Unit cell configuration

The designed unit cell consists of three layers, the top layer is metallic biconic shape imprinted onto a dielectric substrate which is middle layer and its bottom layer is metallic ground. All the metallic layers (top and bottom) are modeled as copper having electrical conductivity $\sigma=5.8\times10^7$ S/m and each having a 0.035 mm thickness. The F4BM dielectric substrate $\epsilon_r = 2.2$, tanδ = 0.001 separates both metallic layers from each other. The designed unit cell was simulated, and its performance was evaluated using a frequency domain solver in CST Microwave Studio 2020. The periodic boundary condition was applied along the x- and y-directions to make an infinite periodic array and the open boundary condition was applied in z-direction. Figure 1 illustrates the designed unit cell geometry, with the following parameters: p = 5.6 mm, h_s = 3 mm, w = 1.45 mm, and l = 3.16 mm.

Figure 1. Configuration of the biconic shape PCMS.

Simulation results and discussions

Using the finite element approach, the proposed design was simulated to assess its polarization conversion performance. Due to the asymmetry of the proposed PCMS, when an EM wave with a particular polarization state imposes on it, the reflected EM wave contains co- and cross-polarized components. In terms of reflection coefficients, co-polarized reflection amplitude is r_yy= ${|E_{yr}|}/{|E_{yi}|}$, and the cross-polarization reflection amplitude is r_xy= ${|E_{xr}|}/{|E_{yi}|}$, the subscript i stands for incident, and r for reflected EM wave, whereas the subscripts x and y show the axis in which the E-field is polarized.

The incident y-polarized wave is split into u- and v-components as indicated in Figure 2, to better comprehend the cross-polarization conversion mechanism. The incident E-field is described by [Reference Kamal, Chen and Yin31]:

Figure 2. The designed PCMS u-v decomposition.

(1)\begin{equation} \overrightarrow{E_i} = {u\overrightarrow{E}_{iu}} +{v\overrightarrow{E}_{iv}}. \end{equation}

The reflected E-field can be defined by [Reference Kamal, Chen and Yin31]:

(2)\begin{equation} \overrightarrow{E_r} = {u\stackrel{\sim}{r_u}} {\overrightarrow{E}_{iu}} + v{\stackrel{\sim}{r_v}}{\overrightarrow{E}_{iv}}. \end{equation}

The reflection amplitudes along the u-axis are represented by the symbol ${\stackrel{\sim}{r_u}}$, while those along the v-axis are represented by the symbol ${\stackrel{\sim}{r_v}}$, respectively. As the proposed PCMS is an anisotropic nature, which produce a $\bigtriangleup\varphi$ between ${\stackrel{\sim}{r_u}}$ and ${\stackrel{\sim}{r_v}}$. If ${r_u}$ ${\approx}$ ${r_v}$ ${\approx}$ 1 and $\bigtriangleup\varphi$ approaches ${180}{^\circ}$, then the surface will change polarization of LP incident EM wave (i.e., x-polarized to y-polarized and vice versa). Figure 3(a) and (b) illustrates reflection amplitude, phases, and the $\bigtriangleup\varphi$ between u- and v-polarized waves, which shows that a linear polarization conversion is achieved because the amplitudes are so close to one another (i.e., ${r_u}$ ${\approx}$ ${r_v}$) and the $\bigtriangleup\varphi \approx 180{^\circ}$. There is no doubt about the metasurface capacity to transform polarization over a wide frequency band of 16.1 GHz. The polarization transformation efficiency of the PCMS is determined from PCR, which is described as [Reference Kamal, Chen and Yin31]:

(3)\begin{equation} \mathrm{PCR} =\frac{|r^2_{yx}|}{|r^2_{yx}|+|r^2_{xx}|}=\frac{|r^2_{xy}|}{|r^2_{xy}|+|r^2_{yy}|}. \end{equation}

If PCR = 1, it means that an LP EM wave is fully converted into its orthogonal equivalent. For y-polarized EM wave, the reflection amplitudes are depicted in Figure 4(a), which shows that it is less than −10 dB from 8.7 to 24.8 GHz with an FBW of $96\%$. The reflected coefficients at x-polarized incidence is shown in Figure 5(a). For the proposed PCMS, the cross- and co-polarization reflection coefficients at x- and y-polarized incidences, i.e., ${r_{yy}}$ = ${r_{xx}}$ and ${r_{xy}}$ = ${r_{yx}}$ are equal. The response of the MS is same for both x- and y-polarized EM waves due to the symmetric structure of the unit cell in the xy plane.

