Impedance mismatch derived coded absorbing materials: for ultra-broadband anti-reflection and scattering field tailored on demand

doi:10.21203/rs.3.rs-2825501/v1

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Impedance mismatch derived coded absorbing materials: for ultra-broadband anti-reflection and scattering field tailored on demand

https://doi.org/10.21203/rs.3.rs-2825501/v1

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The inability of existing electromagnetic wave absorbing materials (EAMs) to manipulate electromagnetic waves in multiple dimensions leads to the failure to satisfy the demands placed on electromagnetic (EM) defense technology by the current complex EM environment. To break this dilemma, this study focuses on the impedance properties of EAMs, conferring additional ability to disperse and deflect reflected waves by encoding EAMs with opposite phase responses in different impedance mismatch modes. Due to the synergy of both absorption and scattering mechanisms, the developed scattering metasurface absorber exhibits excellent anti-reflection performance, with reflectivity below 0.1 in the 7.8-16.7 GHz at 2 mm thickness. Furthermore, a genetic algorithm is employed to tailor the desired scattering field to meet the stealth requirements of specific environments, allowing for the directional transmission of EM energy in the one-dimensional or homogeneous distribution in the three-dimensional. The proposed scattering metasurface absorber constructed by coded EAMs exhibited excellent anti-reflection properties and environmental stealth adaptability, opening up new possibilities for the development of advanced EM defense technology.

Electromagnetic wave absorbing material

Coded metasurface

Broadband RCS reduction

Environmental stealth adaptability

With the widespread application of modern electronic technology in areas such as communication, navigation, and detection[1–4], a range of electromagnetic (EM) defense technologies have been developed to defend against the harmful effects of EM radiation, interference, and detection[5–8]. Electromagnetic wave absorbing materials (EAMs) have emerged as a key technology in EM defense, owing to their ability to absorb EM waves and convert them into thermal energy [9–11]. Depending on the mechanism of EM wave loss, EAMs can be categorized into three main types: dielectric loss materials[12, 13], magnetic loss materials[14, 15], and materials that exhibit both types of losses[16, 17]. EAMs are capable of absorbing EM waves over a broad frequency range by adjusting the EM parameters to achieve a suitable impedance match and loss constant[18–20]. Also, the EM parameters can be influenced by various factors, such as the microstructure and size of the absorbent particles, and their arrangement in the matrix[21–23]. Consequently, at the microscopic scale, various strategies directed at optimizing absorbent particles (such as magneto-electric synergy[24, 25], flake processing[26], and chiral structure[27]) are used to enhance the absorption performance in order to obtain a broad working band under a thin thickness. However, EM waves exhibit many fundamental characteristics, such as amplitude, phase, polarization, and transmission direction[28]. Defense against single-station radar detection typically requires only reducing amplitude, whereas defending against multi-station radar detection necessitates addressing both polarization and transmission direction. So, EAMs can only attenuate amplitude, rendering them ineffective in defending against multi-station radar detection, and thus limiting their applications in electromagnetic defense.

In contrast, metasurfaces are the current focus of research in EM defense due to manipulate electromagnetic waves in multiple dimensions[29–31]. Cui et al. proposed the concept of coded metasurface, and this digital encoding-based metasurface enables flexible control of the scattering field[32]. By implementing a discontinuous phase arrangement at the interface using coding strategies, metasurfaces can disperse and deflect electromagnetic waves in desired directions, thus avoiding detection by multi-station radar systems[33]. Furthermore, the integration of absorption and scattering mechanisms holds great potential for further reducing the radar reflection cross-section (RCS). Unfortunately, due to the extreme dependence of the EM waves on both the shape, size, and thickness of the resonant structures, the polarization and angle sensitivity and the narrow working band (usually only a few frequency points) have restricted badly the practical application of metasurface at present[34]. Although various strategies for broadening the working band, such as multilayer structures[35, 36], fractal patterns[37], and the combination of tunable components[38], have been demonstrated to be helpful to some extent, they often result in increased thickness and complex preparation procedures[39].

