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We report the design, fabrication, and measurement of a broadband metamaterial absorber, which consists of lossy frequency selective surface (FSS) and a metallic ground plane separated by a dielectric layer. The compact single unit cell of the FSS contains crisscross and fractal square patch which couple with each other. Both qualitative analysis by equivalent circuit and accurate numeric calculation show that the coupling between the crisscross and the fractal square patch can enhance the bandwidth with the reflectivity below −10dB in the frequency range of 2-18GHz by producing a third absorption null. In the end, the designed absorber was realized by experiment.
©2012 Optical Society of America
1. Introduction
Microwave absorber is a kind of function material that can be used in stealth technology. The applications in areocraft such as battleplan and missile determine that the absorber must have broadband wave absorbing performance to reduce the probability of being explored. As a potential candidate of high performance wave absorber, the researches of the metamaterial absorber are mostly concentrating on the perfect and multi-bands absorption [1–5]. Usually the Jaumann screen and lossy frequency selective surface (FSS) could realize broadband radar absorber [6–9]. Because of the egregious thickness of the Jaumann screen [6], lossy FSS absorber, which is consist of resistive FSS and dielectric substrate, is the best choice of the broadband absorber [9].
The main means of study the FSS absorber are numeric method and equivalent circuit method [9,10], also some optimization method is necessary due to the parameters determining the wave absorbing performance [11,12]. As to the single layer lossy FSS absorber, broadband wave absorbing performance can be realized through any FSS patterns [8,9]. But the optimal bandwidths of the familiar FSS absorbers have not been reported up to now. On the other hand, unlike the numerous FSS patterns designed in the HIP (high impedance surface) field [13–16], the FSS patterns reported in the lossy FSS absorber by far are simple, such as square patch, crisscross, and ring, whose impedance are represented by series RLC circuit [9]. In this letter, based on the optimized results of the conventional absorber, we report a broadband lossy FSS absorber using crisscross and fractal square patch to form a compact single particle. The reflectivity of the absorber exhibits three apexes in the frequency range of 2-18GHz. Moreover, owing to symmetry geometry, the absorber is independent on the polarization of an incident wave.
2. Optimization of the conventional FSS absorber
Take the square patches shape as an example; the three-dimensional sketch of the lossy FSS absorber is shown in Fig. 1(a) .
The FSS pattern can be changed arbitrarily. Figure 1(b) shows the circuit model of the absorber with simple FSS. In reference [9], the form of the two absorption nulls of the absorber was explained by circuital approach, and the wave absorption performance can be improved by adjusting the square resistance of the FSS. Here we optimize the absorbing bandwidth with the reflectivity below −10dB in the frequency range of 2-18GHz using Powell method. The optimization is performed based on Finite-Difference Time-Domain method. Both the magnitude and bandwidth of the reflectivity are considered in the goal function. The relative bandwidth unsatisfied the reflectivity threshold is nBW, and the average linear reflectivity is Ra which varies from 0 to 1. The goal function is established as follows:
whose optimal value is null. The weight coefficient of the bandwidth and the reflectivity in the goal function is 100 and 1, respectively. In the optimization process, the decrease of the nBW provides the main contribution to the minimum of the goalfunction.After optimizing the parameters of the absorber repeatedly, simulation results of reflection properties of the lossy FSS absorbers with different FSS pattern are obtained. The results are shown in Fig. 2 .
Fig. 2 optimized reflectivity of the conventional lossy FSS absorber with different FSS pattern. (a) The thickness of the absorber is 3mm. (b) the thickness of the absorber is 4mm.
As shown in Fig. 2, the absorbers with simple FSS have two absorption nulls. The bandwidth with the reflectivity below-10dB of the 3mm and 4mm thick simple FSS absorber are 7.1-18GHz and 5.9-18GHz, respectively. Increase the number of the reflectivity apex, especially in the low frequency, could enhance the bandwidth possibly.
3. Design of the broadband absorber
Figure. 3(a) shows schematically the unit cell of the designed absorber as well as the propagation configurations of the incident electromagnetic (EM) wave. The corresponding circuit model is shown in Fig. 3(b).
