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Abstract
Two types of broadband and polarization independent graphene metamaterial absorbers are designed. One is a composite four-ring structure with azimuthally symmetry, the other is a nested multi-ring structure. The nested structure is more compact and has a broader band of absorption. The bandwidth with over 90% absorption is 7.1 THz for the composite four-ring structure. The bandwidth increases to 8.7 THz and 11.9 THz for the nested dual-ring and three-ring absorber, respectively. The wide bandwidth and polarization independent absorption owe to the combination of symmetric multi-resonators with different sizes in unit cell. Physical mechanisms of the broadband absorbers are given by the impedance matching theory as well as the surface current distributions. Instead of one single layer graphene as papers reported before, multilayers of graphene are coated on the dielectric surface to form the metal resonant-multilayer graphene-dielectric-metal ground structure. It is found that both the absorbing width and magnitude increase greatly as the graphene layers increase while a large dip appears when the number of graphene layers is large enough. Moreover, by investigating the absorptions under different graphene permittivities, we find that the reduced graphene permittivity is better to simplify the calculation.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificially engineered subwavelength materials and have been widely investigated due to their low cost, small size and ultrathin thickness compared with the wavelength [1]. Metamaterials can be designed to display fascinating physical properties that cannot be easily accessed in natural materials, such as negative refraction, hyperbolic dispersion and perfect lens [2–7]. These extraordinary electromagnetic properties make metamaterials have potential uses in radar [8], sensing [9], polarization converter [10] and so on. Among these applications, tunable metamaterial absorbers have attracted significant attentions because of remarkable flexibilities [11] and many fruitful results have been obtained from microwave to visible band [1,2,8,12–15].
Graphene is a flat monolayer of graphite with carbon atoms closely packed in a two-dimensional honeycomb lattice [16]. It has excellent mechanical, chemical, and electrically tunable properties, which offer many interesting possibilities for terahertz and optical technologies. Recently, many efforts have been taken for tunable graphene-based metamaterial absorbers in the single-band, multiband and broadband absorptions. It is found that a single-band absorption reaches nearly 100% for graphene metamaterial absorbers and can be controlled via external gate [17–19]. Then, dual-band [20,21] and multiband [22] absorbers with near perfect absorption are obtained to meet the need of multiple absorbing applications. However, bandwidths of the multiband absorbers are usually very narrow and limited. To achieve tunable broadband absorption. Amin et al proposed [23] an ultra-broadband graphene absorber by using 3 layers of asymmetrically patterned graphene. Su et al [7] proposed a tunable broadband terahertz metamaterial absorber based on 10 layers of graphene/MgF2 multilayer structures, and He et al [24] introduced another absorber with 15 layers of graphene-dielectric multi-layered pyramids on a metal sheet, and achieved a wide bandwidth from 8 THz to 100 THz. However, these multilayers structure will make the fabrication more difficult.
Khavasi et al. designed a broadband THz absorber by using periodic arrays of graphene ribbons on a Salisbury-screen-like structure [25]. Yao et al [26] proposed a broadband absorber composed of graphene analog of electromagnetically induced transparency and a metal ground plane spaced by a thin SiO2 dielectric layer. Zhang et al [27] presented an absorber with a dual electric LC metamaterial unit on multilayer structures composed of Au/BaF2/graphene materials. However, these structures mentioned above can only achieve wide absorption in one polarization. To achieve all-direction absorption, Arik et al [28] designed a polarization-independent broadband absorber consisting of periodic array of graphene disks on quarter-wavelength dielectric spacer placed on a metallic reflector. However, it is very difficult to control the graphene due to its discontinuous distribution. Wang et al [13] proposed an ultra-broadband and polarization independent absorber by introducing multilayered and symmetrical patterned graphene. The layers of graphene pattern are separated by dielectric substrates, which would increase the difficulty in fabrication.
