Polarization-insensitive FSS-based perfect metamaterial absorbers for GHz and THz frequencies

Authors


Abstract

New perfect frequency selective surface (FSS) metamaterial absorbers (MAs) based on resonator with dielectric configuration are numerically presented and investigated for both microwave and terahertz frequency ranges. Also, to verify the behaviors of the FSS MAs, one of the MAs is experimentally analyzed and tested in the microwave frequency range. Suggested FSS MAs have simple configuration which introduces flexibility to adjust their FSS metamaterial properties and to rescale the structure easily for any desired frequency range. There is no study which simultaneously includes microwave and terahertz absorbers in a single design in the literature. Besides, numerical simulations verify that the FSS MAs could achieve very high absorption levels at wide angles of incidence for both transverse electric and transverse magnetic waves. The proposed FSS MAs and their variations enable many potential application areas in radar systems, communication, stealth technologies, and so on.

1 Introduction

Metamaterials (MTMs), artificially created electromagnetic (EM) materials, have gained a great attention of the scientific community. The main reason is that MTMs show specific EM features which are not ordinarily encountered in the nature such as negative permittivity, negative permeability, negative refractive index, and so on [Smith and Kroll, 2000; Sabah, 2008; Hwang, 2006; Ziolkowski and Cheng, 2004]. Also, they have extensive potential applications like cloaking [Alù and Engheta, 2008], absorber [Dincer et al., 2013a], super lens [Fang et al., 2005], sensing [Tao et al., 2011], antenna [Si et al., 2013], EM filters [Sabah and Uckun, 2009], and so on [Dincer et al., 2013b; Sabah, 2013; Shadrivov et al., 2005; Odabasi and Teixeira, 2012; Akgol et al., 2011; Lehtinen, 2012; Khodja and Marengo, 2008; Arslanagic et al., 2007; Alù and Engheta, 2007].

In recent years, the scientists who study MTMs have also concentrated on designing metamaterial absorbers (MAs) by using different MTM structures. There are several MA studies in the literature. These studies are commonly realized in the microwave regime. However, for the last few years, researchers have also started to study terahertz and infrared frequency ranges. Kollatou et al. [2013] studied polarization-independent MAs that work in the microwave frequency range. Landy et al. [2008] offered the design of an absorbing MTM element with near unity absorbance of 96%. Sun et al. [2011] designed an extremely broad band absorber based on destructive interference mechanism. Lee and Lim [2011] presented a bandwidth-enhanced microwave absorber using a double resonant MTM.

Tao et al. [2010] introduced design, fabrication, and characterization of a dual-band MA. Their MA shows absorption peaks of 0.85 at 1.4 THz and 0.94 at 3.0 THz. Tao et al. [2008] announced a MA that acts as a strong resonant absorber at terahertz frequencies. However, experimental absorptivity of their structure is demonstrated at 70% at 1.3 THz. Cheng et al. [2012] reported the design, characterization, and experimental demonstration of an infrared dual-band MA having peaks of 74% and 96%.

Kim et al. [2012] studied a broadband terahertz absorber consisting of multilayer glass spheres and polydimethylsiloxane. The absorption is higher than 98% in the frequency range between 0.7 and 2.0 THz. Hu et al. [2013] numerically designed a terahertz MA which has four narrow bands with high absorptivities of 98%, 97%, 98%, and 97% at frequencies of 0.68 THz, 1.27 THz, 2.21 THz, and 3.05 THz, respectively. Dai et al. [2013] proposed and numerically investigated a double-sided polarization-independent plasmonic absorber. Qin et al. [2012] numerically demonstrated the performance of a dual-band terahertz FSS MA. Sun et al. [2012] reported design, fabrication, and measurement of a broadband metamaterial absorber, which consists of a lossy FSS and a metallic ground plane separated by a dielectric layer.

First, we have carefully reviewed the literature on MA studies. Second, we designed and realized several perfect FSS MAs that work in microwave and terahertz frequency ranges. These FSS MAs show perfect absorptivity in single, dual, triple, and even in quadruple absorption bands within the frequency range we have been investigating which is the main objective of this study. All FSS MA structures are investigated with respect to their dependency on polarization angles and incident angles for both transverse electric (TE) and transverse magnetic (TM) waves. Also, the suggested models have very simple geometrical patterns comparing with the other studies in literature [Lee and Lim, 2011; Cheng et al., 2012; Kazemzadeh and Karlsson, 2010; Landy et al., 2008] which allow easy fabrication process and show perfect absorption as well as rescaling (scale-up and down) the structure for other regimes of EM spectrum. Moreover, having perfect absorption at single or multiband gives a distinct advantage on many MA applications [Dai et al., 2013; Tao et al., 2010; Landy et al., 2008; Cheng and Yang, 2010].

