1. Introduction

Perfect electromagnetic (EM) absorbers have drawn considerable interests in photonic research due to many potential applications, such as solar photovoltaics cells, heat radiations, photo-detections [1,2]. Recently, metamaterials, artificial materials composed by subwavelength micro-units (or meta-atoms) arranged in specific orders, have shown unprecedented abilities to manipulate EM waves. Many fascinating physical effects were realized, such as negative refraction [3,4], super resolution imaging [5], optical cloaking [6,7]. In particular, Landy et al. reported a metamaterial-based prefect absorber (MPA) in 2008, designed based on impedance-matching principle via manipulating the system’s electric and magnetic responses simultaneously [8]. Almost at the same time, Teperik et al. proposed a nanostructured metal surface to achieve omnidirectional light absorption aided by surface plasmon resonance [9]. Soon after that, a class of reflection-type metasurfaces, typically consisting of metal-insulator-metal sandwiched structures, were widely adopted to achieve perfect EM-wave absorption, utilizing the magnetic resonance between the top and bottom metallic layers [10,11]. These ideas inspire a series of works on EM wave absorptions ranging from microwave, THz to optical frequency [12–15]. However, while these MPAs have exhibited advantages in miniaturization, most of them still suffer from restrictions such as limited working bandwidth and fixed functionality, being unfavorable for certain applications.

As an important family member of MPAs, THz absorbers attracted much attention recently [13,16]. In particular, graphene-based MPAs exhibit exotic properties thanks to the exotic electronic, optical, mechanical, and gate-tunable properties of graphene [17]. Many graphene-based MPAs were proposed [18–25], which typically consist of graphene microstructures in different shapes, operating based on the plasmonic resonances in such graphene microstructures. However, most of these proposed MPAs still exhibit narrow working bandwidth. Although several approaches [26–32] were established to solve this issue, the proposed structures still possess some limitations, such as complex structure, decreased absorptivity.

In this paper, we propose a broadband and tunable THz wave absorber based on a simple graphene metasurface. Our device is a sandwich structure composed by a single-layer of graphene concentric double ring (GCDR) array and a metallic mirror separated by a thin SiO₂ spacer. Lateral couplings between two graphene rings hybridize the plasmonic resonances in two individual rings, which can significantly enlarge the device’s working bandwidth under certain conditions. Meanwhile, the functionality of our device is insensitive to both incident angle and polarization of impinging THz wave, thanks to the ring geometry and the deep-subwavelength responses of graphene microstructures. Finally, the working frequency band of the proposed device can be efficiently tuned through modulating the Femi energy of the graphene. Our results may point out a new possibility to achieve broadband tunable meta-devices in THz and other frequency domains.

2. Results and discussions

2.1 Geometry and principle of the proposed graphene absorber

Figure 1 depicts the schematic of the proposed graphene-based MPA, which is constructed by a single layer of the GCDR array and an optically thick gold mirror, separated by a $\text{28}\mu \text{m-}thick$lossless SiO₂ spacer with${\epsilon }_{\text{d}}\text{=}3.9$. Here, the concentric inner and outer graphene rings are optimized with$\text{1}\text{.5}\mu \text{m}$separation to induce the plasmonic hybridization effect and thus achieve the desired broadband absorption (see detailed structural parameters in the caption of Fig. 1). Here, the metallic ground plate with a conductivity ${\sigma }_{\text{gold}}\text{=4}\text{.09}\times {\text{10}}^{7}S/m$ will guarantee the complete reflection for the impinging THz wave like a “mirror”. In our proposed device, a layer of ion-gel was spin-coated on the graphene patterns and contacted to the Au electrodes serving as the top gate. Meanwhile, an ultrathin and transparent conductive thin layer was deposited between SiO₂ layer and graphene rings serving as the bottom gate [21].

 

Fig. 1 Schematic of the proposed broadband THz absorber consisting of the GCDRs and the gold mirror separated by a thin SiO₂ spacer. The ion-gel was spin-coated on the graphene nanostructures and contacted to the Au electrodes as the top gate. And an ultrathin and transparent conduct thin layer was deposited between the SiO₂ and graphenes as the bottom gate. The geometrical parameters of GCDRs are $\text{a=5}\text{.5}\mu \text{m,}\text{b=4}\mu \text{m,}\text{c=2}\text{.5}\mu \text{m,}$$\text{d=2}\text{.2}\mu \text{m,}\text{t=28}\mu \text{m,}$ and the lattice constant is$\text{L=15}\mu \text{m}\text{.}$

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In our numerical simulations, we utilize an effective surface conductivity model to describe the graphene layer. It is known that, the surface conductivity of graphene ${\sigma }_{\text{gra}}$ is governed by the Kubo formula that takes both the intraband and interband transitions into considerations [33–35]

The working principle of such reflective MPAs can be understood as follows. While the incident light illuminates the device, anti-parallel currents are excited on both the top graphene layer and the bottom metallic mirror, leading to a strong magnetic resonance [10,11,40,41]. Since the graphene layer and the metallic mirror are very close (i.e.,$\text{28}\mu \text{m}$ or about$\lambda \text{/8}$separation), strong coupling effect leads to an extreme strong near fields that may be dissipated by the lossy graphenes. Guided by our previous work [42], the quality factors of the radiation loss and absorption loss of our device is optimized to equal to each other, which is a straightforward criterion to achieve the perfect absorption functionality around the resonance frequency. In another similar picture, illuminated by the incident light, localized surface plasmon modes or gap plasmon modes will be excited inside the graphene microstructures [21,43,44], resulting in considerable enhancement of light absorption.

