1. Introduction

Metamaterial perfect absorbers (MPAs), a branch of metamaterials, currently have raised extensive interests as they are becoming a crucial component of high-resolution imaging, sensing and detecting systems in the terahertz regime [1–3]. MPAs are often realized by using lossy materials in periodic structures, and the basic mechanism of MPAs is that the incident electromagnetic fields are firmly confined and consumed inside the lossy materials [4–6]. As the first experimental demonstration of MPAs was implemented by Landy et al. in 2008 [6], where a classical sandwiched structure was presented and the incident electric and magnetic fields were independently absorbed by metamaterial resonators. From then on, large amount of structures of MPAs were proposed, but plenty of them were narrow in bandwidth [7–9].

The broadband property of MPAs is of great importance to the practical applications of optoelectronic devices, such as bolometers and solar energy-harvesting devices [10–13]. To achieve broadband absorption, various approaches have been investigated. One common strategy is to utilize multi-resonances by embracing multiple resonators with small differences in geometry size in one unit cell, and the continuously small different resonance frequencies can be merged to form a broadband absorption spectra [14–16]. Another approach of effective broadband structures is to overlay the multi-layered pattern with different geometry parameters separated by dielectric with different thicknesses [17–19]. Meanwhile, the tunable property of absorbers is more attractive in practice due to flexibility [20–22]. Compared with other new materials, graphene is a two-dimensional crystal composed of a monolayer of carbon atoms arranged in a honeycomb lattice and it is extensively adapted due to its fantastic electromagnetic properties [23–27]. Another remarkable property of graphene is that its Fermi level can be dynamically changed by applying an external gate voltage [28,29]. Up to now, multiple graphene-based structures of MPAs have been proposed in the microwave, infrared and terahertz regime [16,19,30–32], and polarization-independent and angle-insensitive broadband absorbers have attracted enormous interest.

On basis of previous work, a novel polarization-independent broadband absorber with near-unity absorption in the terahertz regime is presented here. By combining the gradient diameter of the graphene sheet with circular symmetry of the unit cell, polarization-independent and broadband properties are achieved simultaneously. The results show that the absorber’s normalized bandwidth with 90% terahertz absorption reaches 1.57 THz when the Fermi energy of graphene sheet is set as 0.7 eV under normal incidence. To better understand the mechanism of broadband absorption, the electric field distribution and surface current distribution of the structure are studied and discussed. Furthermore, the tunable property of the absorber is investigated and the peak absorption can be tuned from 19% to 100% by changing the Fermi energy of graphene from 0 to 0.9 eV via electrostatic doping.

2. Design and simulation

This designed unit cell of the metamaterial absorber is illustrated in Fig. 1. Figure 1(b) shows that the proposed absorber is a classical sandwich structure, which is composed of a target-patterned graphene resonator on the top layer and a continuous metallic ground plate spaced by a dielectric substrate. Gold is selected as the ground plate, whose conductivity is described by Drude model with a plasma frequency${\omega }_p=4.35\pi \times {10}^{15}$rad/s and collision frequency${\omega }_c=13\pi \times {10}^{12}$rad/s [33], and the thickness is$n=200nm$. For the dielectric material, we adopt the low loss TOPAS polymer with permittivity$\epsilon =2.35$ [34] and the thickness is$h=27\mu m$. As shown in the Fig. 1(b), the target-patterned graphene layer consists of one circle disk with radius$R=23\mu m$, and an annulus with inner radius$R_{11}=24\mu m$and outer radius$R_{12}=35\mu m$, which is separated by a gap$g=1\mu m$. The perspective view is presented in Fig. 1(c). Graphene is chosen as the material of top layer and its conductivity can be expressed as ${\sigma }_{gr}={\sigma }_{\mathrm{int}ra}+{\sigma }_{\mathrm{int}er}$(unit:$S/m$)with the intraband and interband contributions from the Kubo formula [35,36]. In the Terahertz range, the photo energy $\hslash \omega \ll E_f$,$E_f\gg k_{B}T$, that the contribution of the interband${\sigma }_{\mathrm{int}er}$is negligible compared with the intraband${\sigma }_{\mathrm{int}ra}$which can be expressed as:

 

Fig. 1 Proposed broadband metamaterial absorber with a target-patterned graphene layer. (a) Schematic of the proposed broadband tunable metamaterial absorber. (b) Top view of the unit cell, (c) Perspective view of the unit cell. The geometry parameters of the proposed structure are set as (unit:$\mu m$): $p=75,h=27,R=23,R_{11}=24,R_{12}=35,g=1,n=0.2$.