2 FSS MAs in Microwave Frequency Range

Structure 1 of the FSS MA design is based on omega resonator with gap and octa star strip configuration [Dincer et al., 2013a]. The other designed FSS MA structures are based on various shapes like plus and cross signs with and without a rectangular frame. All such designs contain a resonator, a metallic sheet, and a dielectric substrate. Due to low-cost manufacturing methods and relatively low dielectric loss, the top resonator and bottom metallic plate are separated by the FR4-dielectric substrate and placed parallel to each other. Resonator and the metallic layer are modeled as copper sheets with electrical conductivity of 5.8 × 107 S/m and thickness of  0.036 mm. Particularly, low loss is a very significant factor for MA applications in order to achieve perfect absorption. The thickness, loss tangent, relative permittivity, and permeability of the FR4 are 1.6 mm, 0.02, 4.2, and 1, correspondingly. Figure 1 shows the designed structures with their dimensions.

Figure 1.

Dimensions of the suggested FSS MAs for microwave frequency range: (a) Structure 1 a1 = 10 mm, a2 = 5 mm, a3 = 20 mm, a4 = 2 mm, a5 = 1 mm, and a6 = 14 mm. (b) Structure 2 a1 = 5.909 mm, a2 = 20 mm, a3 = 22 mm, and a4 = 3 mm. (c) Structure 3 a1 = 4 mm, a2 = 6 mm, a3 = 20 mm, a4 = 26 mm, a5 = 24 mm, and a6 = 18 mm. (d) Structure 4 a1 = 18 mm, a2 = 6 mm, a3 = 20 mm, a4 = 29 mm, a5 = 1 mm, a6 = 4.5 mm, and a7 = 24 mm.

3 FSS MAs in Terahertz Frequency Range

Structure 5 and Structure 6 with their dimensions are shown in Figure 2. The designs consist of a resonator, metallic layer, and a dielectric substrate. Resonator and metallic layer are modeled as silver sheet with electrical conductivity of 6.3 × 107 S/m and thickness of  1 um. Silver is soft, white, lustrous transition metal and possesses the highest electrical conductivity of any metal. Resonator and metallic plate are separated by the Quartz (Fused)-dielectric substrate and placed parallel to each other. The thickness, loss tangent, relative permittivity, and permeability of the Quartz (Fused) are 100 um, 0.0004, 3.75, and 1, respectively.

Figure 2.

Dimensions of the suggested FSS MAs for terahertz frequency range: (a) Structure 5 a1 = 360 um, a2 = 300 um, a3 = 80 um, a4 = 200 um, a5 = 40 um, and a6 = 160 um. (b) Structure 6 a1 = 340 um, a2 = 70 um, a3 = 240 um, and a4 = 60 um.

4 Theoretical Analysis

The frequency behavior of the absorption is defined as A(ω) = 1 − R(ω) − T(ω), where A(ω), R(ω), and T(ω) are the absorptance, reflectance, and transmittance, respectively. A(ω) comes from minimizing either reflectivity R(ω) = |S11|2 or transmission T(ω) = |S21|2 at an indicated frequency range.

Reflectivity can be reduced (near zero) when the effective permittivity math formula and permeability math formula have the same value. It is possible to absorb both the incident electric and magnetic field tremendously by accurately tuning math formula and math formula. They can be manipulated to create high absorption. Absorbers minimize the reflection and transmission coefficients of the incident waves at a certain frequency range due to the impedance matching [Dincer et al., 2013a]. In the resonance condition, the effective impedance math formula has to match with the free space impedance Z(ω) = Z0 = 120π Ω, and therefore, the reflection is minimized. This is verified for the Structure 2 as shown in Figure 5 [Landy et al., 2008; Cheng et al., 2012; Sun et al., 2012; Lee and Lim, 2011].

5 Results and Discussion for Structure 1

The numerical simulations of the periodic structure are performed using a commercial full-wave EM solver based on the finite integration technique. The periodic boundary conditions with Floquet port are used in the simulation for all structures.

For the first structure, numerical and experimental results are compared and verified to show the proposed absorber performance. The experimental results show good agreement with the simulation results. Simulated and measured reflection and absorption outcomes are presented in Figure 3, respectively. It can be seen from the simulation that the maximum absorptions of 99% and 84% are observed at the frequencies of 4.0 GHz and 5.6 GHz, respectively. The first peak is about 99% in the simulation and in the experiment, and the second one is measured as 79% in the experiment [Dincer et al., 2013].

