# Broadband Polarization Conversion Metasurface Based on Metal Cut-Wire Structure for Radar Cross Section Reduction

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of Basic Unit and Theoretical Analysis

_{xx}and r

_{yy}) and cross-polarization (r

_{yx}and r

_{xy}) reflection coefficients for both incident x-polarized and y-polarized waves. As suggested by the reflection coefficients in Figure 1d, the structure is able to achieve efficient linear polarization conversion across a wide frequency range of 6–14 GHz, the cross-polarization reflection coefficients (r

_{yx}and r

_{xy}) are greater than 0.85, and the co-polarization reflection coefficients (r

_{xx}and r

_{yy}) are substantially less than 0.3. In addition, at resonance frequencies, the co-polarization reflection coefficients (r

_{xx}and r

_{yy}) reach a minimum, and the corresponding amplitudes are less than 0.1. The corresponding cross-polarization reflection coefficients (r

_{yx}and r

_{xy}) reach a maximum, and the amplitudes are greater than 0.9. This result indicates that the normal incident x(y)-polarized waves are almost completely converted to y (x)-polarized waves, or produced approximately 90° linear polarization deflections.

_{x}= |r

_{yx}|

^{2}/(|r

_{yx}|

^{2}+ |r

_{xx}|

^{2}) and PCR

_{y}= |r

_{xy}|

^{2}/(|r

_{xy}|

^{2}+ |r

_{yy}|

^{2}). In Figure 1f, the linear polarization conversion ratio of the x- and y-polarized waves are as high as 90% and reached 99% at resonance frequencies. Figure 1e,g shows the cross-polarization phases of the “0” and “1” units, and the corresponding phase difference, Δφ

_{10}(Δφ

_{xy}), in the whole 4–16 GHz range. It is observed that the cross-polarization phase difference Δφ

_{10}(Δφ

_{xy}) = ±180° can be obtained, which indicates that the phase gradient of the designed MS is 180°.

_{0}is the free space wavenumber, the ${\epsilon}_{r}$ and d are the relative permittivity and thickness of the middle dielectric layer. The partial reflection and transmission waves arrive at the air-spacer interface again from the reverse direction after the additional propagation phase β in the dielectric spacer [22]. The incident EM wave prompted multiple reflections in this resonance cavity, including co-polarization wave interference cancellation, and cross-polarization wave interference superposition. Based on our previous research [22], the cross-polarization and co-polarization reflection coefficients can be expressed as: ${r}_{yx}={\stackrel{\rightharpoonup}{r}}_{yx}+{\displaystyle \sum _{j=1}^{\infty}{r}_{yj}}$ and ${r}_{xx}={\stackrel{\rightharpoonup}{r}}_{xx}+{\displaystyle \sum _{j=1}^{\infty}{r}_{xj}}$. Thus, we simulate the unit-cell structure without the ground plane, and use MATLAB software to calculate the reflection coefficients and polarization conversion ratio for the x-polarized wave incidence. As shown in Figure 3a,b, the calculated data are in reasonable agreement with the simulated data, further illustrating the working principle of the Fabry-Perot-like resonance cavity. Therefore, we can use the characteristics of the ±180° cross-polarization reflected phase difference based on the metal cut-wire structure elements “0” and “1” and realize polarization conversion by combining different coding combinations.

_{0}and AF

_{1}are the elements “0” and “1”, respectively; and EF

_{0}and EF

_{1}are the scattering fields of the “0” and “1” elements, respectively. The array factor AF

_{2×2}with a 2 × 2 arrangement can be expressed as:

_{0}and AF

_{1}are expressed in the matrices as shown below:

_{0}= AF

_{1}= 2/4 = 1/2. Similarly, coding 01/01 corresponds to AF

_{0}= AF

_{1}= 1/2.

_{t}, the incident fields EF

_{0}and EF

_{1}are expressed as:

_{xx}= $\overrightarrow{{r}_{xx}}{e}^{\overrightarrow{{\phi}_{xx}}}$ is the co-polarization reflection coefficient and r

_{yx}= $\overrightarrow{{r}_{yx}}{e}^{\overrightarrow{{\phi}_{yx}}}$ is the cross-polarization reflection coefficient. From the previous simulated results, we can see that the units “0” and “1” have the same co-polarization reflection phase, and the cross-polarization reflection phase difference is 180°. Therefore, the total scattering field can be expressed as:

_{total}| = r

_{xx}|EF

_{t}|. For a metal plate, the size of the scattering field is |EF

^{i}

_{total}| = |EF

_{t}|, and the scattering coefficient is r

_{xx}= |E

_{total}|

**/**|EF

^{i}

_{total}|. We assume that the RCS reduction of the MS is greater than 10 dB, so the following condition needs to be met:

## 3. Simulation, Experiment and Discussion

_{xx}= 0.318 > 0.316 at the 7.7 GHz peak, and r

_{xx}= 0.301 < 0.316 at the 12.2 GHz peak. According to Formula (10), we can see that the RCS reduction of the MS should be less than 10 dB around 7.7 GHz. Figure 6b also shows that the MSs of coding 01/01 and 01/10 have dips at the above-mentioned frequency, where RCS reduction is less than 10 dB around 7.7 GHz. For the MSs of coding 00/00 and 11/11, it can be seen that the RCS reduction is essentially zero in our frequency range of interest of 5–15 GHz. This is mainly due to the consistency of co-polarization and cross-polarization phases for all basic units, where the RCS of the target can’t be reduced since the cross-polarization components of the scattering field can’t be offset. These simulated results near perfectly verify the above analysis.

