An Ultra-Thin Low-Frequency Tunable Metamaterial Absorber Based on Lumped Element

In this paper, an ultra-thin metamaterial absorber with a stretching transformation (ST) pattern is proposed and fabricated in the low-frequency range. The absorber is composed of dielectric layer, metal patch loading resistor and variable capacitor which produce its tunability. In order to expand the tunable bandwidth, we applied the ST with various coefficients x and y to the unit cell pattern. Measurement and simulated results show that the structure can be tuned to provide a continuously variable reflectivity level of less than –10 dB from 0.68 to 2.13 GHz at bias voltages of 10–40 V. The total thickness of this absorber was only λ/31 of the center frequency. Both measurements and simulated results indicate that this absorber can be thin and achieve a tunable absorption simultaneously.


Introduction
Metamaterial absorbers (MAs) can efficiently dissipate the electromagnetic (EM) energy into heat, resulting in significant reduction of the reflected waves along the echo direction. However, limited to thickness and narrow bandwidth at frequencies below 3 GHz, the MAs will be difficult to be used in practice applications. Thus, MAs with small size and broadband absorption are urgently necessary.
The perfect metamaterial absorber [1] concept was first reported by Landy et al. In the microwave regime, this seminal work soon inspired work in other frequency ranges from terahertz to visible regime due to their potential application [2]. Among these MAs, since microwave MAs are thinner and lighter than the traditional microwave absorbers and can be used in military and commercial areas, which have been become a new research hot topic [3][4][5][6][7]. So far, several methods in common have been devoted to accomplish the wideband absorber. For instance, the absorption bandwidth can be broadened by constructing the metamaterial absorber array with periodic arrangement or superimposing the different resonance modes within a unit cell [8], [9]. Additionally, the fractal metal structures [10] and the multilayer [11][12][13] were realized to design wideband absorber. As a remarkable method, loading with lumped element was utilized to achieve broadband absorption [14][15][16]. Although many efforts towards the improvement of the performance about MAs are flourishing, the low-frequency and broadband absorber are not easily realized without lumped elements or increasing material thickness.
In this work, we present an ultra-thin MA with a stretching transformation (ST) pattern for use in low-frequency applications. The total thickness 6.036 mm is only λ/31 of the center frequency. Using the transmission line (TL) model, we can get the relationship between the resonant frequency and the real part of the input impedance. The equivalent circuit model is introduced to analyze the broadband and tunable absorption for the proposed MA. Then, we change the ST coefficients of unit cell pattern to expand the tunable bandwidth. Finally, we also fabricated and measured the proposed ultra-thin MA. The experiment results are given to validate the good performance of the MA.

Design and Analysis
A schematic of the proposed MA is depicted in Fig. 1(a), which is composed of the dielectric substrate sandwiched with periodic metal electric resonator loaded with resistors and capacitors and ground plane. The material of dielectric substrate is F4BM with dielectric constant 2.65 and the loss tangent is 0.001. Metal patch loaded with resistors and capacitors was placed above the dielectric layer. The middle layer is air and the bottom layer is a full metallic plate. The metallic structures and ground are coppered with conductivity of 5.8 × 10 7 S/m and the thickness of 0.036 mm. The MA is simulated and optimized. A fullwave electromagnetic simulation is performed by using finite-element analysis based High Frequency Structure Simulator (HFSS 14.0). The periodic boundary conditions (PBCs) and Floquet port are utilized to simulate the infinite periodic cells. The resistor and capacitors are simulated using a lumped LRC model. The optimized parameters of   y m Acos ax   In the simulation process, the master-slave boundary is applied to replicate an infinite planar array, and the incident wave is a plane wave with a linear polarization along the (-z) direction. Then, the absorbance of MA A(ω) = 1 -T(ω) -R(ω) is calculated using the frequency-dependent transmittance T(ω) = |S 21 (ω)| 2 and reflectance R(ω) = |S 11 (ω)| 2 obtained from the simulation. The transmission is zero (T(ω) = |S 21 (ω)| 2 = 0) attributed to the metallic plate without patterns on the bottom layer. Thus, the absorbance can be calculated using A(ω) = 1 -R(ω). In effective medium theory, effective permittivity ( = ' + j'') and effective permeability (μ = μ' + jμ'') are generally used to analyze absorptivity, because the characteristic impedance of a material can be defined as Z() = [μ()/()] ½ . But in some cases, electromagnetic parameters are not readily available. So the TL model is a powerful tool to interpret this structure. From Fig. 2(b), we realized that the resonance state exists and may be important for deep absorption. With R = 600 Ω, the absorbability was relatively good. Figure 2(a) shows the resonance frequency varies with capacitance when R = 600 Ω. To numerically analyze the absorption performance, we establish an accurate model for MA. Figure 3(a) shows the equivalent circuit model of MA based on TL theory [17]. By derivation, the equivalent impedance of MA can be expressed by the following formula:  The distributed parameters L d and C d are constant which is determined by the structure with x = y = 1. The values of lumped elements are R and C v , respectively. The real part of Z MA can be substituted with a resistor R', and the imaginary part of Z MA is a capacitor C'.  is the angular frequency of the electromagnetic wave. R' and C' are described by: Figure 3(b) shows the simplified equivalent circuit model. The resonance frequency f of the simplified circuit is described as: According to (2), (3), (4), the real of equivalent impedance at resonance frequency can be expressed by the following formula: ST is applied to the unit cell pattern. The size of the unit cell is (x × P),(y × P), where P is the basic size before ST and x and y are the ST coefficients on each side. The topological structure of the MA pattern significantly affects the resonant frequency of the absorber. A larger unit cell will have a lower resonance frequency. L d and C d represent the distributed parameters, including inductance and capacitance. When the input impedance of the MA matches with that of free space, the real part will be 377 Ω and the imaginary part will be 0. According to (2), (3), (5), the resonance frequency f and the real part at resonance Re(Z MA ) are functions of L d , C d , C v , and R. In this case, the resonance frequency f and Re(Z MA ) depend only on the lumped elements C v and R.
The resonance frequency f varies with the capacitance of the varactor C v as shown in Fig. 4.When the value of resistance was fixed at 600 Ω, the simulated curve with various C v was shown in Fig. 4(a), which coincided well with the calculated curve. The calculated curve of f-C v in Fig. 4(b) was calculated according to (4), which described that the resonant point is a descending function of C v . Figure 5 shows the relationship between f and R. With C v = 1 pF, we get R-f curves when R changes from 300 to 1500 Ω, as shown in Fig. 5(a). Figure 5    On the whole, the resonance frequency f is mainly contacted to C v , while the real part of Z MA at resonance frequency is mainly related on R. The MA which is loaded with a resistor and varactor is designed with a tunable absorber. Using the varactor which provided a variable capacitance at varying bias voltages produces the device's tunability. Resistor reliably generated strong absorption at the resonance frequency, which is realized by using a lumped constant resistance.
It makes sense to expend the tunable bandwidth of MA, based on our qualitative analysis of R and C v . In addition to resistor and capacitor, the structure parameters also have a greater impact on the absorption characteristics. Through varying ST coefficients of the unit cell pattern, the tunable bandwidth can be expanded. We designed five patterns in Fig. 7. The curve of resonance frequency changing with capacitance value under different patterns was shown in Fig. 7. These patterns are conversions of the pattern shown in Fig. 1(a). As we can see from the figure, when the capacitance varies from 0.5 pF to 5 pF, the model 2 has the widest tunable bandwidth.

