposed PCM is obtained at 33 GHz with more than 40 dB RCSR.
It should be noted that due to the limitation of measuring instruments, we can only measure the RCSR of the PCM from 7 to 33 GHz. As it can be observed, there is a good correspondence between simulation and measurements that proves the idea. Notice that some difference between  simulation and measurement results are due to using low-cost commercial available FR-4 substrates that do not have precise specifications, especially at high frequencies.
The proposed metasurface performance is compared with the stateof-the-art references in Table 1. It can be observed that the RCSR bandwidth of this structure is significantly better than those introduced in other studies. It should be mentioned that the proposed metasurface is implemented on low-cost commercially available FR-4 substrate, while the other references are implemented on expensive ones as tabulated in the table excluding [11] that has significantly lower RCSR bandwidth than our study.

Conclusion:
A quasi-fractal PCM metasurface was designed based on polarisation conversion concept to achieve ultra-wideband RCSR. The simple and low-cost proposed metasurface is composed of double-heads arrowed-like unit cell that benefited from the second iteration Koch frac-tal in its arm and cut-line in order to broaden the bandwidth. The unitcell and its 90, 180 and 270 degrees rotated counterparts obtain destructive interference cancellation between their reflected waves. The designed metasurface depicts a good performance in RCSR larger than 10-dB from 7.68 to 40.87 GHz, 136.73% fractional bandwidth.

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