In this paper, we propose two types of broadband and polarization independent graphene-based absorbers based on metallic-graphene-dielectric-metallic structure. The first type is a composite four-ring structure with azimuthally symmetry, while the second type is a nested multi-ring structure. The wide bandwidth and polarization independent absorption mainly owe to the combination of symmetric multi-resonators with different sizes in unit cell. On the other hand, as the graphene layers are coated on the dielectric surface, these absorbers can be easily tuned via varying the chemical potential of graphene, which would improve the response of sensors, bolometers, thermal radiation modulators, and photovoltaic structures, etc.
2. Design and simulations
In this section, a polarization-independent graphene-based absorber consisting of single-ring structure is firstly designed. Then, the influences of geometrical parameters on the absorption are discussed. As broadband absorptions can be obtained by combining two or more resonators with different sizes, a composite four-ring structure and a nested multi-ring structure in the unit cell are proposed to improve the bandwidth and magnitude of the absorption, respectively.
2.1 Single-ring graphene-based absorber
The schematic of the unit cell of the proposed graphene-based absorber is illustrated in Fig. 1. It consists of a ring-shaped metallic resonator and a metal ground plane separated by a dielectric spacer and graphene. The resonator and the ground plate are gold with thickness tm = 0.1 μm [29]. The relative permittivity of the dielectric is εd = 1.6 [30] coated with four-layer graphene with the thickness tg = 0.34 nm of each layer.
Fig. 1 Schematic of the single-ring graphene-based absorber. Parameters are listed as follows: P = 3.6 μm, R1 = 1.6 μm, R2 = 0.25 μm, td = 0.3 μm, tg = 0.34 nm and tm = 0.1 μm.
The graphene permittivity εG can be express as [31,32]
Here ω is the angular frequency, tg is thickness of the single-layer graphene, ε0 is the permittivity in vacuum. σ(ω) = σintra(ω) + σinter(ω)is the surface conductivity of graphene, σintra and σinter are the intraband conductivity and the interband conductivity defined in the following where e is the charge of an electron, μc is the chemical potential, Γ is the phenomenological scattering rate, T is the Kelvin temperature, kB is Boltzmann’s constant, ħ = h/2π is the reduced Plank’s constant. In the simulation, T = 300 K, μc = 0.6 eV, Γ = 2π × 2.42 THz is selected [29]. For the simulation, commercial software CST Microwave Studio is employed, and the time domain solver is used to obtain the transmission S21 and the reflection S11. Open boundary condition is selected along the z axis while the periodic boundary conditions are selected along the x and y axes. The permittivity of graphene is calculated based on Eq. (1) and then imported into the material library of the software. The absorption is obtained through the equation A = 1-S212-S112 [33]. The transmission S21 is ignored in the calculation because the continuous gold ground of the absorber blocks the transmission of the electromagnetic wave. The absorption spectrum of the single-ring graphene-based absorber under normal incidence is plotted in Fig. 2(a), where the solid and dash lines indicate the results of the TE polarization where the electric field is along the x axis and the TM polarization where the electric field is along the y axis, respectively. It is seen that the absorber is polarization independent and has near-perfect absorption of 99% at 37.8 THz. As absorption can be explained by impedance matching theory [34]. Figure 2(b) shows the real part real(z) with solid line and imaginary part imag(z) with dash line for the relative impedance z = Z/Z0, where Z and Z0 are the impedances of the absorber and the free space, respectively. It is seen that the relative impedance z is close to 1 for the absorber at 37.8 THz, which means impedance of the absorber matches with that of the free space. On the other hand, no waves can transmit through the absorber due to the metal film used on the back side. Therefore, the incident wave can be absorbed to the maximum if the impedance is matched [28,35].Fig. 2 (a) Absorption spectra of the single-ring absorber. (b) real and imaginary parts of the relative impedance z of the single-ring absorber.
