Complementary Multi-Band Dual Polarization Conversion Metasurface and Its RCS Reduction Application

Abstract

In this paper, we present a metasurface composed of complementary units that can realize orthogonal linear and linear-to-circular polarization conversion in multi-band. Linear polarization conversion has seven high-conversion frequency bands: 9.1–9.7 GHz, 15.6–17.6 GHz, 19.4–19.7 GHz, 21.2–23.1 GHz, 23.5–23.8 GHz, 26.2 GHz, and 27.9 GHz. Linear-to-circular polarization conversion also has seven frequency bands with axial ratios (ARs) less than 3 dB: 8.9–9.0 GHz, 9.9–14.7 GHz, 19.1–19.3 GHz, 23.2–23.35 GHz, 23.4 GHz, 24.1–25.4 GHz, and 27.2–27.8 GHz, with the generation of multiple bands extended by the combination of complementary units. Then, we utilize the combined polarization conversion unit’s mirror placement to form a 4 × 4 array to realize the phase difference cancellation of the reflective field, giving the metasurface the radar cross section (RCS) reduction function and the dual-band 10-dB monostatic RCS reduction bandwidth: 8.9–9.7 GHz and 15.5–26.1 GHz. The measured and simulated results were essentially identical. Because the design uses the complementary units to form an array to expand the polarization conversion frequency bands, it provides a novel idea for future designs and can be applied to multiple microwave frequency bands.

1. Introduction

Polarization is an important characteristic of electromagnetic waves that is used to represent the time-varying trajectory of the electric field strength vector terminal of electromagnetic waves in space. In modern communication, controlling the polarized state of electromagnetic waves is critical in the transmission and reception of wireless signals, and it has also become a frontier direction of discipline exploration. Metasurfaces, as a special non-natural material, have been applied to the precise control of electromagnetic wave polarization with its easy fabrication, good conversion characteristic, small size, and powerful functionality to manipulate the beams, which can effectively avoid the defects of traditional design methods [1,2,3,4,5,6,7]. In recent years, various polarization conversion metasurfaces (PCMs) have been proposed to realize different polarization conversions, including incident and reflective orthogonal linear polarization (LP-LP) [8,9,10,11], circular-to-circular polarization (CP-CP) [12,13,14,15], and linear-to-circular polarization (LP-CP) [16,17,18,19]. However, most of these metasurfaces realize a single polarization conversion function, and there are relatively few metasurfaces with multiple polarization conversion functions. Therefore, it is urgent to study the multifunctional PCM for different frequency bands. For this demand, the literature [20] proposed various functions of polarization converters, with the linear polarization conversion bandwidth reaching 95.2%. Gao et al. designed a voltage-controlled reconfigurable broadband PCM for LP-LP and LP-CP conversions [21]. In [22], a four-band, multi-function reflective polarization converter based on linear and circular polarizations was proposed.

The development of metasurfaces has also promoted the improvement of RCS reduction technology. The key to RCS reduction is to suppress reflected waves. Metasurfaces such as the frequency-selective surface [23,24,25], frequency-absorbing surface [26,27], electromagnetic band-gap structure [28,29], and artificial magnetic conductor [30,31] can adjust different electromagnetic parameters to realize the absorption, diffuse reflection, and abnormal reflection of reflected waves, thus providing new methods for RCS reduction. Specifically, frequency-selective and frequency-absorbing surfaces exhibit total reflection or transmission characteristics around the resonant frequency of the unit, which can be seen as band-pass or band-resistance filters, to control electromagnetic wave propagation in certain frequency bands. The artificial magnetic conductor has different reflection phases at different frequencies, which can be used to achieve phase cancellation. In particular, when mirroring the PCM when a specific polarization wave is incident, the phase difference of the reflected waves by the two mirror-arranged sub-arrays is $\pi$, and the two waves are cancelled to achieve overall reflected wave suppression [32,33].

