# Study of Energy Scattering Relation and RCS Reduction Characteristic of Matrix-Type Coding Metasurface

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of Matrix-Type Coding Metasurface

#### 2.1. Matrix-Type Random Coding Theory and RCS Reduction Analysis

_{random}for Matlab calculation can be expressed as the following functional form:

^{i}) and ones(2

^{N}

^{−i}) represent the numbers of block matrix 2

^{i}× 2

^{i}, each block matrix composed of 2

^{N}

^{−i}× 2

^{N}

^{−i}is the same random number. The “kron” is matrix multiplication, where the Kronecker product A, B represents the larger matrix formed by the product of all the elements of matrix A and B. The open interval range of random number is (0, 1). The step to obtain the random coding pattern of the MS is as follows: Firstly, the number of different random matrices in the range of (1, N) is counted. Secondly, the number of patterns is calculated. Finally, the random numbers (0 and 1) are added to the discrete binary codes “0” and “1”, and a random coding matrix is obtained through the operation flow chart. Based on the results of simulation and optimization, we choose i = 6 and N − i = 5 to satisfy the preparation and measurement of sample. Therefore, the designed MS consists of a 6 × 6 supercell, with each supercell consisting of 5 × 5 basic units.

_{i}and S

_{s}are the energy density of incidence and scattering, respectively; $|{E}_{i}|$ and $|{E}_{s}|$ are the amplitudes of incident and scattered electric fields, respectively; and $|{H}_{i}|$ and $|{H}_{s}|$ are the amplitudes of the incident and scattered magnetic fields, respectively. The general RCS can also be expressed in the form of dBsm:

_{0}and A

_{1}are the reflection coefficient amplitudes of basic units “0” and “1”, respectively. ${\vartheta}_{0}$ and ${\vartheta}_{1}$ are the reflection phases of two basic units. The ratio of “0” and “1” basic units is introduced, which is defined as α = m

_{0}/m

_{1}, where m

_{0}and m

_{1}are the number of “0” and “1” units, respectively. Further, we introduce α into the formula to express the RCS reduction characteristic with different ratio. However, it can only be used as a qualitative comparison, not a quantitative representation of RCS value. The RCS reduction of 1-bit coding MS under normal incidence can be approximated as:

#### 2.2. Matrix-Type Random Coding Metasurface Arrangement

_{xx}and r

_{yy}) and cross-polarization (r

_{yx}and r

_{xy}) reflection coefficients; the high efficient and broadband polarization conversion features can be achieved in a broadband frequency range. The cross-polarization reflection coefficients (r

_{yx}and r

_{xy}) are greater than 0.8, while the co-polarization reflection coefficients (r

_{xx}and r

_{yy}) are substantially less than 0.35 in the frequency range of 6–15 GHz. The polarization conversion capability is defined as follows [47]: PCR

_{x}= |r

_{yx}|

^{2}/(|r

_{yx}|

^{2}+ |r

_{xx}|

^{2}) and PCR

_{y}= |r

_{xy}|

^{2}/(|r

_{xy}|

^{2}+ |r

_{yy}|

^{2}). As shown in Figure 2d, the linear polarization conversion ratio of the x- and y-polarized waves is as high as 85% and reached 99% at resonance frequencies.

_{0}and m

_{1}are the number of “0” and “1” basic units. As for the two basic units, the reflection coefficients and polarization conversion rates are consistent, the units “0” and “1” can be interchanged, and the meaning of the expression is the same. Figure 3a,b presents the schematics of coding a and b with the ratio α = m

_{0}/m

_{1}= 1/1. Figure 3c,d presents the schematics of coding c and d with the ratio α = m

_{0}/m

_{1}= 5/4. Meanwhile, the coding e and f with the ratio α = m

_{0}/m

_{1}= 2/1 are shown in Figure 3e,f. By applying the matrix-type random coding, the direction of energy scattering can be changed to form a diffuse reflection for the incident EM waves; it is possible to achieve the high efficient RCS reduction characteristic under normal incidence.

^{2}. Figure 4a presents the scattering characteristic of metal plate with a strong normal scattering capability, which can be used as a reference. Figure 4b shows the upright energy scattering direction of coding 0 or 1, which is the same as the energy scattering of metal plate. Figure 4c–h shows the scattering characteristic of coding a to f, the incident EM wave energy scattering is diverged to all around, and the scattering capability is relatively weak at single direction. Thus, these results indicate that the matrix-type random coding MSs have good scattering performance.

## 3. Simulation and Experiment

#### 3.1. Simulation and Analysis of Matrix-Type Coding Metasurfaces

_{0}/m

_{1}= 1/1; the coding c and d present the ratio α = m

_{0}/m

_{1}= 5/4; and the coding e and f present the ratio α = m

_{0}/m

_{1}= 2/1. It can be seen clearly that the RCS reduction curves of different coding sequences with fixed ratio α are basically consistent. The RCS reduction will increase with decrease of the numerical value of α in the whole interested frequency range. The optimal RCS reduction result is presented at α = m

_{0}/m

_{1}= 1/1; these results verify the above theoretical assumptions.

