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A new type of multi-layer metamaterial (MM) absorber is represented in this paper, which behave as a dielectric slab in transmission band and act as an absorber in another lower band. The equivalent circuit model of each layer in this MM absorber has been established. The transmission line (TL) model is introduced to analysis the mechanism of electromagnetic wave traveling through this MM absorber. Both theoretical and experimental results indicate this MM absorber has a transmission band at 21GHz and an absorptive band from 5GHz to 13GHz. A good match of TL model results and measurement results verified the validity of TL model in analyzing and optimizing the performances of this kind of absorber.
©2012 Optical Society of America
1. Introduction
As a kind of novel microwave absorber, metamaterial (MM) absorber has got much attention in recent years. The concept of this sort of absorber was firstly presented in 2008 [1–3], Landy et al utilized three layers structure (two MM layers and a dielectric layer embedded) to absorb all incident microwave. Each MM layer performs either inductive or capacitive separately, the absorber resonates intensively at a single frequency thus the absorbing band is rather narrow [4,5]. A resistively loaded high impedance surface (HIS) with a underneath metallic plane is employed to achieve wideband absorbing in later works [6–8], the absorbing band can be form 5GHz to 25GHz. Although such design makes MM absorber more practical in many applications, restricted by the existence of metal plane, it does not apply to the situation which need microwave be absorbed/reflected in one band and transmit in another, such as a radome. Costa et al presented a novel radome which has a lower transmit band and a higher wide absorbing band by changing underneath metallic plane of HIS to a frequency selective surface (FSS) [9]. For generating two different functional bands, the periods of FSS cell and HIS cell are not the same. In this paper, we present a lumped resistor loaded metamaterial absorber, the absorbing property of which is similar to the resistively loaded HIS absorber. Unlike using different cell size FSS and HIS in previous works [9,10], we adopt a FSS structure whose cell size is the same as HIS cell. This design will produce a transmission band above the absorbing band, which is available in some electromagnetic or optical applications. Besides, it is not sensitive to polarization of incident wave by the symmetry geometry.
2. The TL model of the metamaterial absorber with transmission band
Figure 1 shows a unit cell of the MM absorber with transmission band, which includes three layers: lossy layer, dielectric layer and metallic strips layer.
For the lossy layer, 4 metallic wires connected by lumped resistors at each corner of cell square constitute a conducting ring. The electronic loss generated by induced current flowing through lumped resistor will consume a lot of EM energy when the mm absorber working in resonant band. The triangle patches beside each wire are adopted for tuning resonance. The bottom layer of unit cell consists of 4 metallic strips on every side of the cell square, leaving a hole at center. It can be seen as a grid of metallic mesh structure which is usually utilized to realize band-pass FSS [11]. If the lower frequency of pass band is much higher than the upper frequency of absorbing band, the structure will achieve both absorption and transmission properties. Assuming coupling effects between those three layers negligible, each layer can be individually modeled and the propagation of EM wave can be represented by a TL model, as demonstrated in Fig. 2 .