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In the modeling and simulation, frequency domain solver was selected and the simulated frequency range was set as 0.1 to 3.5 THz. In the boundary condition setting, the x-direction and y-direction were both set as unit cell and the two-sides of the z-direction were Floquet ports. To simulate the graphene more accurately, as the graphene is in fact a single-layer carbon atom material, the graphene sheet was modeled as an equivalent 2D surface impedance layer without thickness which was built from a closed planar circular curve extruding to a surface. Here, we assume the initial chemical potential of graphene is 0.7 eV, relaxation time $\tau =0.1\text{ps}$, and the absolute temperature$T=300\text{K}$.The absorption of the absorber can be calculated as$A(\omega )=1-|S_{11}(\omega ){|}^2-|S_{21}(\omega ){|}^2$,which can be simplified as$A(\omega )=1-|S_{11}(\omega ){|}^2$.The transmission$S_{21=0}$is due to the thickness of the golden ground layer ($n=200nm$) is much thicker than the skin depth of the incident terahertz wave. The$S$parameters can be obtained in the CST Microwave Studio simulation.

3. Results and discussion

To study the absorption spectra of the proposed broadband tunable metamaterial absorber, a numerical full-wave simulation has been performed based on the finite integration algorithm of CST Microwave Studio. We firstly investigate the absorption spectra under normal incidence with and without the graphene sheet, and the results are shown in Fig. 2. From the red curve(absorption spectra with graphene sheet), as expected, broadband absorption is observed that 90% absorption of the absorber reaches 1.57 THz, starting from$f_{\min }\text{=}0.95$THz to$f_{\max }\text{=2}\text{.52}$THz, when the Fermi energy of graphene is set as 0.7 eV. When the graphene sheet is removed from the structure, zero absorption is noted, which is represented by the blue curve.

 

Fig. 2 Simulated absorption spectra of the absorber under normal incidence when the chemical potential of graphene is set to be${\mu }_{\text{c}}=0.7$eV.

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Additionally, we also investigate the influence of the thickness of TOPAS dielectric layer on the absorption. As shown in Fig. 3. The absorption curves appear a red shift when the thickness of TOPAS spacer increases from 24 to 30$\mu m$, and the peak absorption keeps increasing. Adhering to the principle of high absorption in a continuous bandwidth, we choose the thickness of $h=27\mu m$as the best value. It should be noted that, in our calculation, we ignore the loss of TOPAS material itself because it is very low across the THz band.

 

Fig. 3 Absorption spectra of the absorber under different thickness of TOPAS dielectric spacer.

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To better understand the absorption mechanism, we further investigate the electric field distribution and surface current distribution of the absorber, as shown in Fig. 4 and Fig. 5, respectively. Figure 4(a) displays the electric field distribution of the absorber at 0.2, 0.8, 1.6, 2.2 THz in the TE mode, which are represented by the pictures from left to right, respectively. As shown from the first two pictures in Fig. 4(a), weak electric field appears in the structure at 0.2 THz, while a strong electric filed is concentrated on the circle gap and the space between two unit cells along the y-axis at 0.8 THz, respectively. It is easy to find, at 0.2 and 0.8 THz, there exists a classical absorption mechanism that consists of an electric resonance (realized by the top graphene layer) and a magnetic resonance (realized by the top and ground layer). It matches well with the results published in [6], Landy et al, and can be further verified by the following current distribution displayed in Fig. 5. When it comes to 1.6 and 2.2 THz, we can find from the next two pictures in the Fig. 4(a) that the graphene localized surface plasmon resonance is stimulated by the incident electromagnetic wave. Compared with the situation at 0.2 and 0.8 THz, the electric field spreads from the gap to almost the entire graphene pattern with a comparable lower electric field maximum amplitude, but the electric field among the graphene pattern is more uniform and stronger which agrees well with the absorption spectra given above. Figure 4(b) shows the electric field distribution in the TM mode, which is same as that in Fig. 4(a) when rotated by 90$°$.

 

Fig. 4 Electric field distribution of the proposed absorber at 0.2, 0.8, 1.6, and 2.2 THz, (a) for the TE mode, and (b) the TM mode, when under normal incidence with the chemical potential of graphene ${\mu }_{\text{c}}=0.7$eV.

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Fig. 5 Surface current distribution of the proposed absorber at 0.2, 0.8, 1.6, and 2.2 THz, (a) on the front layer; and (b) the back ground layer, when under normal incidence with the chemical potential of graphene ${\mu }_{\text{c}}=0.7$eV.

