Abstract
A millimeter-sized artificial periodic structure material is successfully simulated, showing the characteristics of a thin geometric scale, broadband response, and high wave absorption. The periodic structural units are stacked with metal circles, notched circular rings, and the dielectric material. The design is similar to a quasi-two-dimensional planar structure and maintains the broadband while reducing the number of layers in the stack. In addition, the electromagnetic model of this microstructure is established to study its S-parameters and suction properties through the electromagnetic simulations. Numerical results reveal that when the wave is incident vertically, the absorption is over 90% in the frequency range of 14.4-14.8 GHz and 15.4-20.6 GHz. The absorber features the same absorption for different polarization states.
1. Introduction
Metamaterial is an artificial structural material composed of subwavelength units, either periodic or nonperiodic, with exotic and peculiar physical properties such as negative refractive index or negative magnetic permeability [1–4]. The geometry of this structural material is simple, and different electromagnetic properties can be realized by adjusting the parameters of the structure, such as electromagnetic wave absorption [5–7], electromagnetic wave transmission, or controlling the reflection phase [8–10]. This artificial structural material has received extensive research attention since its proposal, especially in the design of invisibility devices [11–14].
However, the absorption bandwidth of most metamaterial absorbers is narrow, which makes them limited in practical applications. To solve the issues, dual-frequency absorbers, multifrequency absorbers, and broadband absorbers have also been proposed [15–18]. For example, the fractal structure is involved in the design, leading to multiple local resonant circuits and thus contributing to three strong absorption peaks across the S, C, and X bands, respectively [19]. To date, several approaches have been proposed to widen the operating bandwidth. The impedance of the structure can be matched to the free space by using lumped elements such as resistance, capacitances, and diodes, thus reducing the reflection of electromagnetic waves [20]. The electromagnetic energy is converted into heat energy in the resistance and then forms the electromagnetic wave absorption. As for the lumped approach, it is impossible for high-frequency operation and leads to even more complexity. The emergence of indium tin oxide (ITO) with resistance characteristics effectively solves the problem and makes it possible to design the broadband absorber. For example, the design of multilayer planar ITO patterns can create broadband absorption [21, 22]. The absorber with a planar array and a vertical array, improves the wide-angle polarization-independent absorption [23, 24]. However, this structure of the metamaterial absorber is complex in design and increases the thickness of the absorber. On the other hand, multilayer stacked structure becomes a subject of metamaterial design through the stacking of material layers or the stacking of resonant structures. In general, one resonant unit corresponds to one absorption peak. Multiple resonant units produce multiple absorption peaks due to resonance. When these absorption peaks are located close together, the energy of electromagnetic waves is consumed in the dielectric, forming a broadband absorption. The vertically stacked broadband absorber was first proposed by the He group operating at terahertz frequencies [25] and then demonstrated in other frequency regime. At microwave frequencies, Ding et al. and Kim et al. have proposed broadband absorbers by the stacking of longitudinal structures [26, 27]. Based on the longitudinally stacked metamaterial absorbers, Long et al. expand the absorbing bandwidth of the structure by laterally alternately inserting another pyramidal array of small sizes [28]. Although the design of the multilayer stacked structure is simple, the influence of the number of stacked layers makes it difficult and expensive to process this multilayer stacked structure material. Consequently, researchers have designed different structures to improve this problem, such as the broadband absorber with a full dielectric multilayer structure without metal or the absorber with an embedded metal resonant unit [29, 30].
In this work, an artificial structural absorbing material is demonstrated by stacking resonant structures. The design is small in size and thin in thickness, making it easier to process on flexible substrates by introducing the stacking of circles and notched circular rings to enable the structure to be a flat, quasi-two-dimensional planar structure. The S-parameters and the polarization characteristics of the structure are simulated in the electromagnetic software. In addition, the absorption mechanism of the stacked resonant structure is discussed.
2. Results and Discussion
2.1. Design
The unit cell of the proposed structure is shown in Figure 1, which consists of three layers, namely the back metallic plane, the dielectric layer, and the stacking layer. The stacked layer contains two parts: the circles and the notched circular rings, which are stacked in sequence according to the metal-dielectric-metal structure. A copper-metal backplane of thickness 0.018 mm and conductivity is used to design the structure. Flame Retardant 4 (FR4) is used as the dielectric material with a relative permittivity and an electric loss tangent equal to 4.3 and 0.025, respectively. The stack of circles has a total of seven layers, and the stack of notched circular rings has three layers. Detailed geometric parameters are shown in Table 1.