Similarly to the processing Costa et al. adopted [6], lossy layer is modeled by a series RLC circuit, the impedance of which is:
The value of R1 is equal to the resistance of lumped resistor, L1, C1 value can be obtained by the inversion method proposed in [12]. For the structure shown in Fig. 3(a) , C1 = 7 fF, L1 = 4 nH, R1 = 130 Ω. The equivalent circuit model of metallic strips layer is a parallel connection of an inductance L2 and a capacitance C2 [13]. If electric field of incident wave polarizes along the strips, their values are determined by: Where Z0 is wave impedance of free space, α, α’ are grid-parameters, their values are represented through: Where the prime in the sum denotes that the summation is made over all n except n = 0. kx = ksinθcosφ, ky = ksinθsinφ, k is the free space propagation constant, θ and φ are shown in Fig. 1. If EM wave normally incidents into the MM absorber plane, θ = 0°, thus kx = 0, ky = 0. As shown in Fig. 3(b), D is the cell periodicity, p is gap width and q is half width of the strips between two adjacent gaps. According to the theory of microwave network, the transfer matrix of the cascade networks shown in Fig. 2 can be represented as the product of three individual one:Where A, B, C, D are the elements of the transfer matrix, d is the thickness of the dielectric layer, Zm and βm is characteristic impedance and propagation constant of the dielectric layer respectively. The scattering matrix will be calculated through A, B, C, D [14].3. Simulation and experiment results
Figure 3 shows the corresponding parameters of the MM absorber. The yellow portion is copper with thickness of 0.017 mm and conductivity of 5.8 × 107 S/m, the green portion is dielectric with thickness of d = 4 mm and relative permittivity of 2. CST microwave studio is utilized to simulate the scattering matrix of MM absorber. In simulations, the corresponding parameters are optimized and determined by R = 130 Ω, D = 11mm, w = 0.8mm, l = 6.8mm, s = 0.5mm, g = 1.41mm, p = 6mm and q = 2.5mm. To experimentally verify the applicability of TL model, a MM absorber sample is fabricated and the cell parameters of which are the same with what used in simulations. The length and width of FR4 board are both 330mm, the thickness is 4mm with ± 5% error. Surface mount resistors (Panasonic Size 0805) are adopted as lumped resistors, the resistance of which is 130Ω with ± 1% tolerance. There are 30 × 30 cells on two sides of the board, as shown in Fig. 4 .
In experiments, the interesting frequency bandwidth is more than 22GHz, thus four horn antennas of two types are used to as input and output port in different bands. Two double-ridged horn antennas (ETS·LINDGRENTM Model 3115) with the same performances are adopted in 3-18GHz and another two normal horns (XIANHENGDA HD-180DRHA15S) are utilized in 16-25GHz, notice there is an overlapped band about 2GHz between these two bands. The partial S-parameter curves will be formed into an integrated one which covers the band of 3-25GHz. A vector network analyzer (Agilent 8363B) is utilized to measuring the complex S-parameters between two ports, the relationship between S-parameters and transmission/reflection coefficient T(ω)/R(ω) is given by T(ω) = |S12(ω)|2, R(ω) = |S11(ω)|2. Figure 4(a) and 4(b) show the reflection and transmission coefficient curve by using TL model (black solid line), CST simulation (blue solid line with square) and measurement (red dot) of a fabricated sample respectively. It can be seen that S-parameter curves calculated from TL model match the CST results and experiment results well in the whole frequency region, which indicate that the TL model is correct and effective. There are three nulls in the reflection coefficient curve. The first null at 5.5GHz with the value below −17dB is an absorption null, according to the −15dB transmission coefficient shown in Fig. 5(b) . The second one at 13.5 GHz is a partial transmission null because the transmission coefficient at this frequency increases to −7dB. The band between 5.5GHz and 13GHz can be seen as an absorptive band. At about 21GHz, a peak in the transmit curve verifies the existence of transmission band and the maximum transmission coefficient reaches −1.2dB.
To analysis the influence brought by the change of bottom layer, we modeled, simulated and measured the mm absorber sample whose bottom layer is altered by a metal plane. Figure 6 shows the corresponding S-parameter curves. Due to the metal plane, the transmission coefficient is equal to zero, so only reflection coefficient curves have been presented. Comparing those curves shown in Fig. 5 and Fig. 6, it is obvious that the second null in reflection coefficient curve will change from an absorption null at 14.8 GHz to a partial transmission null at 13.5 GHz if the bottom metallic layer is altered to a conducting crossed strips layer, which means the absorption band is decreased. That is because the lower frequency of transmission band is not higher enough than the upper frequency of absorption band, an unexpected overlapped band come out. Changing parameters of metallic strips or using other pattern on the bottom layer will solve this problem.
4. Conclusion
A type of multi-layer MM absorber which possesses a transmission band is represented in this paper. The TL model of this mm absorber have been obtained and verified correct and effective by CST simulation and experiment results. The fabricated sample has a transmission band at 21GHz and an absorbing band from 5GHz to 13GHz. This new-style mm absorber is useful in engineering and should be given more attention.
Acknowledgment
This work was partially supported by the National Science Foundation of China (Grant No.60871069).
References and links
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