We numerically and experimentally investigate a broadband, polarization-independent and wide-incident-angle metamaterial perfect absorber (MPA) based on conductive polymer. By optimizing the electrical conductivity of the polymer, a 16.7 GHz broadband MPA is observed with the absorptivity greater than 80% for both transverse magnetic and electric polarization. The measurement results performed in the range 8-18 GHz show a diametrical concatenation with simulation results and theoretical analysis. The absorption mechanism is explained by demonstrating the influence of polymer conductivity on the dissipated power, the equivalent impedance, and the induced electric field. Our work may contribute to further studies on broadband MPA using for various applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In 2000, Metamaterial (MM), a new class of artificial materials, was demonstrated the first time by Smith et al. . It possesses extraordinary characterizations which are not readily available in natural media, such as negative refraction , induced transparency , and reversed Cherenkov radiation . Such the fantastic properties make MM as a promising candidate for numerous applications in perfect lenses [5,6], invisible cloaking , plasmonic sensors , solar energy conversion , and antenna  with applications ranging from military field to health care and communication.
Another type of MM also attracts attention is metamaterial perfect absorber (MPA), which can consume totally energy of incident electromagnetic (EM) wave. Since the first experimental MPA structure was proposed by Landy et al. in 2008 , many MPA have been demonstrated with operating wavelength from microwave to visible [12–14]. However, the MPA often occurs a narrow frequency bandwidth because its absorption is rooted in electric and magnetic resonances. It limits in practical applications where a broadband absorption is a requirement. To achieve absorption in a large frequency range, several approaches have been proposed and conducted to fabricate [15–24]. A common method that has been widely used is various multi-sized or multi-shaped resonators together [15–19]. However, it is difficult to handle in fabrication since the number of resonators is restricted due to the large unit size, and the absorption performance is sensitive to the resonator size. Another approach is to use multiple vertically stacked layers [20–22], but the designs suffer from the large thickness of the sample, the complexity of fabrication, and production incompatibility. In addition, there have been other methods, such as electronic devices  and plasmonic absorption . Even though there are significant achievements to broaden operating bandwidth of the MPAs, the approaches are usually about modifying the resonance of metal ingredient in the traditional sandwich structure.
Recently, an innovative approach was proposed to obtain MPA based on non-metal materials [25,26] and water [27–29]. Wang et al. proposed a THz broadband MPA based an alloy (Al-Si-Mg) with the bulk conductivity of 4.09 × 105 S/m . Nevertheless, the fabrication process of the alloy and measurement verification of the MPA were not performed. In a common manner, conductive polymer exhibits electrical properties of both metals and semiconductors associated characteristics of conventional polymers. Most researches of conductive polymers are focused to apply for electronic devices, such as batteries , solar cells , electromagnetic shielding , and light-emitting diodes . The use of the conductive polymer in the MPA is very few and not well reported yet . The search of the conductive polymers of composed MPA is still in progress. It is being a promising candidate for substituting traditional metals in the MPA.
In this work, we employed a novel conductive polymer in substitution for traditional copper layers in the MPA. The superiority of the new material is theoretically and experimentally investigated. By optimizing the electrical conductivity of the polymer, the bandwidth of MPA is gained up to 16.7 GHz with absorptivity higher than 80%. Firstly, the composition of the polymer and the manufacturing process of the proposed MPA, polymer ring (PR) structure, is exhibited explicitly. Secondly, the absorption and wave propagation characteristics of the structure are interpreted in comparison with the copper ring (CR) ones by scrutinizing the effective impedance and the absorbed electromagnetic power [36–39]. Besides, the induced electric fields at the resonance peaks are discussed to better understand on the absorption characteristics. Finally, the independence of the absorption properties on the wide-range incident and polarization angle are investigated to support the operational ability. The proposed design strategy is a promising approach to extend the absorption bandwidth of MPAs by utilizing graphene composition in fabrication process.
2. Structure and design
Figure 1 illustrates the geometry of the MPA unit cell with periodicity a = 6 mm. The PR pattern structure is embedded in the FR-4 dielectric substrate, and its thickness, outer radius, and inner radius are tp = 0.105 mm, r1 = 2.3 mm, and r2 = 1.8 mm, respectively. The electrical conductivity, relative permittivity and permeability of the conductive polymer are 700 S/m, 1 and 1, respectively. The permeability and thickness of the dielectric FR-4 layer are ε = 4 and td = 2 mm, and the loss tangent of FR-4 is 0.025. The copper plate covering the whole side has a thickness of tm = 0.036 mm. The simulations are performed by finite integration method in CST Microwave Studio . The EM wave with polarization angle (φ) and incident angle (θ) is shown in Fig. 1(b). Since EM wave cannot penetrate copper plate in the backside of the MPA, we used one waveguide port to imitate wave generator and detector in simulation. The reflected scattering parameter is defined as S11, and the absorption is calculated by A = 1 – S112. The characteristics of conductive polymer in simulation setup are imported from experimental data to the software library.