In summary, the limitations of both the EAMs in multi-dimensional manipulation and the coded metasurface in balancing between working band and thickness are hindering the advancement of current EM defense technology. Therefore, constructing coded metasurfaces with scattering capability using EAMs with broadband performance can maximize the advantages of both to potentially break this dilemma. Moreover, relying solely on EAMs to build elements with phase responses to EM waves, instead of depending on electrically resonant structures, is the key to this problem. For EAMs, there are two different impedance mismatch modes, corresponding to the capacitive and inductive half-circle of the Smith circle. In these two different impedance mismatche modes the EAMs exhibits positive and negative opposite reflected phases, which makes it possible to use the EAMs to construct elements with ultra-broadband reflected phase differences and further to constitute coded metasurfaces. Therefore, with the support of this mechanism, this study presents a novel scattering metasurface absorber (SMA) constructed entirely by coded elements made from soft magnetic EAMs composed of spherical carbonyl-iron particles (CIP) and polyurethane (PU). The proposed SMA rely on no electrically resonant structures, and it offers a combination of thin thickness, wide bandwidth, polarization and angle insensitivity, and dual-dimensional manipulation to EM waves. In addition to keeping the advantages of soft magnetic EAMs with efficient absorption at broad working bands under a thin thickness[40, 41], the proposed SMA can further disperse and deflect unabsorbed reflected waves in the same band due to the discontinuous phase distribution. By adjusting the filler ratio of the CIP, the elements exhibited different reflected amplitudes and phases in a broadband range, and the source of these differences has been clarified by the symmetry model[42]. Then the enhanced anti-reflection performance of the proposed SMA has been validated by experiments and simulations, which derive from the synergy of both absorption and scattering in the same frequency band. Finally, the SMA patterns were optimized by coded strategy and the genetic algorithm to tailor the desired scattering field and thus meet the stealth needs of specific environments. The proposed SMA constructed by coded EAMs exhibited excellent anti-reflection properties and environmental stealth adaptability, opening up new possibilities for the development of advanced EM defense technology.

2.1 Raw materials

In this study, the EAM was prepared using spherical carbonyl-iron particles (CIP) and polyurethane (PU). CIP is an excellent and stable soft magnetic absorber with a regular spherical shape and a smooth surface, while PU plays the role of a matrix for the dispersion and hold of CIP due to its excellent flowability. The CIP was supplied from Shanxi Xinghua Chemical Co. Ltd. The PU was supplied from Shanghai Hecheng Macromolecule Co. Ltd. All raw materials were used directly without any pre-treatment. The magnetic hysteresis loops of CIP particles shown in Fig. 1(c) demonstrate that CIP used is a typical ferromagnetic material with a saturation magnetization intensity of 212.96 emu/g and an intrinsic coercivity of 4.85 Oe. This excellent soft magnetic performance allows the composite of CIP and PU to be the EAM with broadband absorption properties.

2.2 Preparation of scattering metasurface absorbers

The preparation process is shown in Fig. 1(a). Firstly, CIP and PU were mixed separately in different proportions (CIP: PU = 1, 2, 3, 4: 1, mass ratio). To make CIP particles in the PU matrix to get a homogeneous dispersion, mechanical stirring, and sonication were alternately repeated three times for 10 min. Then, the mixture of CIP and PU was coated on the custom mold (200 mm * 200 mm * 2 mm, internal dimensions) to be cured for 24 hours and then de-molded to obtain an EAM of the same size. Next, the EAMs were cut by a laser cutter into a series of elements for subsequent metasurface configuration. Finally, the elements of the same size but different filling ratios were arranged and combined on the aluminum plate (200 mm * 200 mm * 1.5 mm) to form the proposed metasurface. The microscopic morphology of the CIP and PU composite material is illustrated in Fig. 1(b). The SEM shows that the CIP particles are evenly dispersed inside the PU matrix and that the PU fills the gaps between the CIP particles. Also, no absorber particles exhibited any obvious bias aggregation, which proves that the preparation method can ensure the homogeneity of the EAM elements. In addition, the composite material of CIP and PU exhibited excellent deformation properties such as bend, roll, and twist as shown in Fig. 1(d), which is not possible with traditional rigid metasurfaces. A chessboard arrangement of the prepared SMA is illustrated in Fig. 1(e), and all elements are 2 mm thickness.

2.3 Program and simulation

A special genetic algorithm for array optimization was programmed using the commercial mathematics software MATLAB. Different from the traditional genetic algorithm, dynamic recombination, and mutation probability were used to avoid falling into local optimal solutions during pattern optimization of SMA. In addition, the elite retention strategy was used to ensure that each evolution of a population produces the best individuals that are no weaker than the previous generation.

