Dual broadband absorber based on graphene metamaterial in the terahertz range

Ning Hu; Fengling Wu; Li-an Bian; Hanqing Liu; Peiguo Liu

doi:10.1364/OME.8.003899

1. Introduction

Metamaterials, an artificially engineered periodic nanostructure with many exotic electromagnetic properties, has attracted intense attention of the scientific community after the experimental demonstration of negative refractive index materials by Smith et al. [1], and typical metamaterials composed of metallic wires, split-ring resonators (SRRs) and their variation, such as S-shaped and double S-shaped resonators [2–4]. In recent years, metamaterial absorbers have become a widespread research hotspot due to its potential applications for modulators, stealth materials and sensing [5–7]. To achieve high absorption, the electromagnetic resonance should be controlled to achieve the match between the MA and free space. In a match condition, the reflectivity is reduced and the incident EM waves are restricted to loss materials. Since Perfect absorption was firstly proposed by Landy in 2008 [8], various kinds of structures are proposed to realize perfect absorptions including multi-band absorbers [9,10] and broadband absorbers [11,12]. However, these absorbers have fixed operating frequency range and absorption performance once the fabrication is finished, which greatly limits their further applications.

Graphene, a lossy two-dimensional (2D) carbon material, possesses ultra-high electronic mobility, highly confined plasmon propagation and excellent mechanical properties [13]. More importantly, the conductivity and permittivity of graphene can be continuously regulated with the chemical potential in THz range, which is decided by chemical doping or bias voltage [14]. The extraordinary properties of graphene make it a good candidate for the design of tunable MAs. Though the light absorption is only about 2.3% for a single sheet of undoped graphene layer, perfect absorption can be achieved when graphene is patterned to periodic structures and surface plasmon resonances (SPR) is excited. For instance, graphene nanodisks [15], micro-ribbons [16], cross-shaped structures [17], graphene patches [18] as well as graphene and metal combined structures [19] are applied to realize tunable MAs. In addition, G. Yao et. al proposed a dual-band perfect absorber based on periodically patterned elliptical nanodisk graphene structures which are arranged in two vertical directions [20]. The design only has one shape which can greatly simplify the manufacturing process. Whereas, it cannot achieve broadband absorptions. Actually, to sustain high absorption, these absorbers relying on the resonant structures of unit cells usually have narrow bandwidth or limited number of operating bands. Except the graphene-based absorbers during THz range, experimental demonstration of microwave absorber using large-area multilayer graphene-based frequency selective surface (FSS) is conducted for the first time by H. Chen at. Al [21], which greatly expand the application ranges of graphene-based absorber.

To expand bandwidth or achieve multi-band absorption, various structures have been proposed. A typical method is to combine two or more resonators with different sizes together to form a super-unit-cell [22]. Another method is to stack multiple layers of the resonators with different geometric dimensions separated by dielectric layers with appropriate thicknesses [23]. For these kinds of multi-resonator graphene structures, the key lies in making the small frequency different resonances of the absorbers be merged to form a broadband absorption. Besides, a broadband terahertz absorber based on single-layered graphene ribbons with an absorption range from 2.5 THz to 3.8 THz is proposed [24], which use periodic arrays of graphene ribbons with gradient width and has much simple structures. Inspired by that, Qihui. Zhou [25] and Longfang. Ye [26] proposed broadband absorber with ellipse-shaped graphene layer and net-shaped periodically sinusoidally-patterned single-layered graphene structures respectively. Both of them utilize the fact that continuous plasmon resonances can be directly excited on patterned graphene with gradient width and thus broadband absorption is obtained. Nevertheless, a majority of the mentioned above graphene-based broadband absorbers have the drawback of incident angle or polarization dependence. Meanwhile, the absorbers with complicated structures demand extremely fine device fabrication technique and accurate basing voltage. Ref [26] may seem to share no one of the drawbacks, however, it has only one absorption band. Despite the progress have been made, it is still a great challenge to realize broadband and multi-band absorber in a simple structure. Combining those two desirable characteristics is a very difficult task especially incident angle tolerance and polarization is required at the same time.