The effects of geometric parameters of the absorber on the absorption are listed as the follows. Figure 3(a) shows three absorbing curves for different thicknesses of dielectric td = 0.1 μm, 0.3 μm and 0.7 μm with other parameters same in Fig. 1. Figure 3(b) shows the color map of the absorption for td varying from 0.1 μm to 1 μm. The absorption shifts to the lower frequency as td increases. For td = 0.3 μm, the widest and highest absorption is obtained. Figure 4 presents the absorption with various values of outer radius R1 with other parameters same in Fig. 1. It is seen that the absorption shifts to the lower frequency as R1 increases with the magnitude increasing. Then, the absorption disappears as R1 increases to 1.7 μm. Figure 5 shows the influence of inside radius R2 on the absorption with other parameters same in Fig. 1. It is seen that the absorption shifts to the lower frequency with R2 increasing and finally disappears for R2 = 1.2 μm.
Fig. 3 (a) Absorption of the single-ring structure with dielectric thickness td = 0.1 μm, 0.3 μm and 0.7 μm, and (b) color map of the absorption versus td varying from 0.1 μm to 1 μm.
Fig. 4 (a) Absorption of the single-ring structure for R1 = 1.2 μm, 1.4 μm and 1.6 μm. and (b) colormap of absorption with R1 varying from 0.3 μm to 1.8 μm.
Fig. 5 (a) Absorption of the single-ring structure for R2 = 0.25 μm, 0.7 μm and 1.2 μm, and (b) color map of absorption with R2 varying from 0.1 μm to 1.5 μm.
For the ring structure with frequency-selective surfaces, the resonance frequency can be estimated from [36]:
where r = (R1 + R2)/2 is the average radius of the ring, λ and f are the resonant wavelength and resonance frequency, respectively, c is the speed of light in free-space, and εeff is the effective dielectric constant of the substrate. As R1 and R2 increase, the increasing of r makes the absorbing frequency shift to the low frequency. As the thickness of the substrate td increases, the effective dielectric constant of the substrate becomes larger, leading to the resonant frequency decrease too. These explanations are in good agreement with the results in Figs. 3-5.
2.2 Four-ring graphene-based absorber
From the analysis above, the absorption is affected by ring radius greatly. Figure 6 presents a four-ring graphene-based absorber, which has diagonal symmetry by combining four individual single-ring structures with two different sizes of ring radius. The parameters are as follows: P = 3.6 μm, R1 = 1.6 μm, R2 = 0.25 μm, R3 = 1.4 μm, R4 = 0.25 μm, tg = 0.34 nm, td = 0.3 μm, tm = 0.1 μm, T = 300 K, μc = 0.6 eV, and Γ = 2π × 2.42 THz. The four rings have azimuthally symmetry to maintain the polarization independence and a broadband absorption can be obtained which is given in Fig. 7(a). The dot, dot-dashed, and solid lines denote the results of the large-ring, small-ring and four-ring combined by the large and small rings structures, respectively. Both the small and large single-ring structures show a near-perfect absorption, however their absorption bandwidths are very narrow. For the composite four-ring structure, a broadband absorption can be obtained due to the coupling among the neighboring rings. The bandwidth of 90% absorption for the four-ring structure increases to 7.1 THz.
Fig. 6 Schematic of the four-ring absorber. The parameters are as follows: P = 3.6 μm, R1 = 1.6 μm, R2 = 0.25 μm, R3 = 1.4 μm, R4 = 0.25 μm, tg = 0.34 nm, td = 0.3 μm, tm = 0.1 μm, T = 300 K, μc = 0.6 eV, and Γ = 2π × 2.42 THz.
Fig. 7 (a) Absorption of the four-ring absorber. (b) Top view of surface current distribution of the four-ring absorber at the resonant frequency of 40.2 THz under the TE polarization. (c) Top view of surface current distribution of the four-ring absorber at the resonant frequency of 44.5 THz under the TE polarization.
To further clarify the physical mechanisms of the broadband absorber, we show the top view of the surface current distributions at the resonant frequencies of 40.2 THz and 44.5 THz under the TE polarization. As is shown in Fig. 7(b) and Fig. 7(c), the larger surface current occurs at the large ring at the first resonant frequency 40.2 THz, while it focuses on the small ring at the second resonant frequency 44.5 THz. Therefore, the two absorption peaks arise from the electromagnetic resonances of the large and small rings, respectively.