The crisscross and fractal square patch along the electric field direction can be modeled as series RLC circuit (Rf, L1, and C1 in Fig. 3(b)). To ensure the symmetry of the FSS, the crisscross arrange along the magnetic field direction. Electric and magnetic coupling occur between the vertical crisscross and the fractal square patch (see L2 and C2 in Fig. 3(b)). The FSS impedance calculated according to the circuit model shown in Fig. 3(b) is
Qualitative analysis from circuit model implies that compared with the FSS impedance denoted in Fig. 1(b), there are two resonances in the considerable frequency range. Figure 4 shows the imaginary impedance of the FSS (black) acquired from numeric calculation. The designed FSS has the dimensions, in millimeters, of a = 14.46, b = 11.31, c = 2.81, d = 2.88, l1 = 8.41, l2 = 3.21, w1 = 0.39 and w2 = 0.53.
Fig. 4 Impedance of a 4 mm grounded substrate and impedance of the designed FSS with periodicity. The resonances of the FSS and the absorber are highlighted.
Figure 4 indicates that two resonances (ω0, ω1) exist which is consistent with the circuit model analysis. To get an insight into the origin of the resonance, we monitor the surface current densities on the FSS at resonance frequencies as shown in Fig. 5 . The current loop shown in Fig. 5(a) indicates that the existence of ω0 is due to the coupling between the crisscross and the fractal square patch along the magnetic field direction. Figure 5(b) implies that the resonance in the high frequency occurs between the adjacent unit cells along the electric field direction.
The impedance of the grounded dielectric substrate can be obtained from transmission-line method:
The impedance of a 4mm thick substrate with the relative permittivity 1.5 is shown in Fig. 4 (red line). Using the conclusion shown in reference (9), three resonances exist between the FSS and the dielectric substrate (f1, f2 and f3), which indicates that the absorber has three absorption nulls.
To confirm the above analysis, two pieces of FSS absorber with the thickness of 3mm and 4mm are designed and optimized. The results are shown in Fig. 6 .
The results shown in Fig. 6 indicate that the bandwidths with the reflectivity below −10dB of the thin and thick absorber are 6.6-18GHz and 5.27-18GHz, respectively. The comparison of the results shown in Fig. 6 and Fig. 2 illuminates that the coupling in the unit cell of the FSS can produce absorption nulls in the low frequency and enhance the bandwidth of the corresponding lossy FSS absorber. The optimized parameters of the designed absorber are list in Table 1 .
Table 1. Optimized Parameters of the Designed 3mm and 4mm Broadband Absorber
The parameter t, εr and Rs in Table 1 represent the thickness of the absorber, the relative permittivity of the substrate and the square resistance of the FSS, respectively. The other parameters are denoted in Fig. 3(a).
4. Experiment
The feasibility of the broadband absorber was demonstrated by two experimental prototypes. The resistive patterns representing the lossy FSS have been manufactured by the silk printing technique through a photo etched frame. The commercial rigid polyurethane foam was used as the dielectric substrate. The pictures of 180mm × 180mm broadband samples are shown in Fig. 7 .
We verified the absorption performance of the broadband absorber in a microwave anechoic chamber. An Agilent 8720ET vector analyzer and two broadband double-ridged horn antennas are used to emit and receive the EM wave. Owing to the metal ground plane, the transmission is zero and the reflectivity represents the absorption. The measured reflectivity, compared with simulated result, is plotted in Fig. 8
Fig. 8 Comparison of the reflectivity of the broadband absorber between experimental (black curve) and simulated (red curve) results, (a) the thickness of the absorber is 3mm, (b) the thickness of the absorber is 4mm
Three absorption nulls exist in the considerable frequency range, which is consistent with the design result. The difference of the absorption intensity between the experiment and design is reasonably ascribed to the fabrication tolerances, such as the square resistance deviation of the lossy FSS. Both the simulation and experimental results indicate that the coupling in the FSS unit cell induces the absorption null in the low frequency, and lead to the enhancement of the bandwidth of the absorber.
5. Summary
In this paper, we firstly optimize the bandwidth of the conventional lossy FSS absorber with the reflectivity below −10dB in the frequency range of 2-18GHz. The absorbers with simple FSS pattern usually exhibit two absorption nulls. According to the equipment circuit method, we design a broadband lossy FSS absorber with a coupling FSS. The imaginary impedance and resonance currents calculated by numeric method indicate that the coupling lead to the low frequency resonance of the FSS, which will result of a third absorption null for the absorber. The design results show that the bandwidth with the reflectivity below −10dB of the 3mm and 4mm thick absorber can get 6.6-18GHz and 5.27-18GHz, respectively, which are broader than that of the corresponding absorber with conventional FSS pattern. In the end, experiments were carried out to confirm the design results. The fabricated absorber in this paper is light-weighted, thin and broadband, making it a good candidate using in the stealth technology.
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