Figure 3. Simulated u- and v-polarized waves: (a) reflection amplitude and (b) phase difference.

Figure 4. Simulated results of (a) Reflection amplitude for y-polarized wave and (b) PCR.

Figure 5. Simulated results of (a) Reflection amplitude for x-polarized wave and (b) PCR.

Furthermore, both the y- and x-polarized reflection coefficients show the existence of three resonance frequencies at 9.6, 16.4, and 23.1 GHz. Figure 4(b) and 5(b) display the PCR of the proposed PCMS for y- and x-polarized EM wave, which indicates that in the operating band of 8.7–24.8 GHz, the proposed PCMS has a PCR of greater than $90\%$. Moreover, the PCR is $100\%$ at 9.6, 16.4, and 23.1 GHz.

There are numerous applications that need the stability of the PCMS performance when the EM wave hits it from varied angles. To test the angular stability of the design PCMS, numerical simulations are done for oblique incidence with theta ranging from 0^∘ to 60^∘. The simulated reflection coefficients and PCR for oblique incident angles are shown in Figure 6. The proposed MS retains more than $85\%$ PCR from 8.7 to 24.8 GHz up to a 30^∘ incidence angle as shown in Figure 6(b). Furthermore, the PCR and bandwidth of the proposed MS decrease, with increasing incidence angle beyond 30^∘. The proposed MSs have $100\%$ PCR for all the incident angles from 9.5 to 10 GHz.

Figure 6. Angle sensitivity of the proposed PCMS: (a) reflection coefficients and (b) PCR with varied angles from 0^∘ up to 60^∘.

To comprehend the proposed biconic shape polarization converter’s physical mechanism, the surface current analysis has been done at resonance frequencies of 9.6, 16.4, and 23.1 GHz as illustrated in Figure 7. Surface currents are seen to be generated at the upper and lower layer of the MS due to the propagation of EM wave [Reference Kamal, Khan, Chen and Yin32]. It is clearly seen that at 9.6 and 16.4 GHz, the direction currents are anti-parallel on the metallic patch and ground of the PCMS as shown in Figure 7(a) and (b), which produces significant magnetic resonance by producing a circulating field around the incident H-field. This phenomenon increases magnetic permeability, causing the effective surface impedance of the MS to increase and exceed then free space impedance. So, at resonance frequencies of 9.6 and 16.4 GHz, the impedance of the surface increases. Figure 7(c) illustrates that the current directions in the two metallic layers of the PCMS are the same (parallel) at 23.1 GHz, resulting in electric dipole resonance. Therefore, at this resonance frequency, the surface behaves as a PEC, resulting in cross-polarization conversion. Three plasmon resonances are excited by the aforementioned electrical and magnetic resonances, and they provide the basis for the metasurface’s operational principle. The presence of electric and magnetic resonances provides a wide bandwidth as well as a high PCR of the MS. The equivalent circuit of the proposed biconic shape PCMS has been modeled using a transmission line model. The unit cell is represented by three series RLC resonant circuit connected in parallel corresponding to three neighboring superimposed resonant peaks in the polarization conversion band [Reference Yao, Jianbo, Lihua, Shuyun, Yuzhou, Jie and Yicheng33] as shown in Figure 8(a). The metallic resonator is represented by series inductors (L1, L2, and L3) and resistors (R1, R2, and R3). Meanwhile, the dielectric substrate is represented by capacitors (C1, C2, and C3) and resistors (R4, and R5), and the ground metal plate is represented by a short-circuited transmission line [Reference Priyanka, Surya and Siju34]. The values of inductors and capacitors are calculated by using the following formulas:

(4)\begin{equation} L=\frac{\mu_o \mu_r LW}{hc} \end{equation}

(5)\begin{equation} C=\frac{\epsilon_o \epsilon_r LW}{hs} \end{equation}

where L and W are length and width of metal are taken with the help of surface currents mentioned in Figure 7(a–c), respectively, while hs and hc are thickness of dielectric substrate and metallic conductor, and µ_r is relative permeability of surrounding material, and ϵ_r is relative permittivity of dielectric material. The calculated and extracted parameters values from ADS are as follows: $R1$ =0.9 Ω, $R2$ = 0.5 Ω, $R3$ = 0.9 Ω, $R4$ = 25 Ω, $R5$ = 25 Ω, $L1$ = 1.25 nH, $L2$ = 1 nH, $L3$ = 1.3 nH, $C1$ = 0.2 pF, $C2$ = 0.099 pF, $C3$ = 0.032 pF. The reflection coefficient obtained by ADS and CST are compared and shown in Figure 8(b) which validates the equivalent circuit model.

Figure 7. Distribution of surface current on the top and bottom layer of PCMS: (a) 9.6, (b) 16.4, and (c) 23.1 (all in GHz).

Figure 8. Depiction of (a) Equivalent circuit model and (b) comparison between the numerical simulation (CST) and circuit simulation (ADS).

Simulation steps and variation in geometric parameters

The first step to design a PCMS is to choose the dimensions of the MS to achieve the resonances at desired frequency band [Reference Abbasi, Abbas, Alomainy and Imran35]. The following equation can be used to compute an approximate estimate of the resonances

(6)\begin{equation} C=n\lambda_\mathrm{eff}=\frac{nc}{f\sqrt{\epsilon_\mathrm{reff}}} \end{equation}

where C is the circumference of the circle or the largest dimension of the patch and ${\epsilon_\mathrm{reff}}$ is the effective permittivity [Reference Abbasi, Abbas, Alomainy and Imran35]. $\lambda_\mathrm{eff}$ is the effective wavelength, c is the wave velocity in vacuum, and f is the resonance frequency. To achieve magnetic resonance, n should be considered unity. On the other hand, the electric resonances are achieved for n = 2 [Reference Abbasi, Abbas, Alomainy and Imran35]. Four major steps are taken to create the proposed biconic shape design as shown in Figure 9. In step 1, depicted in Figure 9(a), a rotated rectangular patch is simulated with geometric parameters of p = 5.6 mm, h_s = 3 mm, w = 1.45 mm, and l = 5.60 mm, which shows that polarization conversion occur from 10 to 16 GHz and at 28 GHz. In step 2, the length of the rotated rectangular patch is increased in upward and downward direction equally such that the l becomes 6.32 mm, as shown in Figure 9(b). Dual-band polarization conversion occur from 8 to 18 GHz and 28 to 29 GHz. In step 3, some of the rotated rectangular patch parts are removed to create a shape resembling a sand clock, in this sand clock the smaller edge l near the center is 1.07 and the other length is 2.60 as shown in Figure 9(c), polarization conversion occurs from 9 to 19 GHz and at 25 GHz. In step 4, the sand clock shape is optimized to form a biconic shape with geometric parameters p = 5.6 mm, h_s = 3 mm, w = 1.45 mm, and l = 3.16 mm as shown in Figure 9(d), which result in three plasmon resonances, leading to more efficient polarization conversion through an ultra wideband range of 8.7–24.8 GHz. The surface is correlated at three plasmon resonances by these well-designed steps, resulting in a high efficient and wideband PCMS. For a better understanding of how the various geometric parameters (p, h_s, w, and l) of the design unit cell affect its polarization conversion performance. Parametric analysis is performed by changing only one parameter of the design unit cell whereas the other parameters remain constant under normal incidence condition. The PCR and FBW of the design PCMS by changing various parameters are shown in Figure 10. It demonstrates that changing the unit cell parameters has a direct impact on PCR performance and bandwidth. Figure 10(a) indicates that reducing the length and width of the substrate (p) from 6.0 to 4.8 mm reduces PCR while increasing its FBW, and shifting performance toward higher frequencies because of the inverse relation between size and frequency. The parameter (h_s) represents substrate thickness, and it has also influenced the PCR and FBW of the design unit cell. The performance of the designed unit cell is evaluated for four different thicknesses of the F4BM substrate, i.e., h_s = 3.0, 2.5, 2.0, and 1.5 mm, respectively. Figure 10(b) indicates that changing the thickness of the substrate (h_s) from 3.0 to 1.5 mm results in decreases of PCR and FBW, and the frequency band is shifting to higher frequencies. According to Figure 10(c), the width (w) of the biconic shape resonator is reduced from 1.4 to 0.5 mm, which indicates that by reducing the width, the PCR increases while the FBW decreases. In Figure 10(d) by decreasing the length (l) of the resonator from 3.06 to 1.56 mm, it is observed that by decreasing the l, the PCR is decreasing on lower frequencies, its efficiency decreases and shifts the performance band to higher frequencies. So by changing any one of the parameter either PCR will increase or decrease, FBW will be decreased or increased and the band will be shifted toward higher or lower frequencies. The pink curves in Figure 10 indicate the final design unit cell performance.