The electromagnetic responses of the prepared EAM elements with different ratios and the SMAs combined from EAM elements were simulated using the commercial software CST Microwave Studio. The frequency domain solver was used to calculate the reflection loss and the reflection phase of the different elements as well as the S-parameter of the symmetry model. The time domain solver was used to simulate the far-field distribution of the SMA with different patterns, accompanied by open boundary conditions and plane wave excitation. In addition, the waveguide port was used as the source of the horn antenna in the near-field simulation. All simulations were performed at 4–18 GHz and the material parameters involved in the simulation are measured by the air-line method in the vector network analyzer.

2.4 Characterization and instruments

The cross-sectional scanning electron microscope (SEM) of EAM elements of different filling ratios was performed on JSM-5600LV.

A series of coaxial rings with the same material as the EAM elements were pressed using a special mold, and the outer diameter of the rings was 7 mm and the inner diameter was 3.04 mm. Then the complex permittivity and permeability of EAM elements of different filling ratios were measured by Agilent 8722 ES vector network analyzer via air-line method ranging from 4 to 18 GHz.

The reflectivity of both vertical and oblique incidence of the prepared EAMs and SMAs in the frequency range of 4 to 18 GHz was measured by the cantilevered arch method.

3.1 Reflected phase of EAMs

The EM parameters of the four prepared EAMs are shown in Fig. S1 (a-d), with filling ratios of 1:1, 2:1, 3:1, and 4:1, and will be referred to as CIP 1:1 to CIP 4:1, respectively. The measured and simulated results of vertical reflectivity are shown in Fig. S1 (e, f). The absorption performance increases and then decreases with frequency, and the frequency of the absorption peak gradually moves to lower frequencies as the filling ratios increase. This phenomenon can be explained by the interfacial reflection model as shown in Fig. 2(a). The absorber has two surfaces. The surface in connection with air is the front surface and the surface in connection with the metal plate is the back surface. When the incident wave interacts with the absorber, it first comes into contact with the front surface. Due to the impedance difference between the absorber and air, the incident wave is divided into two parts. One part is reflected into the air by the front surface, which is the reflected wave by the front surface (Rf). Another part enters the absorber and propagates until it touches the back surface, where it is reflected and finally transmitted through the front surface into the air, which is the reflected wave by the back surface (Rb). Due to the loss constants, Rb continuously faded as it propagates inside the EAMs. Snell's law shows that Rf and Rb propagate in the same direction and therefore interfere with each other during propagation[43]. When the amplitudes of Rf and Rb are equal and the phase difference is 180°, intensive electromagnetic loss is caused by destructive interference and the energy of the reflected wave is reduced significantly[44]. This model can be calculated by the theoretical formula of quarter wavelength as follows[45]:

$${f}_{m}=nc/4d\sqrt{{\epsilon }_{r}·{\mu }_{r}}(\text{n}=\text{1,3},\text{5,7}\dots )$$

Where f_m is the matching frequency, d is the matching thickness, ε_r and µ_r are the relative permittivity and permeability of the coating, and c is the speed of light in a vacuum.

The above theory is usually used to explain the difference in absorption performance, i.e., the reflection amplitude. But the phase, another key characteristic of EM waves, is not mentioned. To better illustrate the differences in reflected phases of different EAMs, the CIP 4:1 with the maximum filling ratio and the CIP1:1 with the minimum were selected for comparison. And the symmetry model was developed for the interpretation, as shown in Fig. 2(b). The absorber is symmetrized along the back surface in the modeling, while the metal plate is removed. Then the two ports are modeled to respectively receive the reflected waves by the front and back surfaces. In this way, Rf and Rb are separated without interference. In symmetry model, Rf' is still reflected by the front surface and then received by Port 1, while Rb' passes through twice the thickness of the absorber and is received by Port 2. Their respective information (both amplitude and phase) will be received by the two ports separately. It should be noted that in the realistic model, a half wave loss is produced by Rb when reflected by the metal plate, so a phase compensation of 180° is required for Rb'.