In this paper, a new single-layer graphene-patterned absorber based on planar nested electrical split ring resonator (eSRR) is proposed to realize dual broadband absorption. By introducing the asymmetric eSRR unit with four kinds of split rings, multiple resonances are excited with one simple unit structure. Broadband absorption and multi-band characteristics are realized at the same time. There are two adjacent resonances with overlap band in low frequency range and two in high frequency range, thus forming two strong broad absorption bands respectively. With respect to conventional multi-resonator absorber, the asymmetric eSRR structures greatly simplify the manufacturing process. Since the conductivity of the graphene layer can be varied via the applied electric fields or chemical doping, the absorption strength of the proposed dual-band single-layered graphene absorber can be conveniently modulated from 10% to 98%. Though the structure is asymmetric, it is insensitive to polarization angles due to the specific design. Furthermore, the absorber has a range of wide incident angles and polarization insensitivity. The proposed absorber provides a new perspective to design dual broadband absorber and the design scheme can be applied to develop various broadband absorber in other frequency range.

2. Design and simulation methods

The structures of proposed MA are given in Fig. 1, which includes several stacked layers. On the top layer, there is a 100 nm thin ion-gel covered on patterned graphene, which has high capacitance density (fitted to 2.49 $μ F c m^{- 2}$ ) and is used to apply bias voltage on graphene [27]. The ion gel has a high refractive index which is comparable to that of SiO₂ ( $n_{g e l} = 1.43$ ), which can be used for simulations [28]. The Asymmetric eSRR-shaped patterned graphene, arranged periodically along x and y directions with a period of P, is placed on SiO2 dielectric substrate. The width of graphene arms and the length of gaps between them are denoted by w and g respectively. A thin gating layer is placed beneath the graphene sheet, which is composed by polysilicon with the permittivity of $ε_{r p} = 3$ [29]. The DC voltage is applied between the gold electrode on ion-gel and polysilicon to control the conductivity of graphene and realize dynamic characteristic. The SiO2 ( $ε_{s i o_{2}} = 4$ [30]) dielectric substrate with thickness $t_{s i o_{2}}$ is conducive to the growth and etching of graphene while gold film with the thickness of $0.1 μ m$ acting as a ground plate. Since the conductivity of gold is given by $σ_{g o l d} = 4.56 \times 10^{7} S / m,$ the thickness is much bigger than the typical skin depth in THz range. As a result, the EM waves are totally reflected on the ground. The monolayer chemical vapor deposition (CVD) graphene is molded as an equivalent 2D surface impedance layer without thickness in numerical simulations [26]. From the range of terahertz to optical frequency, the surface conductivity $σ (ω)$ , which consists of intraband and interband transitions, is determined by Kubo formula as follows [31,32]:

σ (ω) = σ^{intra} (ω)+ σ^{inter} (ω),

σ^{int r a} (ω) = \frac{2 K_{B} e^{2} T}{π ℏ^{2}} l n [2 \cos h (\frac{E_{f}}{2 K_{B} T})] \frac{i}{ω + i π^{- 1}}

σ^{inter} (ω) = \frac{e^{2}}{4 ℏ} [H (\frac{ω}{2}) + \frac{4 i ω}{π} \int_{0}^{\infty} \frac{H (ε) - H (ε / 2)}{ω^{2} - 4 ε^{2}} d ε,

where

H (ε)

is defined as:

Fig. 1 Structures and geometric parameters of the proposed broadband absorber (a) 3D views of the proposed absorbers where unit cells are arranged periodically along x- and y-directions, and a DC voltage V_g is applied on the gold electrode covered on ion-gel and the polysilicon layer beneath the patterned graphene (ion-gel on the top is not shown). (b) Vertical view of graphene unit cell, the parameters of the absorber are set as $p = 26,$ $d_{1} = 5,$ $d_{2} = 11.8,$ $d_{3} = 6.8,$ $h_{1} = 6.2,$ $h_{2} = 9.8,$ $b_{1} = 9.8,$ $b_{2} = 6.2,$ $w_{1} = 3,$ $g = 0.65,$ $t_{i} = t_{A} = 0.1,$ $t_{1} = t_{p} = 0.02,$ $w = 3,$ Unit: $μ m .$ (c) Side view of absorber unit cell in which the single-layer graphene is molded as an equivalent 2D surface impedance layer without thickness in numerical simulation.