Figure 9. The evaluation steps and simulation results of the proposed PCMS.

Figure 10. Parametric analysis of the proposed unit cell with respect to various parameters: (a) length and width of substrate (p), (b) thickness of substrate (h_s), (c) width of patch (w), and (d) length of patch (l).

RCS reduction with PCMS

RCS is the measure of a target’s ability to reflect radar signals in the direction of the radar receiver. RCS is an important physical parameter to quantify the EM scattering ability of the targets. The RCS of the surface can be expressed as [Reference Fu, Han and Liu36]:

(7)\begin{equation} \sigma _{c} =4\pi \lim _{r\to \infty } r^{2}\frac {\left |{{\overrightarrow E_{rx}} }\right |^{2}}{\left |{{\overrightarrow E_{ix}} }\right |^{2}}. \end{equation}

The RCS reduction from the surface relative to the PEC can be expressed as [Reference Fu, Han and Liu36]:

(8)\begin{equation} RCS\,reduction\,(dB)= 10\log _{10} \left [{{\frac {\lim _{r\to \infty } 4\pi r^{2}\frac {\left |{{\overrightarrow E_{rx}} }\right |^{2}}{\left |{{\overrightarrow E_{ix}} }\right |^{2}}}{\lim _{r\to \infty } 4\pi r^{2}\left |{1 }\right |^{2}}} }\right] \end{equation}

where σ_c denotes the RCS, $\left| E_{rx}\right|$ and $\left| E_{ix}\right|$ are the reflected and incident fields in the far zone of ${r\to \infty}$, respectively, and r is the detecting distance. As previously mentioned, a single-layer biconic shape PCMS is designed. The proposed PCMS is organized in chessboard orientations in this section to better understand its RCS reduction capability. A unit cell and its rotated version are required for the RCS reduction using polarization converting technique. The reflection coefficient of the mirror unit cell is depicted in Figure 11(a). The designed unit cell and its mirror unit cell have a cross-polarization $\bigtriangleup\varphi$ of ${180}{^\circ}$, which are necessary for RCS reduction as illustrated in Figure 11(b). The designed chessboard array simulation is performed in time domain using CST Microwave Studio (2020). A 30 × 30 square chessboard array with a total dimension of 168 mm × 168 mm was designed based on the abovementioned unit cells. The chessboard array consists of four sub-arrays, each sub-array contains 15 × 15 unit cells. Two sub-arrays (1) contain the designed unit cell and the two sub-arrays (0) contain mirror unit cell as displayed in Figure 12. When a plane wave with y-polarized strikes the surface of the proposed square chessboard array, in which the unit cell reflects in-phase waves while its mirror reflects out phase waves, resulting in destructive interference (wave cancellation) and a reduction in RCS occur. Figure 13 presents the monostatic RCS of the proposed array compared to a PEC of the same size. According to the simulation results, the proposed chessboard array reduces more than 10 dB monostatic RCS throughout a large frequency range between 7.9 and 23.4 GHz with an FBW of $99\%$. The highest monostatic RCS reduction of the square chessboard array is −14 dB which is achieved at 9.6 GHz.

Figure 11. Simulated results: (a) reflection amplitude of mirror version and (b) cross-polarization reflections $\bigtriangleup\varphi$ between the proposed unit cell and its mirror version.

