1. Introduction

In recent years, metamaterial graphene absorber (MGA), which is a kind of electromagnetic absorber consisting of metal metamaterial resonator and graphene sheet or structure, has been attracting great interest and making great progress in the past several years [1–6]. Comparing with conventional absorber, the thickness of MGAs is much smaller and the design is more flexible and efficient. However, the absorption bandwidths of most of the common MGAs are often narrow since resonance is utilized in the process of absorption, limiting their potential applications in electromagnetism regions. In order to broaden the absorption band, some efforts have been made from microwave [7, 8], terahertz [9] to optical frequencies [10]. A simple approach is to utilize multi-resonance by combining multiple resonators with different sizes together to form a super unit cell [11, 12]. The second approach is to utilize multilayer structure with different geometric parameters separated by dielectric layers to realize the multi-channel or broadband absorption peaks [13]. However, once the structure of metamaterial absorber is fabricated, the spectral position of the absorption peak and bandwidth are usually fixed. In the practical applications, tunable absorber is more attractive for smart systems due to their great flexibility [14]. Therefore, designing a dynamically tunable broadband THz absorber is of great significance.

Several methods have been reported in literatures to make metamaterial absorber tunable [15–17]. In the microwave regime, one approach to achieve a tunable impedance layer is to combine PIN diodes into the absorber structure [18, 19]. However, the absorbers design and fabrication process are even more complicated since PIN diodes are involved. Meanwhile, these absorbers are also extremely hard to scale down to a higher frequency such as the THz or infrared regimes [20]. A tunable THz absorber based on a microelectromechanical systems (MEMS) technology has been designed [21]. Nevertheless, the complexity of this structure leads to the inevitable difficulties in fabrication and realization because of the aforementioned technological reasons. In order to solve these problems, new materials such as graphene have been utilized to realize tunable absorber in THz and infrared frequency range recently. Graphene, which is a two-dimensional honeycomb structure consisting of one monolayer of carbon atoms [22], has exceptional electrical and optical properties [23–25]. More importantly, graphene-based absorbers can operate as tunable absorbers by changing the chemical potential or bias voltage.

Inspired by earlier works [11, 26], in this paper, an ultra-thin and broadband metamaterial absorber which is frequency tuned by graphene in the far-infrared region is designed. Numerical results show that the broadband MGA presents a reflectivity of less than −10 dB covering from 22.02 to 36.61 THz, with a thickness of 0.76 μm (only 0.09λ at the lowest frequency). By varying an external bias voltage applied to the graphene, absorption band and spectral position of the proposed absorber can be controlled. In addition, the analysis of current and field distribution at theses resonance frequencies is performed to better understand the resonant mechanism. The analysis of power loss density is also performed to further explore the resonant mechanism. The merits of this presented design are much thinner and have a relatively wide tunable characteristic.

2. Modeling and simulation

The designed MGA is shown in Fig. 1. Figure 1(a) is the perspective view and Fig. 1(b) is the single resonator. As shown in Fig. 1(a), the basic unit cell of the designed absorber consists of $2\times 2$ resonant elements and a background plane (thickness is 0.2 μm) which prevents any transmission. Each resonator is located in the center of the corresponding portion and has the different dimensions. The square gold patches coupled with graphene are separated by a dielectric spacer from the gold ground. In order to show the details of each resonator structure clearly, we have drawn the constituent in Fig. 1(b). The metal is selected as gold with conductivity of $\text{σ}=4.56\times {10}^7\text{S}/\text{m}$, and the thickness of each gold patch is 0.1 um throughout. The dielectric constant of the substrate is ε_r = 2 and the thickness is t = 0.46 μm. The period of the proposed unit is p = 10 μm. The other geometric parameters are as follows: L₁ = 2.3 μm, L₂ = 3.1 μm, L₃ = 1.9 μm, and L₄ = 2.7 μm, respectively.

 

Fig. 1 (a) Schematic diagram and geometric parameters of the proposed MGA unit cell (b) schematic of the single resonator structure and angles φ and θ for the cases of oblique incidence.