2.2 Numerical demonstrations of the broadband absorption

We perform finite element method (FEM) numerical simulations to investigate the proposed graphene based THz meta-absorber. To obtain its EM responses, we put one unit cell inside the simulation box that is surrounded by periodic boundaries to describe equivalently an infinitely large MPA slab. A plane wave port is adopted as both the source to shine the device and the receiver to obtain its reflectance spectrum, i.e.,$\text{R}(\omega )=|S_{11}(\omega ){|}^2$. Since there is no transmission for our device designed in a total reflection geometry, its absorption efficiency can be described easily by the equation$\text{A}(\omega )=1-\text{R}(\omega )$.

First, we consider the case that x-polarized THz waves are normally illuminated on the device, as illustrated in Fig. 1. Figure 2(a) depicts the calculated absorption spectra of the proposed graphene MPA (see black line), with its top view shown in Fig. 2(d). It is noted that the proposed device exhibits a high absorptivity of above 90% from 1.18 to 1.64THz. Obviously, there exsits two absorption peaks located respectively at 1.26THz and 1.54THz within the band. To clarify their physical origins, we further calculate the absorption spectra of two simplified graphene metasurfaces with the original GCDRs at the top layer replaced by either the isolated inner ring (see Fig. 2(b)) or the isolated outer ring (see Fig. 2(c)). Obviously, while the impinging wave is incident upon the absorber shown in Fig. 2(b) (top view), a resonance peak appears at about 1.48THz (see red line in Fig. 2(a)), that should correspond to the high-frequency absorption peak of the GCDR structure (see black line in Fig. 2(a)). Analogously, the absorption peak at 1.28THz for the absorber composed by the outer graphene ring (see green line in Fig. 2(a)) should correspond to the low-frequency absorption peak of the GCDR structure (see black line in Fig. 2(a)). Quite interestingly, although both of the two graphene single ring (GSR) metasurfaces (see Figs. 2(b, c)) exhibit limited absorptivity and narrow bandwidth, the GCDRs absorber can function as a perfect THz absorber with a absorptivity of high above 0.9 and a broad working band from 1.18 to 1.64THz. Moreover, while the low-frequency peak is red-shifted from 1.28 to 1.26 THz, the high-frequency peak is blue-shifted from 1.48 to 1.54THz, compared with the two GSR structures. Therefore, the GCDRs absorber can work well within much larger frequency band. Indeed, we purposely utilize the coupling effect between the two GSRs to achieve the good performance of the proposed GCDR absorber [45–47].

 

Fig. 2 (a) Simulated absorption spectra of the proposed GCDR absorber (black line) and two GSR absorbers with the top graphene double ring replaced by the isolated inner ring (red line) and outer ring (green line). (b-d) Top views of three graphene MPAs comprised by the single inner ring, single outer ring and double rings, respectively.

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Next, we perform full wave simulations to verify the plasmonic hybridization model utilized in the proposed GCDR metasurface. Figures 3(a, b) shows the calculated electric field patterns (arrows for the direction and color for the intensity) at the top graphene layer of two GSR absorbers at their absorption peaks, i.e., 1.28THz and 1.48THz. Obviously, illuminated by the impinging light, positive and negative induced charges are accumulated at opposite sides of the graphene ring. The electric dipolar responses depicted in Figs. 3 (a, b) give rise to the absorption peaks at 1.28 and 1.48THz, respectively (see green and red lines of Fig. 2). The electric field patterns for the GCDR absorber at its two absorption peaks are presented in Figs. 3(c, d). The directions of electric field (see arrows) clarify clearly the induced charges of the coupled plasmonic modes being “$+-+-$” at 1.26THz and “$++--$” at 1.54THz, respectively. It implies that the low (high) frequency hybridized mode of the GCDR absorber depicted in Fig. 3(c) (Fig. 3(d)) is formed by two anti-parallel (parallel) dipolar modes of the graphene single rings. Since the inner and outer graphene rings are close in the concentric configuration, their dipolar modes can interact with each other and form the hybridized plasmonic modes. Moreover, due to the coupling effect, the low (high) frequency hybridized mode is red (blue) shifted to 1.26THz (1.54THz), as compared to the resonance mode of GSR absorber shown in Fig. 3(a) (Fig. 3(b)). Such behaviors perfectly justify our idea to realize the broadband THz wave absorption based on the plasmonic hybridization model [45–47], as schematically shown in Fig. 3(e).