The amplitudes and phases of Rf' and Rb' of CIP 1:1 and CIP 4:1 were obtained respectively by symmetry model, as shown in Fig. 2(d, e). The solid line is the amplitude, corresponding to the left axis, and the dashed line is the phase, corresponding to the right axis. The relationship between the absorption performance and filling ratio is visualized by the amplitude difference in reflected wave by the front and back interfaces. For CIP 1:1, the impedance of the absorber is near to air at a low filling ratio. Therefore, the amplitude of Rf is smaller, and more EM waves enter inside the absorber, while the amplitude of Rb is larger due to the weak loss capability (the loss constants as shown in Fig. S2)[46, 47]. As shown in Fig. 2(d), the amplitude of Rb is larger than the Rf in the full frequency band. With the increase of filling ratio, for CIP 4:1, the impedance of the absorber and air gradually mismatched, thus the EM waves that enter inside the absorber are reduced. In addition, the stronger loss performance causes the Rb to be dramatically lost within the absorber, so the amplitude of Rb is lower than Rf in the broad frequency band, as shown in Fig. 2(e). In addition to the amplitude, the phase of the Rf and Rb provides a clear explanation of the generation of absorption peaks. At the phase difference of 180° between the Rf and Rb (13.8 GHz for CIP 1:1 and 6.5 GHz for CIP 4:1), the amplitude of the reflected waves produced by interfering decreases drastically. CIP1:1 and CIP4:1 show the most efficient microwave absorption performance with absorption peaks (-32.1 dB and − 7.7 dB). Such a desirable feature is perfect impedance matching, and the frequency corresponding to the absorption peak is the matching frequency.

By contrast, impedance mismatch is undesirable for EAM, because as the frequency moves away from the matching frequency, the impedance mismatches gradually, and the reflected amplitude increases. However, the variation of the reflected phase is not the same due to the two different impedance mismatch modes which correspond to the upper and lower semicircles of the Smith circle. As shown in Fig. 2(g), when the impedance curve is in the upper semicircle of the capacitive resistance zone, the corresponding frequency is less than the matching frequency and the phase increases to positive. Conversely, when the impedance curve is in the inductive resistance zone of the lower semicircle, the corresponding frequency is greater than the matching frequency and the phase decreases to negative. Figure 2(f) shows that both CIP 1:1 and CIP 4:1 have a reflected phase of 0 at the matching frequency, but both of them show positive or negative opposite phases in the left or right of the matching frequency. Consequently, there is a large phase difference between CIP 1:1 and CIP 4:1 for a wide frequency band. The Generalized Snell's Law shows that when the sources of two waves no coincide but the directions of transmission coincide, the appropriate phase difference can lead to the redistribution of electromagnetic energy in space, namely EM scattering[33]. Generally, two waves with phase differences in the 180 ± 45° will produce desirable interferences. In this study, the phase difference qualified between the reflected waves of CIP 1:1 and CIP 4:1 is in the frequency of 6.6–15.1 GHz, which is a bandwidth difficult to reach for traditional metasurfaces at the same thickness (2 mm).

The symmetry model clarifies the difference in reflected phase between different EAMs, which results from the interference between reflected waves by the front and back interfaces when the impedance is mismatched. Furthermore, the two different impedance mismatch modes lead the phase to go in the opposite direction of positive or negative. This interesting mechanism enables the construction of elements with opposite reflected phases by using only EAMs with no electrically resonant structures. Compared to conventional electrically resonant structures, the proposed EAM elements exhibit significant application advantages due to the broadband both absorption and phase difference and efficient preparation.

3.2 Anti-reflection performance of SMA

To transform the excellent performance of EAM elements in the broadband reflection phase difference and EM wave loss into the efficient anti-reflection capability of SMA, three SMAs with different patterns have been designed by two EMA elements, the CIP 1:1 and CIP 4:1. Where pattern 1 is arranged in stripes, pattern 2 in a chessboard, and pattern 3 in a pinwheel. The elements in patterns 1 and 2 are processed as rectangles with 25 mm sides, and the elements in pattern 3 are processed as right-angled triangles with 50 mm longest sides, while all elements are 2 mm thickness. In addition, the total dimensions of all proposed three SMAs are 200 mm * 200 mm * 2 mm. Figure 3(a-c) shows the three SMAs with different patterns and the measured and simulated vertical reflectivity. The reflectivity results show that although the three SMAs differ in pattern, they are comparable in terms of anti-reflective performance. The reason for this is that the vertical reflectance of the scattering metasurface used for radar reflection cross section (RCS) reduction is only dependent on the proportion of the elements, and the effect of the arrangement of the elements is negligible[48]. According to the RCS reduction formula:

$$RCSR=10\text{l}\text{o}\text{g}{\left({r}_{1}{A}_{1}{e}^{j{\phi }_{1}}+{r}_{2}{A}_{2}{e}^{j{\phi }_{2}}\right)}^{2}$$