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Due to the 0.2 μm-thick bottom metallic mirror (the continuous gold film) is thick enough to suppress all wave transmission (T(ω) = 0), the absorption calculation could then be simplified to $A\left(\omega \right)=1-R\left(\omega \right)=1-{\left|S_{11}\right|}^2$. Absorbance can be maximized by minimization of reflection from the top surface of this proposed structure. Therefore, we can use the reflectivity to express the absorption of the MGA. To verify our design, a full wave electromagnetic (EM) simulation has been performed to get the reflection parameter S₁₁ by using CST. Periodic boundary conditions are set in all xz and yz planes to approximate an infinite array, and a Floquet port is assigned on the top boundary in the z-direction. In the simulation, graphene is modeled as a conductive surface with conductivity calculated form Kubo formula [27]. The conductivity of graphene can be written as follow:

3. Results and discussion

Due to the existing coupling between the resonators, we cannot get an optimal result by directly assembling the four resonators at their right dimensions into one-unit cell. Here, we do not discuss each single resonator structure. By using the particle swarm optimization (PSO) method [28], the final optimal geometrical parameters were obtained and listed in section 2. Under normal incidence with the electric field polarized along x axis, the simulated reflection spectra of the proposed MGA is depicted in Fig. 2. From this simulation result, we can find that the final optimized reflection band below −10 dB ranges from 22.02 to 36.61 THz. It can find that there exists four absorption peaks at 24.25 THz, 26.55 THz, 28.85 THz and 35.08 THz respectively. Here, the graphene sheet is used to enhance the absorption of this absorber. As shown in Fig. 2(a), the reflection band below −10 dB without graphene is only 0.17 THz, much less than the proposed structure.

 

Fig. 2 (a) Simulated reflection spectra as function of frequency. (b) Simulated results for the proposed absorber at different incident angles φ with θ = 0°. (c) Reflection map as a function of the frequency and incidence angle θ with azimuthal angle φ = 0°.

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In practical applications, the polarization insensitivity is a significant property for absorber. Therefore, it is necessary to consider the polarization dependence of the proposed MGA. In the first case, we keep the magnetic field component paralleled to the z-axis and define the angle φ between the wave vector and the x-axis on the xy plane. In the second case, the magnetic field component is paralleled to the y-axis and we vary the angle θ between the wave vector and the z-axis on the xz plane as shown in Fig. 1(b). Reflection characteristics under normal incident planar EM wave with different polarizations have been plotted in Fig. 2(b). It can be observed that the reflection spectrum is a little sensitive to the angle φ, which is attributed to the asymmetric property of this structure.

The influence of incidence angle θ on the reflection characteristics was also investigated. Figure 2(c) presents the reflection spectra as a function of frequency and incidence angle θ. It can be seen that the reflection bandwidth remains −10 dB at the angle of θ = 10°. When the angle θ continues to increase, the reflection bandwidth becomes narrower. This is due to a higher-order mode could appear when incidence angle θ is beyond 10°, which caused the incident magnetic field can no longer efficiently drive circulating currents between the two metallic layers, and then cannot effectively incident magnetic resonance [11].

In order to disclose the resonant mechanism and broadband absorption of the proposed MGA, the surface current and magnetic field intensity distributions at the different resonant frequency were plotted in Figs. 3 and 4. The arrow indicates the direction of flow while the color represents the intensity of the field. Referring to the Fig. 3, it can be seen that the current distributions at the resonance on the front layer are always anti-parallel to the back layer, and each state is different at each resonance frequency. There exists a certain relationship between the structure size and the resonance frequency. Each resonance is mainly localized in a specific patch, where the smaller patch corresponds to the higher frequency.

 

Fig. 3 Distribution of induced surface currents on the front and the back metallic surfaces at the resonance frequencies of (a) 24.25 THz, (b)26.55 THz, (c) 28.85 THz and (d) 35.08 THz, respectively.

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Fig. 4 Distribution of the magnetic field at the resonance frequencies of (a) 24.25 THz, (b) 26.55 THz, (c) 28.85 THz and (d) 35.08 THz, respectively.