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H (ε) = \sin h [ℏ ε / k_{B} T] / {\cos h [E_{f} / (k_{B} T)] + \cos h [ℏ ε / (k_{B} T)]} .

In the formula, $k_{B}$ is Boltzmann’s constant, e is the charge of an electron, $ℏ = h / 2 π$ is the reduced Plank’s constant, $E_{f}$ is chemical potential (Fermi energy), $ω$ is the frequency of the electromagnetic wave, and $T = 300 K$ is the room temperature. $τ = μ E_{f} / e v_{f}^{2} \approx 0.5 p s$ for $E_{f} = 0.5 eV$ is relaxation time with Fermi velocity $v_{f}^{} \approx 10^{6}$ m/s and the mobility $μ = 10^{4}$ cm²V⁻¹s⁻¹, which is moderate and easy to reach experimentally [33,34]. Within the bands of lower THz and far-infrared, the interband conductivity contribution can be neglected and $σ (ω)$ is determined by intraband contribution. Then $σ (ω)$ can be described as $σ (ω) = σ^{intra} (ω)$ and the surface impedance of a graphene monolayer can be obtained through $Z_{g} (ω) = 1 / σ (ω)$ .When the graphene is externally loaded a regulated voltage Vg, its chemical potential $E_{f}$ can be estimated by using the following formula [35].

| E_{f} | \approx ℏ v_{f} {(π a_{0} | V_{g} - V_{D i r a c} |)}^{1 / 2} .

where the constant estimated through a single capacitor model is

a_{0} \approx 9 \times 10^{16} m^{- 2} V^{- 1}

and the Dirac voltage offset caused by the natural doping is VDirac = 0.8 V [36]. Furthermore, the frequency dependent surface impedance of graphene for different chemical potentials is shown in Fig. 2. It can be seen that as chemical potential increases, both real part and imaginary part of the surface impedance decrease with chemical potential. With no states at the Fermi level in its neutral form, a moderate concentration of doping charge carriers n can significantly raise the Fermi energy to high values relative to the Dirac point. (e.g.,

E_{f} = ℏ v_{f} {(π n)}^{1 / 2}

) [37]. When chemical potential increases, the number of charge carriers n in graphene raises dramatically which enhances the electric conductivity. Thus, the surface impedance decreases. In addition, this modulation effect is more obvious when chemical potential is small. When

E_{f}

is large enough, the charge carriers tend to be saturate and the surface conductivity is mainly limited by the mobility of graphene.

Fig. 2 Surface impedance of graphene when chemical potential varies from 0.1eV to 0.6eV (a) Real part and (b) Imaginary part.

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To obtain the specific performance of the proposed structures, the three-dimensional full-wave numerical simulations are performed based on the Finite Element Method (FEM), where periodic boundaries in both x-direction and y-direction are assigned to the unit cell of the absorber. The incident wave was modeled as a Floquet port in z-direction so that both TE and TM polarizations can be easily obtained. Specially, TE and TM polarization are defined as follows: The wave vector k of the incident light is in the xoz or yoz plane (for TE or TM) and the electric field is in the x direction (TE) or in the yoz plane (TM). Adaptive tetrahedral mesh refinement has been used to enhance precision of simulation. The absorbance $A (ω) = 1 - {| S_{21}^{} |}^{2} - {| S_{11}^{} |}^{2}$ is calculated by S-parameters from simulations. Notice that no EM wave penetrates the structure, therefore, $S_{21}^{}$ is closed to 0. Furthermore, the absorption is simplified as $A (ω) = 1 - {| S_{11}^{} |}^{2}$ .

3. Results and discussion

3.1 Simulation results and mechanism analysis

The absorption spectrums for both TE polarization and TM polarization under normal incidence have been calculated and displayed in Fig. 3 when the graphene chemical potential is assumed to be $E_{f} = 0.5 e V .$ Obviously, there are two broad absorption bands (bandwidth is about 0.5 THz and absorptance is larger than 0.95) with the central frequencies of 1.6 THz and 4.75 THz respectively for both TE and TM polarizations. It is can be seen that the absorption curve of TM polarization is close to that of TE polarization but with a small red shift about 0.1 THz, which mainly results from the asymmetric structures in x and y directions and may be eliminated by further optimizing the size parameters of graphene eSRR structure. In addition, we notice that TE polarization shows better absorption performance in first absorption band and almost reaches perfect absorption in such a wide band.