^{2}. According to the law of energy conservation, the main lobe energy is suppressed significantly by enhancing the scattered energy of the side lobes to achieve RCS reduction under normal incidence. The pattern shows that the metal plate has a main lobe throughout the whole band under normal incidence. As shown in Figure 7a,d, relative to the metal plate, the MS has a certain inhibitory effect on the main lobe at 6 and 14 GHz, respectively. As shown in Figure 7b,c, the MS has an obvious inhibitory effect on the main lobe at 10 and 11 GHz, respectively. Based on the above results, it can be suggested that the polarization conversion MS can realize RCS reduction throughout a wide frequency range and can adjust the scattering field dynamically.

^{2}sample was fabricated using traditional printed circuit board (PCB) technology, as shown in Figure 8a. The front and back layers of the sample are covered with copper, and the middle layer is a FR4 substrate with a thickness of 3.5 mm. Using the free space method, we measured the sample in the microwave anechoic chamber (see Figure 8b). The measured sample was fixed in the center of a rotating foam tower, the transmitter and receiver antennas were fixed to the same height, ensuring an angle of 5°. Then, we connected two horn antennas of co-polarization state to two ports of the Agilent Technologies N5244A Vector Analyzer and measured the RCS of the sample.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The element “0” with an angle of 45° to the x-axis; (

**b**) the element “1” rotated 90° counterclockwise about the z-axis; (

**c**) the side view of the basic unit; (

**d**) the reflection coefficient of elements “0” and “1” under normal x- and y-polarized incidence; (

**e**) the reflection phase of cross-polarized wave; (

**f**) the linear polarization conversion ratio of x- and y-polarized wave; (

**g**) cross-polarization reflection phase difference of elements “0” and “1”.

**Figure 2.**Schematic of multiple reflections and transmissions in a Fabry-Perot-like resonance cavity for polarization conversion.

**Figure 4.**(

**a**) 2 × 2 structure arrangement of the 01/10 coding MS; (

**b**) illustration of the 01/10 coding MS; the “0” and “1” indicate the super-cells, and are distinguished by blue and yellow colors; each super-cell consists of 5 × 5 unit-cells of “0” and “1”, shown in Figure 1a,b.

**Figure 5.**Simulation far-field patterns of the scattering of (

**a**) 00/00 or 11/11; (

**b**) 01/01 or 10/10; and (

**c**) 01/10 at 10 GHz for the coding MS.

**Figure 6.**Simulated results of a series of regular coding MSs: (

**a**) RCS reduction of 01/10 coding MS for different super-cell combinations; (

**b**) RCS reduction of the different regular coding MS with 5 × 5 super-cell; (

**c**) RCS reduction of the 01/01 coding MS for normal x- and y-polarized incident waves; (

**d**) RCS reduction of the 01/10 coding MS for normal incident x- and y-polarized waves.

**Figure 7.**Scattering patterns of the 01/10 coding MS and metal plate in the XOZ-plane at (

**a**) 6 GHz; (

**b**) 10 GHz; (

**c**) 11 GHz; and (

**d**) 14 GHz.

**Figure 8.**(

**a**) The fabricated 01/10 coding MS sample; (

**b**) the measurement setup in the microwave anechoic chamber.

**Figure 9.**(

**a**) The simulated and measured reflectance results of the sample; (

**b**) RCS reduction of the sample under oblique incident waves from 0° to 30°.

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**MDPI and ACS Style**

Yang, J.J.; Cheng, Y.Z.; Ge, C.C.; Gong, R.Z.
Broadband Polarization Conversion Metasurface Based on Metal Cut-Wire Structure for Radar Cross Section Reduction. *Materials* **2018**, *11*, 626.
https://doi.org/10.3390/ma11040626

**AMA Style**

Yang JJ, Cheng YZ, Ge CC, Gong RZ.
Broadband Polarization Conversion Metasurface Based on Metal Cut-Wire Structure for Radar Cross Section Reduction. *Materials*. 2018; 11(4):626.
https://doi.org/10.3390/ma11040626

**Chicago/Turabian Style**

Yang, Jia Ji, Yong Zhi Cheng, Chen Chen Ge, and Rong Zhou Gong.
2018. "Broadband Polarization Conversion Metasurface Based on Metal Cut-Wire Structure for Radar Cross Section Reduction" *Materials* 11, no. 4: 626.
https://doi.org/10.3390/ma11040626