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Figure 3(a) shows the surface current distribution at the lowest frequency 24.25 THz. It can find that the surface current is mainly concentrated on the square patch 2 with the largest size. The surface current distribution at 26.55 THz is displayed in Fig. 3(b), with the surface current mainly confined within square patch 4. Figures 3(c) and 3(d) show the surface currents are mainly distributed on the two smaller patches 1 and 3. Obviously, different sizes of the square patch produce different resonance frequencies. Although there exists couplings between square patches 1, 2, 3 and 4, multiple absorption bands overlap with each other to extend the absorption bandwidth.

The magnetic field distributions at the different resonance frequencies are investigated and shown in Fig. 4. The anti-parallel currents formed on the front and back layers give rise to the corresponding magnetic resonance. A similar result can also be observed for the case where the resonance at lower frequency is mainly confined at the large patch, while a higher frequency is at the small patch. At the point of resonance frequency, the absorption is caused by the power losses occurred due to the strong magnetic resonances where the EM wave is coupled in the structure and converted into thermal energy.

Meanwhile, we calculated power flow distribution in the absorber since it can provide detail information about how and where the absorption happens. Figure 5 shows the power flow of the designed absorber from a view in the yz plane at four resonance frequencies. We can see that most of the incoming energy first propagates downwardly along the –z direction in the air gap without penetrating into the structure until it reaches the position where the enhanced electromagnetic field is concentrated, and then whirls into the dielectric substrate, forming vortexes close to the interface between square patches and regions. Figures 5 (a) and 5(d) depict the distribution of power flow in the mid-plane of the patches 2 and 3 at the resonant frequencies 24.25 THz and 35.08 THz, respectively. Things are much different at two frequencies. At lower frequency of 24.25 THz, the power flow mainly distributed in the patch 2, while at the higher frequency of 35.08 THz, the power flow mainly concentrated in the patch 4. However, for resonances at 26.55 THz and 28.85 THz (Figs. 5(b) and 5(c)), the power flow is trapped in the patches 4 and 1, where the sizes are in the middle of four patches. Compared Fig. 4 with Fig. 5, we can find that the vortexes locate exactly at the places where the magnetic field concentrates.

 

Fig. 5 Calculated power flow distribution at the resonance frequencies of (a) (a) 24.25 THz, (b) 26.55 THz, (c) 28.85 THz and (d) 35.08 THz, respectively.

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4. Tunable MGA

Graphene can be used for amplitude tuning in the infrared spectrum [29]. Therefore, it can serve as a tunable material by controlling the bias voltage on the graphene layers. Here, by varying the Fermi level of graphene through controlling the bias voltage, we realized the working bandwidth dynamically tune between broadband absorption and narrowband absorption. Figure 6 displays the simulated reflection spectra with different Fermi level. It can find that when the Fermi levels μ_c1 = 0.1 ev, μ_c2 = 0.2 ev, μ_c3 = 0.4 ev and μ_c4 = 0.4 ev are applied between each graphene patch and bottom metal reflector, the bandwidth of below −10 dB reaches approximately 12.88 THz and the peak position is at 29 THz. However, when no bias voltage load on graphene patch 1, 2 and 4, and only μ_c3 = 0.4 ev, the working bandwidth becomes narrow. Meanwhile, the magnitude of the reflection is increased. In fact, there are many combinations of bias voltages loaded between graphene patches and bottom metal. Thus, the absorption bandwidth can be modulated arbitrarily.

 

Fig. 6 Reflection spectra with different Fermi level

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5. Conclusion

In summary, we have designed and numerically verified a broadband infrared absorber based on metamaterial and graphene. The simulated results have been demonstrated that the 90% absorption band (S₁₁< −10 dB) spans from 22.02 to 36.61 THz with a thickness of 0.056-0.09 free-space wavelength. By dynamically varying the graphene’s chemical potential via the voltage biasing, the absorption band can be adjusted actively. In addition, this type of MGA is relatively sensitive to the incident angle θ. We believe that our study will provide more flexibility in designing dynamically tunable devices through graphene and could be used in many promising applications, such as smart absorbers, photovoltaic devices and tunable sensors.