Fig. 3 The absorption spectrums of the proposed absorber for different polarizations where graphene chemical potential $E_{f}$ is set as 0.5 eV.

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To explore the underlying mechanism of absorption, the simulated electric field amplitude (|E|) distributions for TM polarization on xoy and yoz planes of the proposed absorber are given in Fig. 4. Furthermore, the general surface currents are also indicated by the white arrows, where the density of the arrows indicate the current intensity. For the first absorption band (from 1.4 THz to 1.9 THz), strong electric field concentrates at the vertical gaps, indicating that the electric dipole resonances are excited along the two side arms of the unit structure. However, there is obvious electric field on the horizontal gaps at 1.45 THz while it is much weakened at 1.85 THz, leading to the increase of absorption frequency. As we can see, the current path is shortened at 1.85 THz compared to that at 1.45 THz, which further confirms that the resonance length is gradually changed and so will be the absorption frequency. As the equal resonance length varies gradually, the first broadband absorption is obtained. Significantly, the upper and lower frequency limits are determined by the shortest and longest resonance length respectively. For the second absorption band (from 4.5 THz to 5.1 THz), there is no evident circle currents along the unit structure while the electric resonances occur at the horizontal arms of the unit. The electric fields are distributed on the arms near the gaps at 4.6 THz while the middle horizontal arms show stronger electric fields at 5.0 THz. Therefore, second absorption band is mainly contributed by the vertical electric resonances excited on the horizontal arms. Specifically, we notice that confined fields are distributed at the edges of the horizontal gaps, which means electric resonances are also excited between the adjacent horizontal arms at 4.6 THz. Both kinds of electric resonances contribute to the absorption performance and this will also be discussed in next section. As frequency increases, the electric fields no longer distribute at the gaps and concentrates on the middle of horizontal arms. At 5.0 THz, the absorption is caused totally by vertical electric resonances occur at three horizontal arms. Hence, second broad absorption band is gained. In addition, from the electric field distributions on the yoz plane of the proposed absorber we can see tight field confinement around the graphene sheet on the top layer and adjacent dielectric substrate for both absorption bands, which means all the electric fields are trapped and then dissipated on the graphene layer and all absorptions are caused by electric resonances alone, which are in agreements with the above analysis. Though the conclusion is discussed under TM polarization, similar situation occurs at TE polarization and the mechanism of absorption is exactly same.

Fig. 4 The distributions of the electric field and surface currents of the proposed absorber with the graphene chemical potential $E_{f} = 0.5 e V$ under normal incidence at (a) 1.45 THz (b) 1.85 THz (c) 4.6 THz and (d) 5.0 THz. For each picture: xoy plane with z = 0 (left) and yoz plane cut along AA’ (right). The white arrows represent currents where the density of the arrows indicate the current intensity. The electric field is along y-direction and wave vector k along positive z-direction.

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To better understand the physical mechanism of the proposed absorber, two important parameters are also discussed. Figure 5 (a) and Fig. 5 (b) shows the relationship of absorptance and the width of graphene arms w and the length of gaps g respectively. As shown in Fig. 5 (a), when w varies from $5 μ m$ to $2 μ m$ , first absorption band remains almost constant. The reason is that first absorption band is associated with the electric resonances excited along the side arms and have little relationships with the horizontal arms. However, second absorption band tunes to a narrow absorption band since the absorption peak at 5.0 THz is disappeared as long as w varies. Because the absorption at 5.0 THz is caused by the horizontal arms in the middle, the absorptance is sensitive to the change of w. For another parameter g as we can see in Fig. 5 (b), the absorptance for both absorption band is not sensitive to the change of g and remains stable when g varies from $0.3 μ m$ to $0.9 μ m .$ Specially, we set g as 0 and find that first absorption band is greatly destroyed with an absorptance less than 0.5. As we know, the electric field concentrates at the vertical gaps in first absorption band. When the gaps vanish, the condition for electric resonances are not satisfied anymore and the absorptions are greatly weakened as a result. Although second absorption band still keeps good absorption characteristics, the absorption performance at 4.6 THz is significantly weakened as gaps disappear. This further confirms that there are electric resonances excited between the adjacent horizontal arms at 4.6 THz due to the existing of gaps, which contributes partly to the absorption at 4.6 THz. When g tunes to 0, the electric resonances no longer exist. By discussing the relationships of absorptance and parameters, we further explore the physical mechanism of the proposed absorber and find out how the parameters influence the absorptance in first absorption band and second absorption band respectively. Therefore, it is possible for us to manipulate the absorption performances of two absorption bands respectively without influencing another one.