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2.2. Simulation Results and Discussion
The comparison of and normalized absorption of the two structures are shown in Figures 2(a) and 2(b). The absorption is calculated as where the reflection and transmission are obtained from and , that is , . The metallic back plate blocks transmission, resulting in zero transmission. Thus, the reflection coefficient determines the absorption characteristics. It should be noted that the value of less than −10 dB means a 90% absorption. The band with absorption larger than 90% in the red curve is ranging from 15.792 GHz to 20.592 GHz. Compared with the nonnotched structure, the circular rings with two-notch structure have lower and higher absorption in the frequency band ranging from 15.792 GHz to 20.592 GHz. The polarization characteristics of the circular rings with two-notch structure are shown in Figures 2(c) and 2(d). of TE mode and TM mode are quite different. This is due to the fact that structure does not have a 90-degree rotational symmetry. When the direction of the notch is in the -direction, of the structure is mutually opposite to the structure with the notch in the -direction. Thus, the structure is sensitive to the polarization.
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2.3. Optimized Design
The improved model is shown in Figure 3. The number of layers of the notched circular rings has changed from three layers to seven layers. The overall thickness of the structure reduces from 3.358 mm to 1.605 mm. The optimized and modified parameters are shown in Table 2.
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2.4. Optimized Simulation Results and Discussion
The band with absorption larger than 90% is ranging from 14.4 GHz to 14.8 GHz and 15.4GHz to 20.6GHz in Figure 4(b). The relationship between wavelength and frequency is . The wavelength and size of the structure decrease as the frequency increases. In Figure 5(a), the top circle radius affects the highest operating frequency of the structure, and the smaller radius means a wider band. Here, the structure contains only a stack of seven layers of circles. However, this leads to discontinuities in the band with an absorption rate above 90%. Hence, the formation of a broad and continuous absorption band at high frequencies requires a sufficient number of layers to be stacked and the dimensions of the circles to be close together. Figures 5(b) and 5(c) shows the comparison of and the normalized absorption for the two structures. The addition of the notched circular rings enhances the ability of the structure to absorb electromagnetic waves without increasing the thickness and provides a continuous band with an absorption rate above 90%.
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The four-notch structure is simulated under different polarizations and oblique incidence in Figure 6. Here, is defined as the angle between the E field and the -axis and is defined as the angle between the wave vector and the normal. As the increases, the absorption of structure has a slight change. Under TE mode, the absorption rate is still above 85% when the angle varies from 0° to 30°. The absorption rate drops rapidly when is 45° and maintains 70% absorption. For TM polarization, at 16-18GHz, the absorption of the structure decreases with increasing angle . The structure is able to maintain an angular stability of 40°. Thus, the absorber exhibits relatively high absorption under large incident angles for both TE and TM polarizations. The structure is insensitive to the polarization. The performance of the proposed absorber and some published absorbers are listed in Table 3. In comparison to the published absorbers, the proposed absorber has lower layers and has an advantage in thickness and dimension.
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3. Analysis
The effective medium theory method [31–33] is used to calculate the relative impedance of the optimized structure in the frequency range of 14GHz-22GHz. The real part of the relative impedance is close to one, and the imaginary part is close to zero, indicating that the structure has low reflectivity. where is the reflection coefficient; is the impedance of the free space; is the impedance of the absorbing material; and is the normalized impedance.
The electric loss tangent is defined as . is the real part of the relative permittivity, and is the negative part of the relative permittivity. The real part indicates the ability of the material to store the electric energy, and the imaginary part indicates the loss of the electric energy. Figure 7(b) shows the relationship between the relative permittivity and the absorption performance of the optimized structure. Here, it is assumed that the real part and imaginary part of the relative permittivity do not vary with the frequency and temperature. As the electric loss tangent decreases, there is a sharp drop in the absorption magnitude, and the range of the band is reduced significantly. This also confirms that the imaginary part affects the loss capacity of material when the real part is the same.