As is shown in Eq. (2) and Eq. (3), the surface conductivity of graphene is significantly related to the chemical potential μc, which can be tuned by the electrostatic doping [37] or applying bias voltage [38]. Figure 8(a) presents the absorption with various values of chemical potential μc. The dash, solid and dot lines denote the results of μc = 0.2, 0.6 and 1.0 eV, respectively. Color map of absorption varying values of μc is plotted in Fig. 8(b). It is clear that the absorption shifts to the higher frequency as μc increases. For μc = 0.6 eV, the absorption seems to be better with large width and high magnitude.
Fig. 8 (a) Absorption of the four-ring absorber with μc = 0.2 eV, 0.6 eV and 1.0 eV. (b) Color map of the absorption with μc varying from 0.1 eV to 1.0 eV.
In addition, the expression of graphene permittivity may affect the absorption. As mentioned above, the graphene conductivity can be expressed as σ = σintra + σinter. But in some case, the intraband conductivity σinter is negligible, which means σ(ω) can be reduced to [39]:
Furthermore, another simplified form of expression is used in [9], where the complex permittivity of graphene is modeled as:where ωp2 = (e2μc)/(tdε0πħ2) is equivalent plasma frequency. Figure 9(a) and Fig. 9(b) show the real and imaginary parts of the relative permittivity of graphene calculated by different methods. It is seen that the relative permittivities used in different references [9,31,39] are almost the same. Figure 9(c) presents the results of absorption using the three permittivities of graphene in Fig. 9(a) and Fig. 9(b), other parameters of the absorber are same with those in Fig. 6. The solid, dot and dash lines denote the results of σ = σintra + σinter , σ = σintra and the simplified form in Eq. (6), respectively. It is seen that absorptions of the absorber are same for the three different expressions of graphene. Therefore, to simplify the calculation, the reduced permittivity of graphene can be used in the simulation.Fig. 9 (a) Real part and (b) imaginary part of the relative permittivity of graphene calculated by different method (c) Absorption of the four-ring absorber using three forms of permittivity
Figure 10(a) shows the influence of layers of graphene on the absorption. The dash, dot, solid and dash-dotted lines are corresponding to the results with no, one, four and eight layers of graphene. It is seen that the absorption reduces greatly without graphene on the structure. More interesting, the absorption changes slightly when only one layer of graphene is put on the structure. However, when the number of graphene layers increase to four layers, both the width and magnitude of the absorption increase greatly. While the dip between the two peaks seems to increase as eight layers of graphene are added. Figure 10(b) presents the color map of the absorption with graphene layers varying from 1 to 10 layers. It is seen that the bandwidth of the absorption is very narrow when only one layer is added. Then, the bandwidth increases greatly when two layers are introduced. Finally, a small dip among the absorptions appears as number of graphene layers increases. In the simulation, the multi-layer graphene is obtained by overlapping monolayer graphene on the model.
Fig. 10 (a) Absorption of the four-ring absorber using none, one-layer, four-layer, and eight-layer of graphene (b) Color map of the absorption with layers varying from 1 to 10.
To figure out the physical mechanism of the absorption under different layers of graphene, Fig. 11 shows the distributions of electric field Ez at the first absorption frequency of the four cases in Fig. 10 (a). Figure 11(a)-(d) show the top views of Ez at the first resonant frequencies f = 34.6 THz, 35.3 THz, 40.2 THz, and 39.8 THz for the structures with no, one, four and eight layers of graphene, respectively. It is clearly seen the near-field response mainly focuses on the two edges of the large rings along x-direction for no-layer or one-layer graphene structures. The electric fields expand into the surface of graphene when four-layer or eight-layer graphene are introduced. Figure 11(e)-11(h) present the Ez distribution in yoz plane at x = 0. It is obvious that the distributions of the fields in Fig. 11(e) and Fig. 11(f) are similar, while in Fig. 11(g) and Fig. 11(h), more electric fields are bounded into the interface between the dielectric and graphene. This phenomenon can be explained by graphene plasmon resonances [40]. The graphene plasmon resonances will restrict the propagation of incident wave to the interface between the dielectric and graphene, which contributes to the high absorption as a result.