where ${r}_{1}$ and ${r}_{2}$ are the occupancy ratios of the two elements, ${A}_{1}$ and ${A}_{2}$ are the corresponding amplitudes, and ${\phi }_{1}$ and ${\phi }_{1}$ are the corresponding phases. Fig. S3 shows the calculated reflectivity of the three SMAs is less than 0.1 in the 7.8–16.7 GHz. And the reflectivity is identical for all three SMAs because the area ratio of both two elements is 1/2. In addition, the experiment and simulation are in general agreement with the calculated theoretical results, which proves further the excellent anti-reflection properties of SMA prepared fully from the EAM elements.

The stability of anti-reflection performance under oblique incidence is an important indicator for assessing the stealth performance. In the past, metasurfaces dependent on electrically resonant structures required strict on the incident wave, including frequency, polarization, and angle of incidence. Obviously, by removing the dependence on the electrically resonant structures, the full medium EAM strategy maintains the broadband properties and eliminates polarization sensitivity to some extent. For oblique incidence, both TE and TM polarized waves need to be considered, the former with the electric field vector normal to the incident plane and the latter with the magnetic field vector normal to the incident plane. As shown in Fig. 3(d-f), the anti-reflection performance of the three SMAs was experimented with incidence angles of 20° and 40° (angle to the plane normal) under TE and TM polarized waves, respectively. The performance attenuation at oblique incidence is slight compared to the corresponding vertical reflectivity. The results demonstrate that the proposed SMAs maintain excellent anti-reflection performance under incidence angles for both TE and TM polarized waves over a wide range of 0–40°. In conclusion, the combination of absorption and scattering endows SMA with broadband and efficient anti-reflection performance and allows it to maintain performance over a wide range of angles.

To clarify the role of absorption and scattering in reflectivity reduction, Fig. 4(a) shows the energy ratios of absorption, scattering, and reflection for the SMA of Pattern 1 under the vertical incidence, indicated by different colors. The blue part is the energy absorbed by the SMA, calculated by averaging the absorptivity of the two elements. The light-yellow part is the reflected energy distributed in the normal direction, obtained from the reflectivity of the SMA. While the dark-yellow part is the energy distributed in directions other than the normal, derived from total energy minus the above two parts. Obviously, the bulk of the energy is absorbed, and the majority of the unabsorbed is anomalously reflected and then deflected to all directions by the SMA, while only a little of the energy is reflected in the normal direction. Figure 4(b) shows the average ratios of energy dissipation in the range of 4–18 GHz. The absorption portion is 67.6%, the scattering portion is 22.6%, and the reflection portion is only 9.8%. Also, among the energy reflected by SMA, only 30.5% of the energy is reflected along the normal direction while 69.5% is scattered, which is an ability lacking in conventional EAMs. To demonstrate the scattering stealth mechanism, near-field simulations of the proposed SMA were run in the commercial simulation software CST. As shown in Fig. 4(c), the two EAMs elements, CIP 1:1 and CIP 4:1, are arranged in Pattern 1 on an aluminum plate to form the SMA, with a horn antenna as the signal source to transmit the 12 GHz line polarized EM wave against the SMA. The two planes in which the incident and reflected waves are located are modeled, and the latter is shown in particular. The direction of propagation of the EM wave can be observed through the electric field intensity displayed on the plane, which shows the three reflected waves propagating in different directions due to the SMA. Snell's Law indicates that the reflected wave is in the same plane as both the incident wave and the plate normal[43]. However, the direction of two waves along the yellow arrow is against Snell's Law, thus anomalous reflected waves are formed and scattered to other regions in space. Supporting information animations show the comparison of near-field simulations between an SMA and a traditional EAM. As shown in the animation in the supporting information, the proposed SMAs can manipulate both the amplitude and propagation direction of the basic characteristics of EM waves, while traditional EAMs can only manipulate the amplitude.