 

Fig. 3 (a-d) Simulated electric field patterns (arrows for the direction and color for the intensity) at the top graphene layers of three absorbers shown in Fig. 2 at their corresponding absorption peaks (see inset for the frequency). (e) Energy-level diagram to describe the plasmonic hybridization effect in the proposed GCDR absorber due to the mutual coupling between its inner and outer graphene rings.

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2.3 Verification of incidence-angle-insensitive, polarization-independent and frequency-tunable properties

The proposed GCDR metasurface exhibits robust functionalities that are highly desired in practical applications. Figures 4(a, b) depict the simulated absorption efficiencies versus the frequency (x-axis) and incident angle (y-axis) for transverse electric (TE, i.e., E field along y direction) and transverse magnetic (TM, i.e., H field along y direction) polarization. Here, the Fermi energy of the graphene is fixed at$E_f\text{=0}\text{.5e}V$. It is noted that, for both polarizations, our structure can sustain a rather broad absorption band while the incident angle varies from 0° to 60°. In addition, some minor differences show up here. For TE polarization case (see Fig. 4(a)), as the incident angle increases, the two resonance modes red shift slightly with an additional resonance absorption peak appearing in the high frequency domain, leading to an enlarged absorption band. As for TM polarization case (see Fig. 4(b)), with the increase of incidence angle, the two resonance modes almost do not shift with their quality factors increased a little bit, leading to a slightly shrunk absorption bandwidth. The overall reduction of the absorptivity is inevitable because the interactions between incident electric field and the patterned graphene rings become weaker as the incident angle increases [48]. In general, the functionality of our device is insensitive to the incident angle, thanks to the deep subwavelength property of the graphene based metasurfaces.

 

Fig. 4 Calculated absorptivity (color map) as function of the frequency (x-axis) and the incident angle (y-axis), illuminated by (a) TE and (b) TM polarized waves.

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Next, we investigate the polarization-angle dependence of the proposed graphene absorber. Figure 5(a) depicts its absorption spectra with the polarization angle _$\phi$of incident waves varied to $0^{\circ },{15}^{\circ },{30}^{\circ },{45}^{\circ }$, respectively, for the normal incident case. Obviously, the absorptivity of our device is invariant strictly to the polarization angle$\phi$. It is quite understandable considering that the proposed GCDR absorber possesses the rotation-invariance symmetry. Figure 5(b) depicts the electric field pattern on the top graphene layer at 1.26THz (one of the absorption peaks) for several different$\phi$cases. As the polarization angle is varied, the hybridized plasmonic modes can be always excited inside the structure, just with their orientation angles rotating with the incident electric field simultaneously.

 

Fig. 5 (a) Absorption characteristics of the proposed absorber for normally incident waves with different polarization angle$\phi$. Here,$\phi$represents the angle of the incident electric field relative to x-axis. (b) The simulated electric field patterns on the top graphene layer at the first absorption peak (1.26THz) for$\phi {\text{=0}}^{\text{o}},\phi {\text{=15}}^{\text{o}},\phi {\text{=30}}^{\text{o}},\phi {\text{=45}}^{\text{o}}$.

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The absorption band of the proposed GCDR absorber can be further modulated via tuning the gating voltage applied on the graphene. As described by Eq. (2), the surface conductivity of graphene is almost linearly dependent on its Fermi energy in THz regime. Supposing that an electric gate is applied on our device, the Fermi energy of the graphene can be modulated continuously with the tuned gate voltage, thus enabling its electrically tunable property. Figure 6 shows the broadband absorption spectra as the function of the frequency (x-axis) and the Fermi energy (y-axis). Interestingly, as the Fermi Energy changes from 0.35eV to 0.65eV, the broad absorption band moving form 0.98~1.36 THz to 1.36~1.94THz with the absorptivity kept at above 80%. The increased bandwidth is due to the different blue shifting tendencies of two hybridized plasmonic modes.

 

Fig. 6 Calculated absorptivity (color map) as function of the frequency (x-axis) and the Fermi energy (y-axis) of the proposed GCDR absorber for normal incident case.

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3. Conclusion

In summary, we proposed a simple graphene metasurface to achieve broadband, tunable, polarization-independent and incident-angle-insensitive THz perfect absorption. Plasmonic hybridization [49] helps enlarge the absorption bandwidth, while the working frequency can be further tuned through gating the graphene. Compared to the conventional metallic meta-absorbers, the graphene-based devices can be much more subwavelength. The deep-subwavelength resonances and the specific ring geometry eliminate the incidence-angle and polarization-state sensitivities of the proposed device. Compared to previous multi-layer broadband absorbers [22,30], our deign is much simpler and is thus convenient for practical applications. We believe that this idea may inspire other tunable and broadband meta-devices working in both THz and other frequency domains, including heat radiators, smart absorber, tunable sensors, etc.