Simulation and Discussion
The feasibility of the proposed absorber is demonstrated by prototypes with the size of 300 mm × 288 mm. The prototypes of absorber have been fabricated using a common printed circuit board method on the substrates with the thicknesses of 1 mm and they are illustrated intuitively in Fig. 8(a), where the ST coefficients are x = 0.8, y = 1. Capacitance is controlled by using bias line to load different voltages. The bias lines with the same voltage are connected together. The measurement setup is composed of a vector network analyzer (Agilent N5230C) and two linear polarized standard-gain horn antennas. The antennas are placed vertically to the sample to ensure normal incidence. One horn antenna is used to transmit, and the other horn antenna receives the reflected waves. Figure 9 shows the measured reflectivity curves of MA for different voltage. As we changed voltage from 10 to 40 V using the power control system, the resonant point covered a frequency band of 0.68-2.13 GHz with the reflectivity below -10 dB. The experimental results show good agreement with the simulated results. There are small discrepancies such as the depth of the peak but these discrepancies can be accepted in both the simulation and the measurement system.
For comprehensive comparison, we define the relative volume Rv of a unit cell as follows: where λ 0 is the wavelength of the center frequency for absorption bandwidth and Tv is the total volume of a unit cell. In order to synthesize the relative absorption bandwidth BW of these absorbers in reference, we have evaluated the cost-efficient bandwidth BW CE defined as: In reference, the resistive surface has been applied for increasing absorption bandwidth. Obviously, the intrinsic advantages of the proposed absorber include not only that it can be easily implemented using the inexpensive printed circuit board fabrication techniques but also that it exhibits low-profile and wideband absorption. From Tab. 1, it is seen that our proposed design performs the smallest relative volume Rv and the most cost-efficient bandwidth BW CE (3295.5) of a unit cell.

Conclusion
In conclusion, we have designed and fabricated a tunable MA which performed broadband absorption at lowfrequency controlled by the bias voltage. By establishing the TL model, we obtained the function of the resonance frequency, real part of input impedance and loaded. To demonstrate the tunability and strong absorption, we analyzed ST coefficients to the unit cell pattern. The calculated results suggest that the capacitance modulates the imaginary part of the input impendence, producing the tunability, while the resistor mainly adjusts real part, producing the strong absorption. For further optimization of ST coefficients, we realized that the value of x and y effectively expand the tunable bandwidth. Finally, we measured the reflectivity curves of MA for different voltage. Measurement results show that the structure can be tuned to provide a continuously variable reflectivity level of less than -10 dB from 0.68 to 2.13 GHz, and the total thickness 6 mm is only λ/31 of the center frequency. Measurements are in good agreement with results obtained from simulations. The proposed MA shows great promise for a variety of application such as detectors and solar cells in the future.
He has authored and coauthored more than 100 technical journal articles and conference papers, and holds one China soft patent. His research interests include smart antennas, electromagnetic metamaterial and their antenna applications. HuanHuan YANG has received the M. Eng. degree in Electronic Science and Technology from the Air Force Engineering University, Xi'an China, in 2012. His research activity has been focused in polarized reconfigurable antenna He has authored and coauthored more than 30 scientific papers in major journals and international conferences. His research activity has been focused in the broadband perfect metamaterial absorber and its application for RCS reduction of antennas. He is a reviewer of Applied Physics Letter, Journal of Applied Physics, IEEE Transactions on Microwave Theory & Techniques, IEEE Transactions on Antennas & Propagation, IEEE Antennas Wireless Propagation Letter, Electronic Letters and Microelectronics Journal.
Liaori JIDI was born in SiChuan province in 1994. He received the B. S. degree from the Information and Navigation College, Air Force Engineering University in 2017. He is now a graduate student. His research interest is in electromagnetic metamaterial. He has been working with the EMC Lab. His research activity has been focused in the broadband perfect metamaterial absorber and its application for RCS reduction of antennas.