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The surface current distribution on the front graphene layer and back ground layer is next investigated to further verify the results described by the electric field distribution. As shown in Fig. 5, at 0.2 and 0.8 THz, the maximum current on the top layer flow from bottom to top while it is inversed on the back ground layer, the current at 0.8 THz is larger than that at 0.2 THz, which agrees well with the electric field distribution described above. When it comes to the 1.6 THz, the surface current on the back ground layer is much different with the distribution at 0.8 and 0.2 THz. On the front graphene layer, the current emits from the bottom and converge on the top mainly along the center graphene and gap, and the current in the back ground layer keeps the same flow direction with the top layer, which is different with the magnetic resonance shown at 0.8 and 0.2 THz. The surface current distribution is mainly resulted by the graphene plasmon resonance which is consistent with the results described in [28], Vakil and Nader Engheta.

The absorption spectra of absorbers under different polarization angles and oblique incidence angles are essential to applicable devices. Firstly, the influence of polarization angles to the absorption of the absorber is investigated. As shown in Fig. 6, we can see that the absorption curve remains highly consistent when the polarization angles vary from 0$°$to 90$°$with a step width 10$°$. The polarization-independent property of the absorber is mainly attributed to the circular symmetry of the unit cell, which consists of a cubic substrate and nummular pattern.

 

Fig. 6 Simulated absorption spectra of the absorber for different polarization angles from 0° to 90° with step width 10° under normal incidence.

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Next, the absorption spectra under oblique incidence in both the TE and TM modes are studied, as shown in Fig. 7(a) and Fig. 7(b), respectively. In the simulation, the incidence angles vary from 0$°$to 80$°$with the step width of 10$°$. We can see the peak absorption keeps larger than 90% up to 70$°$incidence angles for the TE mode and 65$°$for the TM mode, respectively. Besides, the broadband absorption remains more than 75% with a bandwidth of 1.6 THz over a wide range of incidence angles up to 60$°$for the TE mode and 75$°$for the TM mode, respectively. Meanwhile, the absorption spectra occur a blue shift with increasing incidence angles.

 

Fig. 7 Absorption contour map of the absorber as a function of incidence angles and frequency under oblique incident angels from 0$°$to 80$°$with the step width 10$°$,(a) for the TE mode, and (b) for the TM mode. where ${\mu }_{\text{c}}=0.7$eV.

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Furthermore, the electrically tunable property of the broadband absorber is investigated at the end. Graphene is one kind of tunable material which is often used to tune the absorption amplitude. The surface conductivity of graphene sheet relates largely to its Fermi energy, which can be controlled by electrostatic doping or applying bias voltage [28,37]. Here, we implement the dynamically tunable property of the broadband absorber by varying the Fermi level of the graphene sheet located on the top layer of the unit cell. As shown in Fig. 8, the absorption amplitude changes from 19% to near 100% absorption with the Fermi energy varying from 0 to 0.9 eV. Here, the wide range of Fermi energy of graphene sheet can be modulated by sol-gel top gating method [37].

 

Fig. 8 Absorption spectra of the absorber with different Fermi energy of graphene sheet from 0 to 0.9 eV.

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4. Conclusion

We proposed and demonstrated a broadband tunable metamaterial absorber which effectively takes advantage of the graphene surface plasmon resonance in the terahertz regime. Some valuable properties are found in the absorber, such as polarization-independence and angle-insensitivity. According to the full-wave numerical simulation, the results show a broadband width of 1.57 THz with a central frequency 1.83 THz under normal incidence when the Fermi level of graphene sheet is set as 0.7 eV. Besides, the absorption of the absorber remains unchanged for almost any polarization angles, and the broadband absorption remains more than 75% over a wide range of incidence angles up to 60$°$for the TE mode and 75$°$for the TM mode. Additionally, we performed analysis of the electric field distribution and surface current distribution of the absorber to better understand the mechanism of broadband absorption in the structure. The tunable property of the absorber is also investigated by controlling the Fermi level of graphene sheet located on the top layer, and the peak absorption can be tuned from 19% to near 100% by changing the chemical potential from 0 to 0.9 eV via sol-gel top gating method. The proposed absorber is designed with a compact single-layered graphene pattern which enables the ease of fabrication, and it can be scalable to the infrared and visible frequencies for many promising applications such as tunable sensors, filters and photovoltaic devices.