3. Materials and fabrication
The conductive polymer is prepared from three components including polyethylene glycol (PEG) 4000, polysorbate 80, and multilayer graphene. Normally, PEG 4000 is well known as insulating compounds due to their poor electrical conductivity . On the other hand, graphene exhibits very high electrical conductivity , hence, blending graphene into a polymer as PEG 4000 to make a conductive polymer is reasonable. Figure 2(a) illustrates the manufacturing process of the conductive polymer. Firstly, 300 g PEG 4000 is heated to 120 °C, adding 1.51 g polysorbate and stirring for 30 min, which resulted in hydrophobically modified polyethylene glycol. In the compound, polysorbate 80 plays an important role as a high medial adhesive between PEG 4000 and graphene to make better uniformity. Subsequently, 41.2 g multilayer graphene is added to this mixture and stirred at temperature 135 οC for 1 h to obtain conductive polymer (graphene-embedded hydrophobic-modified polyethylene glycol composites). The electrical conductivity (σ) of polymer can be controlled via various amounts of multilayer graphene. With above chemical components, the electrical conductivity of the conductive polymer is σ ≈700 S/m. Finally, this polymer is infiltrated into the ring patterns on FR-4 dielectric layer heated at 150 οC. The fabricated absorber prototype which consisted of 256 unit-cells and a total size of 100 × 100 mm2 is exhibited in Fig. 2(b).
4. Results and discussions
Based on the full-wave simulation, the simulated absorption spectra of the PR MPA compared with the conventional CR MPA in the frequency range of 8-28 GHz is presented in Fig. 3(a). The electrical conductivity of the polymer and copper are 700 and 5.8 × 107 S/m, respectively. In the case of the CR structure, the absorption spectra consist of two resonant frequencies at around 10.0 GHz (f1) and 25.8 GHz (f2) and their absorptivity are 29% and 59%, respectively. While, two peaks are slightly shifted to around 10.8 and 23.8 GHz in the case of PR MPA and the absorptivity of two absorption peaks increases to 95% (f1) and 100% (f2). Especially, those two absorption peaks increase and merge with each other to create a broader absorption band. The absorption bandwidth is gained up to 16.7 GHz with absorptivity better than 80% (absorption bandwidth of 95.7%). These results indicate that the conductive polymer plays an important role to obtain the broadband MPA.
The absorption capability of the proposed PR and CR structures can be demonstrated by the theory of impedance matching [43–45]. At the absorption frequency, by controlling the electric permittivity ε(ω) and the magnetic permeability µ(ω), the effective impedance of the MPA is perfectly matched with free space. Based on the real part and imaginary part of reflection (S11(ω)) and transmission coefficients (S21(ω)), the effective impedance can be calculated as:
The extracted effective impedance spectra of the PR structure in comparison with the copper ones are plotted in Fig. 3(b). It can be seen that, at the resonance frequencies, the imaginary parts of the effective impedances are equal zero, hence, satisfying the effective medium theory . The real part of PR MPA not only match better with free space impedance than the copper ones but also match in a wide range from 9 to 26 GHz. As a result, the PR MPA can reflect less EM power to the surrounding region leading to higher absorption than the copper ones.
The physics under the absorption behavior at two resonance peaks is pointed out by investigating the induced electric fields. Theoretically, the absorbed EM power can be calculated from the electric field (E) by using equation [46,47]:Figure 4 exhibits the simulated electric field at two absorption peaks in the x-y and y-z plane. At the first resonance, the electric field locates on the inner edge of the PR [Fig. 4(a)] and locates within one unit-cell [Fig. 4(c)]. While, the second resonance is caused by the induced electric field on the outer edge [Fig. 4(b)] and concentrate on the region between neighboring unit cells [Fig. 4(d)]. It improves that the first absorption peak is attributed to the magnetic resonance [13,15] and the second ones is characterized by the interaction of adjacent unit cells.
For better understanding about the higher absorption of the PR MPA than the copper one, the contribution of the electrical conductivity to the absorption characteristic is clarified. Normally for conventional metamaterial absorber like the copper ring structure, the resonance is easily controlled by turning the structural parameters including the dielectric thickness. It is because of the strong magnetic permeability dispersion which is derived from the Kramers-Kronig relations at resonance frequencies . However, for the regions outside the resonance, the change of structural parameters is not much physical meaning due to weak dispersion of magnetic permeability. We replaced copper with conductivity of 5.8 × 107 S/m to conductive polymer with conductivity of 700 S/m. The physical mechanism behind the high broadband absorption is pointed out by demonstrating the influence of the electrical conductivity to the effective impedance (Eq. (1)) and the absorbed electromagnetic power (Eq. (2)). The relationship between the electrical conductivity and the effective permittivity according to angular frequency (ω) is followed as:Eq. (1). Following the Eq. (2), the absorbed power is evaluated from the imaginary part of the effective permittivity which is strongly depended on the electrical conductivity. So that the electrical conductivity of the polymer is directly affected to the absorbed electromagnetic power. The optimized value of σ brings the best impedance matching and absorption results.