Furthermore, as shown in Fig. S4, the far-field simulations demonstrate the advantages of the proposed SMAs for RCS reduction compared to EAMs. The EAMs can only reduce the maximum of the reflected beam due to the phase is continuously distributed, while the main reflected beam is always unique. Although the reflectivity of the three SMAs is close, which is determined by the energy in the normal direction, there are considerable differences in the far-field shape. Apart from the lobe in the normal direction, Patterns 1, 2, and 3 have 2, 4, and 8 main lobes and the far field maximums are − 4.74 dB, -6.43 dB, and − 9.19 dB, respectively. Because as the number of flaps increases, the limited reflected energy is more evenly dispersed in three dimensions, so the maximum energy gradually decreases, which contributes to the stealth performance under multi-station radars. In conclusion, the inverse mutation of the phase distribution in the 2-D plane transforms the energy concentration in the 1-D direction into the homogeneous distribution in 3-D space, with the reflected energy pooling in the nearby spatial region forward the SMA rather than propagating farther away. After absorption by the EAM elements that make up the SMA, the remaining reflected energy is further dispersed into several fractions and deflected away from the normal direction of propagation, thereby defeating detection.

3.3 Specific environmental stealth adaptation of coded SMA

SMAs with different patterns exhibit various far-fields, which shows the potential of the EAM elements for scattering field tailoring to meet the stealth needs of specific environments. Phased Array Theory demonstrates that waveform and beam direction can be changed by phase-compensating for different regions, so it is essential to develop tools for guiding the pattern of SMA design[49]. To increase the variety and freedom of scattering field tailoring, the four EAM elements were coded as shown in Fig. 5(a), where CIP 1:1, CIP 2:1, CIP 3:1, and CIP 4:1 were coded as 00, 01, 10, and 11 respectively. By coding, an arbitrary random SMA array in the physical world is transformed into a 16*8 matrix in the mathematical world. A 128-bit binary number consisting of 1 and 0 can be formed by expanding a 16*8 matrix by rows, thus each random SMA array corresponds to a 128-bit binary number, which means the connection between the physical and mathematical worlds is established. The purpose is to guide the array of random SMA using powerful computer technology to tailor the required scatter field. Figure 5(b-c) show the reflected amplitude and phase of the coded EAM elements in the 4–18 GHz. Notably, the size of all coded elements is 25 mm * 25 mm * 2 mm.

The scattering field of a random metasurface under the vertical incidence can be calculated by the superposition principle[50]:

$${E}_{Total}={\sum }_{m,n}{A}_{(m,n)}\text{exp}\left\{j\left[{P}_{(m, n)}+kd\text{sin}\theta \left(\left(n-\frac{1}{2}\right)\text{cos}\phi +\left(m-\frac{1}{2}\right)\text{sin}\phi \right)\right]\right\}$$

Where $E$ is the superposition field strength, $k$ denotes the wavenumber in free space, $d$ denotes the side length of the elements, ${A}_{(m,n)}$ and ${P}_{(m,n)}$ denotes the reflected amplitude and phase of the $m$ row and $n$ column elements, and $\theta$ and $\phi$ denote the elevation and azimuth angles, respectively. By this formula, the corresponding scattering field can be calculated quickly for a random SMA. The subject was modeled in the commercial mathematical software MATLAB, and a special genetic algorithm (GA) was written to find the optimal array to meet the requirements of the particular far-field waveform. Figure 6 shows the computational process diagram and the profile of the GA. By setting different fitness functions which represents specific stealth requirements, the GA can iterate continuously to obtain the optimal solution and finally generate the suitable SMA[51].

For example, when the practical requirement is the directional propagation of the reflected wave towards a non-threatened area, the fitness function is:

$${Fitness}_{1}={E}_{Total\left(\text{30,50}\right)}$$

With the selection of this fitness function, each generation of individuals evolves towards the direction of maximum energy at 30° in elevation and 50° in azimuth, eventually generating an SMA with the demanded pattern. With the selection of the ${Fitness}_{1}$, each generation of individuals evolves towards the direction of maximum energy at 30° in elevation and 50° in azimuth, eventually generating an SMA with the demanded pattern. Figure 7(a-c) show the SMA pattern optimized by GA at 8 GHz, 10 GHz, and 12 GHz respectively, and Fig. 7(d-f) show the corresponding both absorptivity and phase matrices of the SMA elements, where the size of the circle indicates the absorptivity and the color indicates the reflected phase. The binary number was transformed into an SMA and then modeled and simulated in CST, with Fig. 7(g-i) shows the corresponding results of the far-field. The far-fields of the three SMAs show obvious beam deflection in the same direction. And Fig. 7(j-l) shows the presence of a red region representing high energy in the upper right-hand quarter, which proves the directional concentration of the energy distribution. It needs to be noted that because ${E}_{Total}$ is an even function about $\theta$, the far-field distribution has symmetry, so symmetric beams appear in the far-field. Moreover, the limited number of elements in the array as well as the boundary difference led to accuracy errors between the simulation and calculation results, whereby the energy distribution deviated modestly from the intended direction.

