# Dual-Mechanism Absorptive Metasurface with Wideband 20 dB RCS Reduction

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## Abstract

**:**

## 1. Introduction

## 2. Design Principle of Metasurface

_{1}and A

_{2}represents the amplitude of the reflected EM waves of unit cells “1” and “2”. Parameter $\alpha $ is the ratio of two unit cells and $\alpha =\frac{{n}_{1}}{{n}_{1}+{n}_{2}}$, $1-\alpha =\frac{{n}_{2}}{{n}_{1}+{n}_{2}}$, where ${n}_{1}$ is the number of unit cell “1” in whole metasurface while ${n}_{2}$ is that of unit cell “2”. The phase difference of two unit cells is ${\phi}_{d}$, which can be expressed as:

_{1}= A

_{2}= 1. The relationship between RCS reduction and parameter $\alpha $, ${\phi}_{d}$ can be expressed by Figure 2. The maximum range of ${\phi}_{d}$ appears at $\alpha $ = 0.5. In order to obtain 10 dB RCS reduction, the phase difference needs to be at (180° − 37°, 180° + 37°), which is consistent with the conclusion of AMC chessboard [14]. For RCS reduction above 20 dB, the phase difference needs to be at (180° − 11°, 180° + 11°). However, for the resonance phase, it is an extremely harsh constraint for two unit cells to meet the phase difference of 180° ± 11°. Therefore, the reduction effect using phase cancellation, which could get more than 20 dB RCS reduction, is only for individual frequency points. If “1” has 10 dB absorption property while “2” is lossless (A

_{1}= 0.316, A

_{2}= 1), the relationship can be expressed by Figure 3a. The 20 dB maximum range of ${\phi}_{d}$ appears at $\alpha $ = 0.78 from 180°− 24° to 180° + 24°, which is wider than 180° ± 11°. If “1” and “2” both have 10 dB absorption property (A

_{1}= A

_{2}= 0.316) (see Figure 3b), the 20 dB maximum range of ${\phi}_{d}$ appears at $\alpha $ = 0.5 and the range from 180° − 37° to 180° + 37°, which is wider than 180° ± 11°.

## 3. Results and Discussion

#### 3.1. Unit Cell Design

_{r}and Z

_{d}denote the equivalent impedance of the periodic structure and the substrate layer, respectively. Z

_{r}is a complex value that can be expressed by Z

_{r}= R + jX. Z

_{in}is the input impedance of this network. The reflection coefficient of the unit cell can be expressed as

_{0}is the intrinsic impedance of a vacuum, d and ${\epsilon}_{r}$ are the thickness and relative permittivity of the substrate layer, respectively. Thus, the reflection amplitude and phase can be expressed as

_{1}, A

_{2}, P

_{1}, P

_{1}, X

_{1}, X

_{2}, R

_{1}, R

_{2}. It is complex and time-consuming to optimize and select the eligible two unit cells. Thus, to simplify the process, we firstly design one absorption unit cell “1” and then choose the other counterpart.

_{1}= 5 mm, b

_{1}= a

_{1}− 3 mm, the height of h = 3 mm and dielectric loss of tan δ = 0.00081 is utilized as the dielectric spacer. For “1”, the sheet resistance of resistive film patterns is 10 Ω/sq, and the reflection phase and amplitude curves are shown in Figure 6b. The 10 dB absorption bandwidth is 9.9–17.5 GHz, but that of 20 dB is only 10.9–12.2 GHz.

_{r}are shown in Figure 7. When the sheet resistance value remains unchanged and only the length of the outer square ring varies, the curves of the real part R are almost overlapped, but the imaginary part X varies obviously. In another case, when the parameter a remains unchanged, and only the sheet resistance value varies, an opposite result will happen. Thus, according to the rule shown in Figure 7 and the relationship shown in Figure 5, unit cell “2” that meets the phase and absorption requirements can be designed.

#### 3.2. Metasurface Design and Simulation

#### 3.3. Metasurface Fabrication and Measurement

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The relationship between RCS reduction and parameter α, ${\phi}_{d}$ when “1” and “2” have no absorption.

**Figure 3.**The relationship between RCS reduction and parameter α, ${\phi}_{d}$ when (

**a**) “1” has 10 dB absorption property, “2” not, (

**b**) “1” and “2” both have 10 dB absorption.

**Figure 6.**Schematic of the two unit cells (

**a**) unit cell “1” and (

**c**) unit cell “2”. The amplitude and phase curves of reflectivity of the two unit cells, (

**b**) unit cell “1” and (

**d**) unit cell “2”.

**Figure 7.**The impedance analysis of two square resistive film rings. (

**a**) Sheet resistance = 10 Ω/sq, parameter a varies from 4.5 to 6 with 0.5 step. (

**b**) Parameter a = 5 mm, sheet resistance varies from 5 to 25 mm with 5 step.

**Figure 8.**The phase difference between “1” and “2”. The green rectangle represents the phase difference region of 180° ± 37°.

**Figure 9.**The 20 dB reduction area of (

**a**) 12 GHz (

**b**) 13 GHz and (

**c**) 14 GHz. (

**d**) The overlap area of these three frequency points.

**Figure 10.**(

**a**) The simplest subarray of ratio $\alpha $ = 0.75. (

**b**) The schematic diagram of the whole metasurface.

**Figure 11.**(

**a**) Simulated RCS curves of designed metasurface with TE and TM polarization, and equal-size PEC plane. (

**b**) Simulated RCS reduction curves of designed metasurface and surface composed only by unit cell “1”.

**Figure 12.**The simulated 3D far-field patterns of (

**a**) equal-size PEC plane, (

**b**) surface composed only by unit cell “1”, (

**c**) traditional chessboard cancellation metasurface, and (

**d**) designed dual-mechanism metasurface.

**Figure 13.**(

**a**–

**e**) The different arrangements of the whole metasurface with the same ratio $\alpha $ and their 3D far-field patterns. (

**f**) The RCS reduction curves of these metasurface arrangements.

**Figure 14.**The operating characteristics when illuminated by TE and TM polarized waves at 15°, 30°, 45° angles of incidence.

**Figure 15.**(

**a**) The sample of dual-mechanism absorptive metasurface. (

**b**) The testing platform of the anechoic chamber. (

**c**) The production process of the overprinted metasurface.

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**MDPI and ACS Style**

Yuan, F.; Chen, Q.; Zheng, Y.; Fu, Y.
Dual-Mechanism Absorptive Metasurface with Wideband 20 dB RCS Reduction. *Crystals* **2022**, *12*, 493.
https://doi.org/10.3390/cryst12040493

**AMA Style**

Yuan F, Chen Q, Zheng Y, Fu Y.
Dual-Mechanism Absorptive Metasurface with Wideband 20 dB RCS Reduction. *Crystals*. 2022; 12(4):493.
https://doi.org/10.3390/cryst12040493

**Chicago/Turabian Style**

Yuan, Fang, Qiang Chen, Yuejun Zheng, and Yunqi Fu.
2022. "Dual-Mechanism Absorptive Metasurface with Wideband 20 dB RCS Reduction" *Crystals* 12, no. 4: 493.
https://doi.org/10.3390/cryst12040493