In this work, a novel, complementary, multifunctional PCM is proposed. The designed complementary surface double units have the function of polarization conversion. By combining the two complementary units, a metasurface that realizes orthogonal linear polarization conversion and linear-to-circular polarization conversion is finally designed. Both linear polarization conversion and linear-to-circular polarization conversion have seven frequency bands. Moreover, a mirror-symmetrical RCS reduction surface is designed using this PCM, which realizes double broadband monostatic RCS reduction and improves the performance of related works.

2. Structural Design and Principle

The designed PCM unit is shown in Figure 1. The overall structure is divided into three layers: the PCM unit on the top layer, the FR4 dielectric substrate ($\epsilon =4.4$, $tan\delta =0.02$) with a thickness of H = 1.2 mm in the middle, and the bottom layer being a perfect electric conductor (PEC). Unit 1 is a diagonal structure formed by orthogonal placement of two rectangular patches with equal arm lengths, and unit 2 is formed by stacking three square patches at a certain distance. The two units are complementary, as shown in Figure 1a. The optimized geometric dimensions are L = 8 mm, C = 0.1 mm, and W = 1.95 mm. Figure 1b,c shows that the complementary metal surface units are placed at an angle of 45 degrees along the X-axis (Y-axis). The two units can be combined into a square patch, and both have polarization conversion functions. Figure 1c explains the principle of polarization conversion from the physical theory of electromagnetic waves. Assuming that the electromagnetic wave is incident along the x polarization direction, and the incident electric field $E_i$ is decomposed into orthogonally polarized waves along the U-axis and V-axis, we can obtain the following:

$$E_i=\stackrel{\rightharpoonup }{x}{E}_i{e}^{j\phi }=\left(\stackrel{\rightharpoonup }{u}{E}_{iu}+\stackrel{\rightharpoonup }{v}{E}_{iv}\right)e^{j\phi }$$

(1)

$$E_r=\stackrel{\rightharpoonup }{u}{E}_{ru}+\stackrel{\rightharpoonup }{v}{E}_{rv}=\left(\stackrel{\rightharpoonup }{u}{r}_u{E}_{iu}{e}^{j{\phi }_u}+\stackrel{\rightharpoonup }{v}{r}_v{E}_{iv}{e}^{j{\phi }_v}\right)e^{j\phi }$$

(2)

where $E_{iu}$ and $E_{iv}$ are the magnitudes of the incident field components on the U-axes and V-axes, respectively, and ${\phi }_u$ and ${\phi }_v$ are the phases of the corresponding components. Because the bottom is an ideal metal floor structure, it exhibits total reflection characteristics under the incidence of electromagnetic waves, so we find $r_u=r_v=r$. However, under the incidence of U- and V-polarized waves, the resonant structures of the unit in the two directions are different, and the reflective waves have a phase difference $\Delta \phi =\left|{\phi }_u-{\phi }_v\right|$. When $\Delta \phi ={180}^{°}$, Equation (2) becomes

$${\mathit{E}}_r=r\left(\stackrel{\rightharpoonup }{u}{E}_{iu}{e}^{j{\phi }_u}+\stackrel{\rightharpoonup }{v}{E}_{iv}{e}^{j\left(\pi -{\phi }_u\right)}\right)e^{j\phi }$$

$$=r\left(\stackrel{\rightharpoonup }{u}{E}_{iu}-\stackrel{\rightharpoonup }{v}{E}_{iv}\right)e^{j{\phi }_u}{e}^{j\phi }$$

$$=\stackrel{\rightharpoonup }{y}{E}_r{e}^{j{\phi }_u}{e}^{j\phi }$$

(3)

Through the above derivation, we complete the transformation from the incident wave with x polarization to the reflective wave with y polarization. Because the PCM is placed symmetrically along the diagonal, the incident conditions of the x polarization and y polarization are exactly the same, and the conversion principle is also suitable for the y-polarized incident wave and the x-polarized reflective wave. Similarly, when $\Delta \phi ={90}^{°}$, the synthesized wave is circularly polarized, and the structure realizes the function of linear-to-circular polarization conversion.