The influence of dielectric thickness on the absorbance is plotted in the Fig. 5(c). As can be seen that, the best absorption is observed when td = 2 mm. The dielectric thickness is a key factor to control the reflectivity and the absorptivity of the MPA and the optimal value of dielectric thickness can be extracted from the interference theory [44,49]. In our work, the optimum value of the dielectric thickness is computed as 2.0 mm.
Figure 5(a) illustrates the numerically simulated absorption spectra of the conductive polymer according to electrical conductivity. It can be seen that the absorptivity of the PR structure strongly depends on the conductivity of the polymer. However, this relationship is not proportional to conductivity at the same simulation setup condition. Clearly, when the conductivity of polymer is higher than 5000 S/m, the absorption spectra have two absorption peaks which are similar to the case of the CR [Fig. 3(a)]. When the conductivity of polymer decreases from 105 to 500 S/m, two absorption peaks are gradually merged to a broadband absorption and increasing absorptivity. At low conductivity (still satisfy the good conductor condition), i.e. 100 S/m, the absorption spectrum has only one absorption peak with low absorptivity. In this case, the skin depth is calculated as 0.55 mm, much greater than proposed tp, as a result, low absorptivity obtained. Therefore, the conductivity of the polymer plays a key role to achieve the broadband absorption. Additionally, Fig. 5(b) displays the absorbance working with various polymer thickness when the electrical conductivity is kept at 700 S/m. It is obviously seen that the absorption of the PR MPA is strongly depend on the thickness of the ring. This dependence can be explained by the transmission (T) and reflection (R) coefficients deriving from Eqs. (4) and (5), respectively, where η and ηe are the intrinsic impedances of the CR or PR and equivalent medium . In this case, due to the same components excepting the top layer, we assume that the equivalent medium comprising the air, the bottom layer and the dielectric substrate. Thence, only the CR and PR are verified and compared in normal incident angle and not to mention the dissipated-EM power in dielectric spacer.
To verify the advantage of conductive polymer, the prototype of PR MPA is fabricated by optimizing polymer conductivity of S/m. The measurement is performed in a standard chamber to achieve the most accurate results of the reflection coefficient. One standard gain linearly polarized antenna which can simultaneously transmit EM wave and receive reflection signals is connected to a vector network analyzer (Hewlett-Packard E8362B) to determine the absorption as the equation of A = 1 – S112. The simulated and measured absorption spectra have executed for various dielectric thickness to not only indicate the influence of the absorption on dielectric thickness but also establish the agreement between simulation and measurement. The comparison of experimental results with simulated absorption spectra are presented in Fig. 6. It is noted that the experimental examination is only performed in the X and Ku band due to the limitation of the measurement device. The results indicate that the measured results are in a good agreement with the simulated ones with an ultra-broadband absorption for all cases. Interestingly, the thicker dielectric, the better of absorption obtained. By contrast, the measured absorption result of MPA based on copper ring structure is already presented in our previous research  with narrow bandwidth (approximately 0.4 GHz absorption bandwidth higher than 80%).
Figure 7(a) illustrates the simulation results of absorbance spectra according to the different polarization angles of normal EM wave. By rotating the transmitting horn antenna direction or the MPA sample, the polarization angles from 0 to 80 degree are investigated. The results retrieve that the absorption lines are absolutely consistent in the large range of polarization angles due to high symmetry of ring structure. In order to evaluate the operational competency, the dependence of oblique incident angle in both transverse electric and magnetic polarizations on absorption spectra are meticulously exhibited in Figs. 7(b) and 7(c), respectively. The simulation results demonstrate that the absorption spectra of the proposed polymer structure are virtually unresponsive in the range [0, 60] degree of incidence angle in the TM and [0, 40] degree for TE radiations. The computational evaluation of the total reflection coefficient for TE and TM modes corresponding with the perpendicular and parallel polarizations is departed from Fresnel equations [47,50].
We have demonstrated a novel ultra-broadband, polarization-independent, and wide angle MPA based on the conductive polymer in the GHz region. The marvelous absorption characteristic of the proposed MPA energetically depends on the electrical conductivity of the polymer which requires deliberate manipulation in the fabrication process. The simulated absorption bandwidth is gained up to 16.7 GHz with absorptivity better than 80% and wholly agree with the measured result when the conductivity of the polymer is 700 S/m. The energy aspect is also approached for better understanding in to the influence of polymer electrical conductivity on the absorption characteristic. It is worth noting that no such conductive polymer based MPAs have been previously investigated in both simulation and experiment at GHz regime. Our propose material and structure open up many directions for application and development of MPA.
Vietnam National Foundation for Science and Technology Development (NAFOSTED) (103.02-2017.67); Vietnam Academy of Science and Technology (VAST) (VAST.CTG.01/17-19).
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