In addition, when the practical application requirement is the best RCS reduction performance, the fitness function is

$${Fitness}_{2}=-\text{m}\text{a}\text{x}\left({E}_{Total(\theta ,\phi )}\right)$$

With the selection of this fitness function, each generation of individuals evolves in the direction of reducing the maximum energy of the far-field. Likewise, the optimal SMA patterns for RCS reduction were generated by computing iterations at 8 GHz, 10 GHz, and 12 GHz, respectively. Figure 8(a-c) show the optimal SMA pattern and Fig. 8(g-i) show the corresponding far-field simulation results. The optimal SMAs at each frequency exhibit excellent RCS reduction performance. Numerous wave lobes of close energy are evenly distributed in the spatial region adjacent to each SMA and the maximum far-field energies are − 11.77 dB, -11.14 dB, and − 9.69 dB, respectively. In addition, the homogeneity of the energy distribution is also demonstrated by the significant occupation of the cool-colored regions in Fig. 8(j-l).

The wide variety of far-field distributions demonstrates the environmental stealth adaptability of SMAs, such as the ability to transmit reflected waves directionally in a non-threat direction or evenly distributed in a three-dimensional area close to the SMA without propagating farther away. With the power of GA, the pattern of the SMA make of coded EAM elements for specific waveform requirements can be designed easily, which facilitates the practical application of the proposed SMA.

In conclusion, inspired by the coded metasurface, this work proposed a novel scattering metasurface absorber prepared completely from coded EAM elements without any electrically resonant structures. Compared to the limited stealth performance of traditional EAMs with a sole absorption mechanism, the proposed SMA with both absorption and scattering mechanisms shows powerful RCS reduction performance due to the manipulation of energy distribution in the 3-D space. Firstly, the symmetry model has shown that the reflected phase difference of the different EAM elements is derived from the different impedance mismatches which will generate opposite reflected phases respectively. This mechanism enables EAM elements to exhibit a wide reflected phase difference at thin thicknesses. The elements used, CIP 1:1 and CIP 4:1, shown 6.6–15.1 GHz reflected phase difference bands at 2 mm thickness, which is hard to achieve with traditional metasurfaces. Then the advantage of the broad bandwidth of the reflected phase difference translates into the enhanced anti-reflection performance of SMA, with reflectivity below 0.1 in the 7.8–16.7 GHz due to the synergistic effect of the dual mechanism of absorption and scattering to EM waves. Finally, to meet the stealth needs in specific environments, element encoding strategies and genetic algorithm were developed to optimize the SMA array to generate the desired scattering fields, such as the directional transmission of EM energy in 1-D or homogeneous distribution in 3-D. The proposed SMA creatively constructed fully from coded EAM elements with efficient broadband anti-reflection performance and specific environmental stealth adaptation pioneers a new path for advanced EM defense technology.

Funding

This work is supported by the National Natural Science Foundation of China (52071053, U1704253, 52103334), the China Postdoctoral Science Foundation (2020M670748, 2020M680946), and the Fundamental Research Funds for the Central Universities (DUT20GF111).

Author contribution statement

Wei Chen: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Writing - original draft. Yuping Duan: Project administration, Funding acquisition, Supervision, Writing – review & editing. Jiangyong Liu: Conceptualization, Writing – review & editing. Tuo Zhang: Formal analysis, Writing – review & editing. Yupeng Shi: Formal analysis, Writing – review & editing. Xinran Ma: Methodology, Writing – review & editing. Lingxi Huang: Funding acquisition, Writing – review & editing. Huifang Pang: Funding acquisition, Writing – review & editing.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflict of Interest

The authors declare no conflict of interest.

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Impedance mismatch derived coded absorbing materials: for ultra-broadband anti-reflection and scattering field tailored on demand

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Abstract

Figures

1. Introduction

2. Method And Strategy

2.1 Raw materials

2.2 Preparation of scattering metasurface absorbers

2.3 Program and simulation

2.4 Characterization and instruments

3. Results And Discussion

3.1 Reflected phase of EAMs

3.2 Anti-reflection performance of SMA

3.3 Specific environmental stealth adaptation of coded SMA

4. Conclusion

Declarations

References

Additional Declarations

Supplementary Files

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