Figure 3.

Simulated-measured reflection and absorption for the proposed microwave FSS MA Structure 1 [Dincer et al., 2013].

Moreover, the bandwidth calculations are also performed to show the quality of the proposed absorber. For this purpose, the fractional bandwidth (FBW) of the absorption region is calculated. FBW can be found by the ratio of the bandwidth of the absorber to the center frequency. In other words, it can be calculated as FBW = Δf/f0, where Δf is the half-power bandwidth and f0 is the center frequency. For the first resonance, these parameters are calculated as Δf = 0.19 GHz, f0 = 4.0 GHz, and FBW ≈ 4.76% from the simulation and Δf = 0.25, f0 = 4.02 GHz, and FBW ≈ 6.21% for the experiment. For the second resonance, the related parameters are found as Δf = 0.182, f0 = 5.64 GHz, and FBW ≈ 3.23% from the simulation and Δf = 0.31, f0 = 5.6 GHz, and FBW ≈ 5.53% from the experiment. These computations signify that the proposed structure has a good-quality character [Dincer et al., 2013].

6 Results and Discussion for Structure 2

We numerically analyzed and compared the results in order to obtain characteristics of the others FSS MAs. The FSS MA shows perfect single-band behavior that occurs at around 10 GHz in the reflection spectrum; which means perfect single maxima in the absorption (Figure 4a). Absorption level in the resonance is about 99.69% in the simulation. As it can be seen, the reflection has only the magnitude of 0.05 at the resonance frequency in this case.

Figure 4.

Proposed microwave FSS MA Structure 2. (a) Simulated reflection and absorption for the proposed microwave absorber. (b) Simulated results of the absorbing performance under different polarization angles for the case of normal incidence. (c) Simulated results of the absorbing performance under different polarization angles for TE and TM polarizations.

In the second investigation, the effects of the incident angle on the performance of the absorber are examined. Figure 4b shows the frequency responses of the reflection and absorption behaviors for the stated process. Even though a tiny shift is observed when the incidence angle is changed, it is in a negligible level which is also the case in the other studies in the literature [Lee and Lim, 2011; Dincer et al., 2013] It can also be said that the suggested absorber provides very good absorption for all incident angles. Particularly, for the resonance frequency of 10 GHz, the variation in the absorption with respect to the frequency is very small and the absorption peak is still around 99%. It continues to provide the same characteristics for all incident angles because of the symmetry of the structure.

As the next investigation, the effect of the polarization on the frequency response of the absorber is examined. The simulated absorption characteristics as a function of the frequency for the transverse electric (TE) and for the transverse magnetic (TM) polarized EM waves for different polarization angles are found by simulation, and the results are presented in Figure 4c. It is seen that the main peak of the absorption is around unity again (99%) for both TE and TM cases at the normal incidence. A similar shift is also observed in the frequency axis, but the shift in the resonance frequency is still very small.

In order to confirm the obtained numerical results, we analytically investigated the absorbing performance of Structure 2 given for the microwave frequency region and the results are shown in Figure 5 (a similar shift is also observed in the frequency axis as in Figure 4). First, we analytically analyzed the proposed FSS MA for the couple (conventional metamaterial absorber) and decouple (metamaterial unit only without ground plane) models at normal incidence. Second, we proposed the extended interference theory model which is applicable to oblique incidence condition. math formula is the reflection coefficient of layer 1 from region 1 to region 1, math formula is the transmission coefficient of layer 1 from region 1 to region 2, math formula is the transmission coefficient of layer 1 from region 2 to region 1, and math formula is the reflection coefficient of layer 1 from region 2 to region 2. The overall reflection wave of layer 1 from region 1 back to region 1 can be calculated according to the proposed interference theory for suggested FSS MA model as [Jackson, 1998; Chen, 2012; Wanghuang et al., 2013]

display math(1)
display math(2)
display math(3)
display math(4)

where β = kh corresponds to the complex propagation phase, k is the wave number in area 2, and h is the propagation distance from layer 1 to the ground plane. Since the transmission is zero (T(ω) = 0) because of the ground plane, the absorption can be retrieved through A(ω) = 1 − | ∑ S11|2 [Kazemzadeh and Karlsson, 2010; Zeng et al., 2013; Huang and Chen, 2013].

Figure 5.

Analytical results of the absorbing performance of Structure 2.