Fig. 11 Top view of distributions of the z-component of electric field Ez for (a) without graphene at 34.6 THz (b) with one-layer graphene at 35.3 THz, (c) with four-layer graphene at 40.2 THz, and (d) with eight-layer graphene at 39.8 THz. Ez distribution in yoz plane at x = 0 (e) without graphene (f) with one-layer graphene (g) with four-layer graphene, and (h) with eight-layer graphene.
2.3 Nested graphene-based absorber
A broadband absorption can also be obtained by combining several resonators with different sizes in another way. The schematic of the unit cell of the nested graphene-based absorber is illustrated in Fig. 12. Parameters of the nested dual-ring and three-ring absorber are as follows: P = 3.9 μm, R0 = 0.3 μm, R1 = 1.55 μm, R2 = 1.5 μm, R3 = 1.4 μm, R4 = 1.25 μm, R5 = 1.2 μm. The three-ring absorber is formed by introducing one ring slot in the inner ring of the dual-ring structure. Figure 13 shows absorption of the nested absorbers with dual-ring and three-ring structures, individually. It is seen that the wider absorption can be obtained by introducing more ring resonators within the unit cell. The bandwidth of 90% absorption is 8.7 THz and 11.9 THz for the dual-ring and three-ring structures, respectively. To understand the mechanism of the broadband absorption, top view of the surface current distributions at 47 THz are shown in Fig. 14(a) and Fig. 14(b) for the nested dual-ring and three-ring structures, respectively. It is obvious that the antiparallel currents occur in neighboring rings, which implies that the high absorption mainly originates from the hybrid oscillations of neighboring rings due to their strong coupling.
Fig. 12 Schematic of the nested dual-ring and three-ring absorber. The parameters are as follows: P = 3.9 μm, R0 = 0.3 μm, R1 = 1.55 μm, R2 = 1.5 μm, R3 = 1.4 μm, R4 = 1.25 μm, R5 = 1.2 μm.
Fig. 14 (a) Surface current distribution of the nested dual-ring absorber at the resonant frequency of 47 THz under the normal y-polarized incidence. (b) Surface current distribution of the nested three-ring absorber at the resonant frequency of 47 THz under the normal y-polarized incidence.
3. Conclusion
In conclusion, a single-band graphene metamaterial absorber reaching nearly 100% at 37.8 THz is designed, and influences of geometric parameters of the absorber on the absorption are analyzed. It is found that the widest and highest absorption may be obtained by optimizing thickness of the dielectric and radius of the ring. Based on this simple single-ring absorber. Two types of broadband and polarization-independent absorbers are designed. For the composite four-ring structure with azimuthally symmetry, the 90% absorption bandwidth is about 7.1 THz. For the nested dual-ring and three-ring absorber, the bandwidth of 90% increases to 8.7 THz and 11.9 THz, respectively. The wide absorption is explained by using impedance matching theory and surface current distributions. The absorbers are composed of metal-graphene-dielectric-metal structure, which can be easily tuned via the chemical potential μc of graphene coating on the dielectric surface, and more suitable for practical applications.
Furthermore, the influence of layers of graphene on the absorption is investigated for the composite four–ring structure, and four layers of graphene is selected to obtain the wide and high absorption. It is also found that the absorption has little change for the absorber when three different expressions of graphene conductivity are used in the simulation.
Funding
National Natural Science Foundation of China (No. 61875017 and 61107030); State Key Laboratory of Millimeter Waves (No. K201703); Fundamental Research Funds for the Central Universities.
Acknowledgments
We would like to thank Dr. Syed Mohsin Ali Shah in Beijing University of Posts and Telecommunications for his grammar and language support in the manuscript.
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