Figure 12. The proposed square chessboard array made up of unit cell and its mirror unit cell.

Figure 13. Simulated RCS: (a) monostatic RCS with respect to equal size PEC and (b) normalized monostatic RCS reduction.

The simulated results of the 2D bistatic RCS for the proposed $30 \times 30$ square chessboard array under the normal incident at 9.6, 16.4, 23.1, and central frequency 15.6 GHz are depicted in Figure 14, which shows that the strength of the main lobes is decreased. At frequencies 9.6, 16.4, and 23.1 GHz, the proposed chessboard array’s RCS reduction is about 28, 22, and 25 dB for normal incidence, less than the PEC maximum RCS respectively. The reduction in bistatic RCS is due to reflected EM waves (in-phase and out-phase wave) scattering into four directions rather than a single lobe reflection. The three-dimensional scattered radiation patterns of the bistatic RCS reduction of the proposed chessboard array and PEC of the same sized are depicted in Figure 15. In case of PEC, the incident wave reflect back in a single lobe in the source direction but in case of the proposed square chessboard array the incident wave is scattered into four sub-lobes at different directions due to destructive interference caused by the unit cell and its rotated version. Figure 15 indicates that the proposed chessboard array has minimum reflection at the source direction as compared to PEC.

Figure 14. PEC and designed PCMS 2D scattering patterns at resonance frequencies: (a) 9.6, (b) 16.4, (c) 23.1, and (d) central frequency 15.6 (all in GHz).

Figure 15. Simulated 3D scattering performance at 9.6 GHz, 16.4 GHz, and 23.1 GHz of (a) PEC and (b) the proposed chessboard array.

Fabrication and experimental results

The proposed $30 \times 30$ square chessboard array is fabricated in order to experimentally check the results of the simulation under the normal incidence. Figure 16(a) shows the fabricated prototype of the proposed square chessboard array. To test the proposed prototype, two horn antennas operating in 5–30 GHz band are positioned in the far field, 2 m from the surface. The two horns are connected to the KEYSIGHT N5224A vector network analyzer surrounded by absorbers, the wave is transmitted using one horn and received using the other as illustrated in Figure 16(b). Furthermore, the fabricated sample and the two horn antennas are aligned in monostatic RCS measurement. The measured results of the proposed prototype are compared to a similar sized PEC surface performances. Figure 17 displays a comparison of the measured results of the square chessboard array and simulation results. The developed metasurface measured and simulation results show good correlation over a wide frequency range, which validate that the developed PCMS attain wideband with effective RCS reduction. The performance comparison of our work with previously published works with respect to PCR and RCS bandwidth, size, thickness, and relative bandwidth is presented in Table 1. The PCR and RCS reduction bandwidth, relative bandwidth, of the proposed PCMS is greater than that of the comparable works. Also the proposed PCMS has a small size than all the referenced work, and small thickness except [Reference Zheng, Guo and Li28, Reference Jia, Liu and Guo41]. The proposed PCMS achieved wideband with a single resonator and in the all other references the wideband is achieved by using two or more resonators. In [Reference Mu, Lv and Ni10], double split-ring patches were used, in [Reference Tiwari, Pathak and Vp12] Γ-shape is used, in [Reference Zheng, Guo and Li28] two oblique asymmetry triangle split rings are used, in [Reference Lu, Cao and Gao37] an I-shaped ring symmetrical structure is used, in [Reference Zhang, Cao and Gao38] combination of a ring and a cross resonator are used, in [Reference Shu, Zhang and He39] split-ring unit cell is used, in [Reference Zheng, Li and Zhang40] N-shaped metallic pattern is used, in [Reference Jia, Liu and Guo41] periodic array of square patches, patch connected with ground through vias are used. These structures were developed using more metallic layers or a more complex pattern. The developed PCMS is constructed on a low cost, light-weight, and extremely thin F4BM substrate that makes it easier to use.

Figure 16. Images of (a) fabricated sample and (b) an experimental setup.

Figure 17. Comparison of the simulated and measured monostatic RCS results.

Table 1. Performance comparison of the square chessboard metasurface with previous research