^{2}at 5, 8, 9.5, 10, 13, and 16 GHz. According to “energy conservation law”, the main lobe energy can be suppressed by enhancing the scattering EM energy of side lobe, so an effective RCS reduction can be achieved under normal incidence. The metal plate has a strong main lobe in whole interested frequency range. As shown in Figure 6a,f, the MS has almost no inhibitory effect on main lobe at 5 and 16 GHz. Figure 6b,e shows that the main lobe energy of MS has a certain suppression compared with the metal plate at 8 and 13 GHz. The scattering EM energy is scattered to all around, as shown in Figure 6c,d, which indicates the MS has a significant inhibitory effect on main lobe at 9.5 GHz and 10 GHz, respectively. Generally, the closer it is to the center frequency of the basic unit, the better the effect of reducing RCS can be achieved. Thus, the matrix-type random coding MS allows a wideband and high efficient RCS reduction by adjusting the scattered field simply compared with works proposed before [15,16].

#### 3.2. Measurement and Analysis of Matrix-Type Coding Metasurface

^{2}, and the thickness of overall design is 3.57 mm. Each sample consists of 6 × 6 supercells and each supercell consists of 5 × 5 basic units of “0” or “1”. As shown in Figure 7c, the two samples were measured in the EM anechoic chamber, the transmitting and receiving horns were fixed on the same height level in front of the foam tower. The horn antenna connected to Agilent Technologies N5244A Vector Analyzer was used to measure the RCS of samples. Firstly, the empty darkroom was calibrated before measuring the MS sample. Secondly, the metal ball was placed on the foam tower for calibration as a reference. Thirdly, the MS sample and metal plate were placed on the foam tower for testing to get the RCS value. In measurement, the area of the MS sample was the same as the metal plate. Finally, the RCS reduction of MS sample plate could be obtained by comparing the RCS value of the MS with the metal plate.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Basic unit “0”; (

**b**) basic unit “1”; (

**c**) the reflection coefficients of “0” and “1”; (

**d**) the linear polarization conversion ratio for the normal incident x- and y-polarized wave; (

**e**) the cross-polarization phase of “0” and “1”; and (

**f**) the cross-polarization phase difference of “0” and “1”.

**Figure 3.**Arrangements of six matrix-type random coding MS: (

**a**,

**b**) coding a and b with the ratio α = m

_{0}/m

_{1}= 1/1; (

**c**,

**d**) coding c and d with the ratio α = m

_{0}/m

_{1}= 5/4; and (

**e**,

**f**) coding e and f with the ratio α = m

_{0}/m

_{1}= 2/1.

**Figure 4.**Far-field scattering results of: (

**a**) metal plate; (

**b**) coding 0 or 1, and matrix-type random coding MS; (

**c**) coding a; (

**d**) coding b; (

**e**) coding c; (

**f**) coding d; (

**g**) coding e; and (

**h**) coding f at 9.5 GHz.

**Figure 5.**(

**a**) RCS reduction of matrix-type random coding MS with different ratio combinations of “0” and “1” units; and (

**b**) RCS reduction of coding a at x- and y-polarized wave incidence.

**Figure 6.**2D scattering patterns of the coding a and metal plate in the xoz-plane at: (

**a**) 5 GHz; (

**b**) 8 GHz; (

**c**) 9.5 GHz; (

**d**) 10 GHz; (

**e**) 13 GHz; and (

**f**) 16 GHz.

**Figure 7.**The matrix-type random coding MS templates: (

**a**) coding a; (

**b**) coding b; and (

**c**) the measurement setup at microwave anechoic chamber.

**Figure 8.**The simulated and measured reflectances of the MS samples at x- and y-polarized wave incidence: (

**a**) coding a; and (

**b**) coding b.

**Figure 9.**Measured RCS reduction of samples under normal incidence and oblique incidence of 10°, 20°, and 30°: (

**a**) coding a; and (

**b**) coding b.

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**MDPI and ACS Style**

Yang, J.J.; Cheng, Y.Z.; Qi, D.; Gong, R.Z.
Study of Energy Scattering Relation and RCS Reduction Characteristic of Matrix-Type Coding Metasurface. *Appl. Sci.* **2018**, *8*, 1231.
https://doi.org/10.3390/app8081231

**AMA Style**

Yang JJ, Cheng YZ, Qi D, Gong RZ.
Study of Energy Scattering Relation and RCS Reduction Characteristic of Matrix-Type Coding Metasurface. *Applied Sciences*. 2018; 8(8):1231.
https://doi.org/10.3390/app8081231

**Chicago/Turabian Style**

Yang, Jia Ji, Yong Zhi Cheng, Dong Qi, and Rong Zhou Gong.
2018. "Study of Energy Scattering Relation and RCS Reduction Characteristic of Matrix-Type Coding Metasurface" *Applied Sciences* 8, no. 8: 1231.
https://doi.org/10.3390/app8081231