3. Simulation Analysis

To better understand the polarization conversion performance of the designed unit, we used the Floquet port in the simulation software with the master-slave boundary to simulate the infinite array condition. Figure 2a,b illustrates the reflection coefficients of unit 1 and unit 2 when an x-polarized wave is incident. The resonance points of unit 1 were at 17.9 GHz and 20.1 GHz, while the resonance points of unit 2 were at 7.2 GHz, 12.3 GHz, and 19.7 GHz. Their cross-polarized reflection coefficients $R_{yx}$ were 0 dB at these frequency points, and the co-polarized reflection coefficients $R_{xx}$ were very small, indicating that polarization conversion occurred. We characterized the polarization conversion by the polarization conversion ratio (PCR), which is defined as follows [34]:

$${\mathrm{PCR}}_x=\frac{R_{yx}^2}{R_{yx}^2+R_{xx}^2} ;{ \mathrm{PCR}}_y=\frac{R_{xy}^2}{R_{xy}^2+R_{yy}^2}$$

(4)

Under the incidence of x-polarized waves, the PCRs of units 1 and 2 are shown in Figure 2c. At the corresponding resonance frequency, the PCR reached 100%, explaining that the conversion of the x-polarized incident wave to the y-polarized reflective wave was completely realized.

In order to realize the functions of multiple polarization conversion on the metasurface, we also explored the circular polarization conversion function of the units. We used the axial ratio (AR) to describe the circular polarization conversion characteristics. When AR < 3 dB, it can be considered that the electromagnetic wave is a circular polarization wave. The AR is expressed by the following formula [35]:

$$\mathrm{AR}={\left(\frac{{\left|R_{xx}\right|}^2+{\left|R_{yx}\right|}^2+\sqrt{a}}{{\left|R_{xx}\right|}^2+{\left|R_{yx}\right|}^2-\sqrt{a}}\right)}^{\frac{1}{2}}$$

(5)

$$a={\left|R_{xx}\right|}^4+{\left|R_{yx}\right|}^4+2{\left|R_{xx}\right|}^2{\left|R_{yx}\right|}^2\cos \left(2\Delta \phi \right)$$

(6)

The ARs of units 1 and 2 are shown in Figure 2d, and it can be seen that the 3-dB circular polarization bandwidths of unit 1 were dual-band 15.0–15.9 GHz and 23.72–26.11 GHz, and the 3-dB axial ratio bandwidths of unit 2 were 6.55–6.83 GHz, 7.69–10.96 GHz, 13.61–14.92 GHz, 19.08–19.45 GHz, and 19.83–19.98 GHz. Therefore, both units 1 and 2 realized the polarization conversion function of multi-band linear polarization incident to circular polarization reflection.

Observing Figure 2, we found that there were many polarization conversion frequencies for unit 1 and unit 2, but they were not evenly distributed in the entire solution frequency band, and the conversion bandwidths of the two units did not overlap with each other. Therefore, we could synthesize the conversion characteristics of the two complementary units, which may extend the polarization conversion frequency bands. Based on this idea, we finally designed a combined polarization conversion unit, using the same simulation method to analyze it. The designed structure is shown in Figure 3. Unit 1 and unit 2 are crossed to form a symmetrical structure.

The reflection coefficient and PCR of the structure are shown in Figure 3a,b. The figure shows that the combined unit $R_{xx}<-10 \mathrm{dB}$ had seven resonant frequency points, the PCR of the corresponding frequency point was 100%, and it had seven PCR bandwidths >90%: 9.1–9.7 GHz, 15.6–17.6 GHz, 19.4–19.7 GHz, 21.2–23.1 GHz, 23.5–23.8 GHz, 26.2 GHz, and 27.9 GHz. In addition, the phase difference of the co-polarized and cross-polarized reflection coefficients are shown in Figure 3c. The phase difference is defined as $\Delta \phi ={\phi }_{xx}-{\phi }_{yx}$ when $\Delta \phi =0, \pm \pi$. It can be known from the knowledge of the polarization phase that the linear polarization conversion occurred at this time. The phase differences of $R_{yx}$ and $R_{xx}$ at the seven resonance points in the figure all satisfied this condition, suggesting that the complete conversion of x polarization to y polarization was achieved. When comparing the simulation results of the two units, it was found that there was a difference in the offset of the conversion frequency bands, and the new resonance frequency bands were generated. The main reason for this is that after the combined structure, the periodic units changed. The change in the inductance or capacitance generated by the coupling between units 1 and 2 in the overall equivalent circuit resulted in a shift in the resonant frequencies, especially in the relatively high frequency band of 23.5–28 GHz. This change in the equivalent circuit excited two new resonant frequency bands that contributed to the polarization conversion at higher frequencies. As a result, the newly formed unit could expand the frequency and bandwidth of linear polarization conversion.