In order to verify the character of the resonance frequency of 10 GHz for the suggested design, the electric field and surface current distributions are presented as shown in Figure 6. It was observed that the suggested geometry provides circulating, parallel, and antiparallel current distributions (symmetric and asymmetric resonance modes) at the resonance in the pattern. The circulating and antiparallel currents are responsible for the magnetic response while the parallel currents are in charge for the electric response. Thus, the mentioned currents are driven by strong magnetic and electric coupling. High concentration of the electric field around the corners validates the symmetric current which is created by the coupling of the electric dipoles. This causes to a supply-independent electric response. Therefore, strongly localized EM field enhancement is established at the resonance frequency.

Figure 6.

Electric field and surface current distributions at the resonance frequency of 10 GHz for the proposed Structure 2.

7 Results and Discussion for Structure 3

The numerical results are evaluated and verified to show the performance of the suggested absorber. Simulated reflection and absorption results are presented in Figure 7, respectively. By simply placing a frame around the Structure 2, a second resonance frequency point was obtained and we have successfully achieved a dual-band absorption. It can be seen from the simulation that the maximum absorption of 99.78% and 98.80% are observed at 10.66 GHz and 11.23 GHz, respectively. The corresponding reflection values are 0.04 and 0.10 at the first (10.66 GHz) and the second (11.23 GHz) resonances. It can be seen that the proposed model acts as a dual-band absorber in which both absorptions are perfect (Figure 7a).

Figure 7.

Proposed microwave FSS MA Structure 3. (a) Simulated reflection and absorption for the proposed microwave absorber. (b) Simulated results of the absorbing performance under different polarization angles for the case of normal incidence. (c) Simulated results of the absorbing performance under different polarization angles for TE and TM polarizations.

Additionally, the effects of incident and polarization angles on the characteristic of the designed dual-band FSS MA are observed. The incident angle is rotated from 0° to 180° with 30° steps. Figure 7b demonstrates the absorption performance of the proposed dual-band FSS MA model for different incident angles. It can be seen that the proposed model provides very good absorption for all incident angles. When the incident angle is changed, only very small differences occur. This shows that the suggested FSS MA perfectly provides incident angle independency. This can be seen as an added value to the performance of the proposed FSS MA.

In addition, Figure 7c illustrates the simulated absorption dependency as a function of frequency with respect to the polarization angle between 0° and 180° with 30° steps for the transverse electric (TE) and the transverse magnetic (TM) polarized waves. The first mode and the second mode are located approximately at around 10.65 GHz and 11.16 GHz. The frequency shift can be defined by the change of the polarization state. As understood, there are very small and negligible differences between TE and TM cases when the polarization angle is changed since the proposed model is a flexible and a multidirectional structure. The important issue is that the first mode for some polarization angles and polarization types is greatly enhanced. The simulated results show that the dual-band FSS MA can be operated for a wide range of incident angles and arbitrary polarizations.

8 Results and Discussion for Structure 4

In order to realize perfect absorption in three bands, we have designed a cross-shape geometry for the interior part and a frame with two vertical gaps which increases the capacitive effect is placed, resulting in an extra band. We numerically analyzed and compared the results in order to obtain characteristics of the other FSS MAs. The FSS MA shows multiband absorption (Figure 8). Three different resonances occur at around 8.82 GHz, 9.95 GHz, and 10.91 GHz in the reflection spectrum, thus yielding three peak points in the absorption meaning that the triple band perfect absorption is achieved. The first peak is about 74.86%, the second peak is 99.34%, and the third one is 88.86% in the simulation. It can be seen that the reflection values have only resonance magnitude of 0.50 at first, 0.08 at second, and 0.33 at third resonance in this case (Figure 8a).

Figure 8.

Proposed microwave FSS MA Structure 4. (a) Simulated reflection and absorption for the proposed microwave absorber. (b) Simulated results of the absorbing performance under different polarization angles for the case of normal incidence. (c) Simulated results of the absorbing performance under different polarization angles for TE and TM polarizations.

In the second examination for the Structure 4, the effects of the incident angle on the performance of the absorber are investigated. Figure 8b exhibits the frequency response of the reflection and absorption for the indicated process. It can be seen that the suggested structure provides very good absorption for all incident angles. Particularly, for the resonance frequencies, the variation in the absorption with respect to the frequency is very small and the absorption peak is still around up to 80%. It continues to provide the same feature for all angles of incidence.

As the next exploration, the effects of the polarization on the frequency response of the absorber are examined. The simulated absorption characteristics as a function of the frequency for the transverse electric (TE) and transverse magnetic (TM) polarized EM waves for different polarization angles are found by simulation, and the results are presented in Figure 8c. It can be seen that the proposed FSS MA shows polarization-dependent behavior since TE and TM absorption peaks are located at different frequency points for the same polarization angle. This result is caused by the asymmetric characteristic of the proposed FSS MA structure. In particular, one can see from the figure that even though the maxima occur at the same frequency points for all angles, depending on the polarization angle, we obtain dual- (90°), triple- (0°, 60°, 120°, and 180°), or quadruple- (30° and 150°) band absorption within the indicated frequency range for TE-incident case. Similar behavior was obtained for TM-incident case as dual- (0°), triple- (90°, 30°, and 150°), or quadruple- (120°, 60°) band absorption within the indicated frequency range.