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To better understand the absorption mechanism of the circular rings with a four-notch structure, the electromagnetic field at resonant frequencies is depicted in Figure 8. It reveals that the electromagnetic field is absorbed at some part of the structure. At 15.96 GHz, the electromagnetic distribution is at the bottom of the stacking of circles and notched circular rings. With the gradual increase in frequency, the distribution of the electromagnetic field also gradually moves to the upper layer. This is consistent with the relationship between the frequency and the wavelength. Metals and dielectrics are the two major constituents used for constructing metal-dielectric metamaterial absorber structures. The material of the circles and notched circular rings of varied sizes is copper, which provides the electric response by coupling strongly to the incident electric field at the resonance frequency. The dielectric layers play a role in controlling the electromagnetic fields. Due to the high electric loss tangent, FR4 layers consume energy and create a wave-absorbing effect. Each resonant unit corresponds to a specific resonant frequency. Since the size of the adjacent metal layers is close, at resonant frequencies, the electromagnetic field is not distributed in a particular dielectric layer. That is, several neighboring metal layers and dielectric layers together form a resonance. Within a consisting of a mix of resonators of various sizes, the stacking of the circles and notched circular rings creates the effect of broadband absorption. In addition, the distribution of the electromagnetic field is influenced by the polarization modes. Under TE mode, the electric field distribution of the stacking of circles is concentrated in the y direction, and the magnetic field distribution is concentrated in the x direction. The situation under TM mode is the opposite of the TE mode. However, the electric field of the notched structure in the two polarization modes is concentrated on both sides of the notched circular rings, and the magnetic field is concentrated in the middle of the notched circular rings. The surface currents at 17.4 GHz and 20.3 GHz under TE mode and TM mode are shown in Figures 9 and 10. The movement of free electrons in metals results in an induced surface current under the applied electric field. Antiparallel currents are formed on the upper and lower surfaces of the copper circle, resulting in a magnetic resonance. The dielectric layer enables the generation of a magnetic response between the two metal layers. Therefore, the stack of copper and dielectric FR4 creates an impedance match in the structure, allowing the energy of electromagnetic waves to be consumed in the absorber.
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4. Method
4.1. Simulation Settings
All numerical design and characterizations are conducted through the simulations in the software CST Studio Suite. The frequency domain solver and floquet port are selected to simulate the periodic structure. The periodic boundary conditions are applied along the x-axis and y-axis. The electromagnetic wave is incident along the negative direction of the z-axis, and the port is set at a distance of 2 from the model structure. The adaptive mesh is selected for analysis to improve the accuracy of the simulation model. The convergence threshold is set at 0.01 to meet the accuracy of most simulation models, and the convergence number is set at 3 to avoid pseudo convergence.
4.2. Discussion on Fabrication and Measurement
The proposed absorber is stacked in sequence according to the metal-dielectric-metal structure. Micronano etching and metal deposition processes can be used to achieve the fabrication of the multilayer metamaterial structure. The patterned structure of each layer can be formed by the micronano etching process. Copper films are deposited on the surface of the dielectric substrate. Seven composite layers are then sandwiched using an adhesive (whose dielectric constants are the same as FR4). As shown in Figure 11, we made samples of a two-notch circular ring structure, and waveguide method was used to verify the absorption [34]. It only needs small-scale test samples, and the measurement system is also simple. One port of the waveguide is installed on the structure which is cut to the same size as the inner aperture of the port, including four units of the sample. The length of the waveguide is 20 cm to meet the far-field incidence conditions. The absorber has a back metallic plate, so that . The other port of the waveguide is connected to the CMT M5180 network analyzer. By measuring , we can obtain the corresponding absorption. It can be seen that the simulation and experimental results have some consistency. At 15.7 GHz-18 GHz, the absorption rate of the sample is over 80%. The four-notch circular rings structure can be fabricated and measured using the same method described above.
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5. Conclusion
In this paper, a new artificial structural absorbing material is proposed through the costacking of circles and notched circular rings. The numerical results show that the absorption of designed structure is above 90% in 14.4-14.8 GHz, and 15.7-20.6 GHz. The overall thickness of the absorber is 1.605 mm. The circular rings with four-notch structure have a 90-degree rotational symmetry, and the structure is insensitive to the polarization. The proposed absorber has good angular performance with the incident angle up to about 45° for TE-polarized incidence whereas 40° for the TM case. In addition, based on the simulation of the electromagnetic field distribution and surface current, the mechanism of the stacked artificial structural absorbing material is discussed. Metal and dielectric layers provide the electric response and magnetic response, respectively. The electromagnetic responses cause the change in the impedance of the structure, which result in the consumption of the incident wave energy. Each of the resonant structure corresponds to the absorption of the corresponding frequency band, and as the stacked structure layer increases, the absorption band increases accordingly. The costacking of the two structures effectively enhances the absorption capacity of the structure. Compared to single-shape stacking, stacking of multiple resonant structures can form a continuous broadband absorption while reducing the number of stacking layers and have value for the engineering implementation.
Data Availability
The data that support the findings of this study are available from the corresponding author on reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
Authors greatly appreciate the meaningful discussion with Prof. Zhengyu Ye on the structure and the proposal for optimization from Prof. Erik D. Goodman.