In addition, the basic conditions of the circular polarization conversion must be satisfied. In the case that the co-polarized reflection coefficient $R_{xx}$ and the cross-polarized reflection coefficient $R_{yx}$ have the same amplitude, the phase difference between them must be satisfied ($\Delta \phi =\pm n\pi /2$, where n is an odd number). It can be seen from Figure 3a that the possible frequency band for circular polarization conversion occurred near the intersection with the $R_{xx}$ and $R_{yx}$ coefficients, where the amplitudes of them were roughly equal, and the linear-to-circular polarization conversion could be completed as long as the phase difference condition was satisfied. From Figure 3d, it can be seen that there were seven bandwidths with ARs less than 3 dB: 8.9–9.0 GHz, 9.9–14.7 GHz, 19.1–19.3 GHz, 23.2–23.35 GHz, 23.4 GHz, 24.1–25.4 GHz, and 27.2–27.8 GHz. Meanwhile, when observing Figure 3c, it is found that at these frequency bands, the phase differences between co-polarization and cross-polarization were around $-{270}^{°}$, $-{90}^{°}$, ${90}^{°}$, and ${270}^{°}$, which satisfies the circular polarization conversion phase. Therefore, the combination unit realized the conversion from the incident linear polarization wave to the reflective circular polarization wave in the above frequency bands.

We also analyzed the conversion under oblique incidence conditions, and the incidence angle was set to 0–45 degrees, as shown in Figure 4. What follows is category discussion: (1) for linear polarization conversion, compared with normal incidence, a PCR under 15 or 30 degrees of incidence had six conversion frequency bands, and 45 degrees had only 4 conversion frequency bands, indicating that oblique incidence would reduce the number of frequency bands for linear polarization conversion. When the frequency band was below 18 GHz, the oblique incidence had only a small effect on the frequency band of linear polarization conversion, which is basically consistent with the normal incidence and mainly affects the linear polarization conversion at higher frequencies. Therefore, the linear polarization conversion under oblique incidence conditions still maintained more than 4 conversion bandwidths, especially below 24 GHz. (2) Regarding circular polarization conversion, the oblique incidence had no effect on the circular polarization conversion at 8.9–9.0 GHz but had a great impact on the broadband of 9.9–14.7 GHz, while the oblique incidence in the higher frequency band only had an offset effect on the frequency bands. Therefore, the circular polarization conversion could still maintain the multi-band function under oblique incidence, and the whole was still stable in the higher frequency band.

Finally, the PCM based on the combination of complementary units could realize the linear orthogonal and linear-to-circular polarization conversion functions of seven frequency bands as shown in Figure 5. The combined unit structure generated new resonances under the incidence wave which could significantly improve the conversion function of higher frequency bands. Additionally, the experiments show that the multi-band conversion function of the metasurface could still be well maintained under an oblique incidence of 0–45 degrees, and it had angle insensitivity.

4. RCS Reduction

The polarization conversion characteristics of the PCM are described above. In the working frequency bands of the metasurface, under a normal incidence, the cross-polarization reflection amplitude of the basic unit was almost the same as that of the mirror image, but the two phases were opposite. Therefore, the PCM unit’s mirror arrangement and the RCS reduction in a certain frequency band could be realized by using the phase cancellation method of the scattered field.