9 Results and Discussion for Structure 5

We numerically analyzed and compared the results to obtain characteristics of the other FSS MAs. The FSS MA shows perfect absorption at around 0.83 THz in the reflection spectrum, which results in perfect single maxima in the absorption (Figure 9a). The resonance is about 99.92% in the simulation. As seen, the reflection has only the magnitude of 0.02 at the resonance frequency in this case.

Figure 9.

Proposed terahertz FSS MA Structure 5. (a) Simulated reflection and absorption for the proposed terahertz absorber. (b) Simulated results of the absorbing performance under different polarization angles for the case of normal incidence.

In the second investigation, the effects of the incident angle on the performance of the absorber are examined. Figure 9b shows the frequency response of the reflection and absorption behaviors for the stated process. It can be seen that the suggested absorber provides very good absorption for all incident angles. The lowest absorption is occurring at around 0.83 THz as 97.14% for 120° and the highest absorption is observed at around 0.88 THz as 99.98% for 60°. As a result, the change in the incident angle only shifts the resonance frequency, but the quality of the absorbance is not affected by this change. This is caused by the symmetry of the crossed structure according to the origin.

10 Results and Discussion for Structure 6

We numerically analyzed and compared the results in order to obtain the characteristics of the other FSS MA obtained by Structure 6. The FSS MA shows perfect single-band behavior at around 0.99 THz in the reflection spectrum, thus perfect single maxima in the absorption is observed as shown in Figure 10a. The resonance is about 99.98% in the simulation. One can see that the amplitude of the reflection is 0.01 at the resonance frequency in this case.

Figure 10.

Proposed terahertz FSS MA Structure 6. (a) Simulated reflection and absorption for the proposed terahertz absorber. (b) Simulated results of the absorbing performance under different polarization angles for the case of normal incidence.

In the second investigation, the effects of the incident angle on the performance of the absorber are evaluated. Figure 10b shows the frequency response of the reflection and absorption for the stated process. To observe the shifts of the resonance frequency with respect to the incident angle, a wider frequency range is taken into consideration as shown in Figure 10b. It can be seen that the suggested absorber provides a very good absorption for 0°, 120°, 150°, and 90° with the absorptions of 88.11%, 98.07%, 87.22%, and 99.98%, respectively. The lowest absorption is occurring at around 1.05 THz as 46.95% for 60°, and the highest absorption is observed at around 0.99 THz as 99.98% for 90°. Although the structure does not provide a good incident angle independency, it has good resonances with small shifts for all incident angles except for 60°.

11 Discussion and Conclusion

In summary, we have presented microwave and terahertz FSS MA structures. Six different structures were examined in terms of their absorption behaviors and polarization and incidence angle independencies. All of these structures show perfect absorption, and they can also be tuned easily by rescaling the structure for other frequencies. Obtained results confirm this claim. While the numerical result of the first structure are examined and verified experimentally, those of the second structure are confirmed by the analytical results. By taking them as reference, the remaining structures were investigated thoroughly. Geometries of the models are chosen to be simple so that the fabrication and adjusting to the other desired frequency bands would be simple by just changing the dimensions. Furthermore, presented FSS MA structures have quite distinct advantages like multiband absorption peaks, flexibility, mechanical tunability, incident and polarization angle independency for some of the proposed structures, and so on.

According to the results, the investigated FSS MAs provide perfect absorption at resonance frequencies independent of the polarization state and incident angles. In some cases of the polarization states and incident angles, the absorption value can be enhanced. The proposed structures successfully provide dual, triple, and even quadruple absorption bands within the frequency range we have been investigating. One of the most important selling points of our structure is that they work well in both microwave and terahertz frequency regime. Numerical studies support and verify this conclusion. Therefore, the verified polarization and incident angle-independent FSS MAs (with many advantages such as simplicity, flexibility, mechanical tunability, and perfect absorption) can be used as perfect absorbers and can be a good candidate for the applications of stealth, sensor, modulators, wireless communication, medical imaging, and so on.

Acknowledgments

M.K. acknowledges the support of TUBITAK under project 113E290 and partial support of the Turkish Academy of Sciences. Authors would also like to thank the Editors and anonymous reviewers for their suggestions to improve the paper.

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