The plane of RCS based on the PCM is shown in Figure 6. The whole structure is composed of 4 × 4 units, and the single direction is 2 × 2 units, which are arranged with mirrors up, down, left, and right. The surface was simulated with the radiation boundary, and the simulation results are shown in Figure 7. The control group was a metal plane of equal size. We used RCS reduction to represent the RCS capability. The calculation formula of RCS reduction is expressed in Equation (7) [36], where $E_{rx}$ and $E_{ix}$ represent the reflective field and incident field in the far region, respectively, and $r$ represents the detection distance:

$$\mathrm{RCS} \mathrm{reduction}\left(\mathrm{dB}\right)=10 \lg \left[\frac{\underset{r\to \infty }{\lim }4\pi r^2\frac{{\left|E_{rx}\right|}^2}{{\left|E_{ix}\right|}^2}}{\underset{r\to \infty }{\lim }4\pi r^2{\left|1\right|}^2}\right]$$

(7)

RCS reduction peaked at 9.2 GHz and 16.5 GHz, and the 10-dB dual-band RCS reduction bandwidths were 8.9–9.7 GHz and 15.5–26.1 GHz, while the maximum reduction reached 25.8 dB. Therefore, the metasurface achieved a broadband dual-frequency monostation RCS reduction effect. When observing the functional frequency bands of the PCM and the RCS metasurface, it is shown that the 10-dB reduction bandwidth included the frequency band of the polarization conversion. In particular, the frequency at the reduced peak was roughly coincident with the first two resonant frequencies of polarization conversion, and the polarization conversion at this time was the best, resulting in the generation of the reduced peak, which verifies that our designed PCM can achieve excellent RCS reduction function. The small error of the bandwidth of the two was mainly caused by the finiteness of the array. PCM uses Floquet ports to simulate infinite periodic conditions, while the RCS surface is simulated with finite elements.

At 15–45 degrees of oblique incidence, the reduced peaks were shifted, but the impact on the reduced peak in the lower frequency band was small and only had a greater impact on the peak in the higher frequency bands. The maximum reduced peak decreased, and with the increase in the incident angle, the reduced peak bandwidth between 15 and 25 GHz was gradually reduced, but the overall 10-dB dual-band reduction function was still maintained. This indicates that the effects of the angle on the conversion ability of the PCM and the reduction ability of the RCS metasurface were similar. Therefore, the RCS reduction metasurface based on PCM also had angle insensitivity under an oblique incidence of 0–45 degrees.

To better understand how the designed metasurface achieved RCS reduction, we present a 3D scattering field of the control metal plane and the designed RCS plane at the peak reduction point. It can be seen from Figure 8 that at 9.2 GHz, compared with the metal plane, the scattering field of the PCM mirror plane had no main lobe, and the main lobe was suppressed by the phase difference of the reflective field, which exhibited a diffuse reflection state. At 16.5 GHz, the designed plane divided the main lobe into four scattered beams, which were reflected in different directions, diminishing the effect of the main lobe and weakening the side lobes to accomplish RCS reduction.

Figure 9 shows the bistatic RCS effect at the peak frequency points. Two observation angles are set: $\phi =0^{°}$ and $\phi ={90}^{°}$. The results show that at 9.2 GHz, the RCS plane at two observation angles achieved a good bistation RCS reduction in the interval $\theta \in \left[-30,30\right]$. At 16.5 GHz, the value of the bistation RCS in the entire $\theta$ angle range was below −20 dB, showing a perfect bistation RCS reduction function, and the two-angle observation had the largest reduction, reaching 25.8 dB when $\theta =0^{°}$. The results of monostatic and bistatic RCS show that the designed mirror PCM-RCS metasurface can achieve perfect results in a wide frequency band.

5. Fabrication and Measurement

To verify the correctness of the simulation results, we fabricated and measured the metasurface. The samples are shown in Figure 10, where Figure 10a,b shows the PCM and the RCS reduction metasurfaces, respectively. The same-sized metal plane was used as a reference to obtain the actual RCS reduction. The measured device placement and environmental schematic are shown in Figure 11. The samples were tested in an anechoic chamber with two horn antennas connected to the vector network analyzer (VNA), and the frequency range was 5–30 GHz. In the process of measuring the reflection coefficient, both the co-polarized and cross-polarized reflection coefficients should be measured. When measuring co-polarization, two horn antennas are placed in the same direction. When measuring cross-polarization, the transmitting horn antenna is placed horizontally, and the receiving horn antenna is placed vertically. In monostatic RCS measurement, the center of the sample is at the same height as the two antennas, where the separation angle of the two antennas should be less than 5°, and the distance between the antenna and the sample should be more than 2 m to satisfy the far-field scattering pattern. Figure 12 shows the comparison of the measured and simulated results. It can be seen from the figure that the measured reflection coefficient also had multiple polarization conversion frequency bands, and the frequency range was not much different from the simulation results. The measured wide frequency bands of the monostatic RCS were 9.1–9.8 GHz and 15.3–25.8 GHz. The final reflection coefficient and RCS reduction were roughly consistent with the measured results and the simulation results, which verifies the correctness of our design. The small errors were mainly caused by the fabrication process, the measurement errors, and the finite size of the metasurface.

A comparison of the performance of this work with the other literature is shown in

Table 1. Comparisons between this work and other references.

Ref.	Freq. (GHz)		$\mathbf{Size} (\mathbf{Width}\times \mathbf{Length}\times \mathbf{Thickness})$	RCS Reduction Band (GHz)
	LP-LP $\mathbf{(}\mathbf{PCR} \mathbf{\ge }\mathbf{90}\mathbf{\%}$)	LP-CP $\mathbf{(}\mathbf{AR} \mathbf{\le }\mathbf{3} \mathbf{d}\mathbf{B}$)
[7]	4.63–5.54	6.65–7.62	$0.25 {\lambda }_{°}\times$$0.25 {\lambda }_{°}\times$$0.05 {\lambda }_{°}$	3.49–3.62 5.94–6.69
[21]	3.9–7.9	4.9–8.2	$0.32 {\lambda }_{°}\times$$0.32 {\lambda }_{°}\times$$0.12 {\lambda }_{°}$	---
[22]	4.19–4.40 6.8–7.64 11.54–13.07 14.98–15.30	3.95–4.14 4.75–5.95 8.35–8.8 14.35–14.6	$0.147 {\lambda }_{°}\times$$0.147 {\lambda }_{°}\times$$0.042 {\lambda }_{°}$	---
[34]	9.4–14.0 15.5–20.9	---	$0.43 {\lambda }_{°}\times$$0.43 {\lambda }_{°}\times$$0.13 {\lambda }_{°}$	10.2–14.0 15.3–20.7
This work	9.1–9.7 15.6–17.6 19.4–19.7 21.2–23.1 23.5–23.8 26.2 27.9	8.9–9.0 9.9–14.7 19.1–19.3 23.2–23.35 23.4 24.1–25.4 27.2–27.8	$0.45 {\lambda }_{°}\times$$0.45 {\lambda }_{°}\times$$0.07 {\lambda }_{°}$	8.9–9.7 15.5–26.1

, from which it can be seen that the PCM we designed had the most conversion bands as a function of line-to-line orthogonal and line-to-circle polarization conversion and had a wide bandwidth coverage. The RCS reduction metasurface designed using this PCM also had the 2 widest 10-dB reduction bandwidths, further validating the validity of this work. Overall, our work improves the performance and metrics in the field of PCMs, promotes the research of multifunctional PCMs, and provides new ideas and performance designs for electromagnetic stealth design of metasurfaces.

6. Conclusions

In general, the multi-band PCM can not only realize the effect of an x (y)-polarized wave incident to y (x)-polarized wave reflection but also achieve the characteristics of linear-to-circular polarization, and the unit of PCM is obtained by combining complementary square units, which expands the bandwidth compared with a single unit. Simultaneously, the mirror-combined PCM surface can realize the broadband 10-dB RCS reduction function by using phase cancellation of the reflected waves, and the bistatic RCS reduction effect is also remarkable. Through physical fabrication, the simulation results are consistent with the experimental verification results. Therefore, the proposed PCM can be applied to the design of multifunctional polarization converters for the X, Ku, K, and Ka microwave frequency bands while providing methods for antenna RCS reduction, polarization beam modulation, and electromagnetic stealth design of military equipment.