Fig. 5 The simulated normal incidence absorption spectrums in TM polarization as a function of frequency and geometric parameters (a) w, the width of graphene arms and (b) g, the length of gaps in eSRR. The graphene chemical potential is set as $E_{f}$ = 0.5 eV and the unit is $μ m .$

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The proposed dual broadband metamaterial absorber can be experimentally by the following procedures [27,38,39]: monolayer graphene grown by chemical vapor-phase deposition on copper foil is transferred to SiO2 substrate, which is coated with a thin polysilicon layer via atomic layer deposition (ALD). Then the continues graphene is patterned into closely packed asymmetric split ring arrays using e-beam lithography with poly (methyl methacrylate) (PMMA) as an electron beam resist. Oxygen plasma (40W, 500 mT, 15 s) is used to etch away the exposed area, leaving the periodic pattern of graphene asymmetric split rings protected by a PMMA layer, which is then removed with acetone. After that, the patterned graphene is covered with ion-gel which is contacted with gold electrode. Finally, a gold film is added to the structures at the bottom to enhance absorption.

3.2 Frequency tunability and robustness of broadband absorber

The tunability of absorption frequency will be investigated in detail in this section since it is a significant characteristic in practical application. The surface conductivity of the graphene can be tuned by varying its chemical potential via electrostatic biasing, thus leading to the variation of absorption performance. Figure 6 indicates the absorption spectra as a function of terahertz frequency and the chemical potential under normal incidence for TE and TM polarizations respectively. Apparently, there are evident regulation effects on absorption strength for both polarizations. For TE polarization, it is obvious that absorptance declines for both absorption bands as $E_{f}$ decreases, while the second absorption band is more sensitive and drops to less than 0.1 when $E_{f}$ varies from 0.5 eV to 0.3 eV. Since the electric resonances are caused by patterned graphene, the regulation effect of graphene conductivity with chemical potential is more obvious in high frequency range as shown in Fig. 2, resulting that the second absorption band is more sensitive to chemical potential. As for first absorption band, though it changes more slowly compared to second absorption band, the absorption strength can be further weakened by decline chemical potential (not shown here). TM polarization shows a similar performance except that there is a more obvious red shift as chemical potential declines, which means the chemical potential not only influences the absorption strength, but also the absorption frequency simultaneously.

Fig. 6 The simulated normal incidence absorption spectrums of the proposed absorber for (a) TE polarizations and (b) TM polarizations when chemical potential various form 0.5 eV to 0.2 eV.

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To investigate the robustness of proposed MA, Fig. 7 shows the absorption spectrums as the function of incident angle $θ$ (defined as the angle between the direction of wave travel and negative z-direction) and operating frequency for TE and TM polarization respectively. It is found that the absorber exhibits excellent performances with relatively stable absorbance and bandwidth over a wide range of oblique incidence angles for both polarizations. For TM polarization, the peak absorptance remains more than 70% until $θ$ exceeds 75 degree for first absorption band and 70 degree for second absorption band. The absorption frequency range is almost constant as $θ$ varies. As $θ$ exceeds 75 degree, absorptance drops dramatically for both absorption bands. Since the absorption is associated with electric resonances on patterned graphene, which is excited by electric fields parallel to patterned graphene surface. The tangential components of the electric field decrease as θ increases, which leads to the destroy of electric resonances and furthermore the absorption. For TE polarization, the situation is similar except that the absorption peaks split to two for large incidence angles. In addition, there is slightly blue shift for second absorption band, which may be caused by some parasitic resonances occurred at the larger incident angle. From another point of view, the absorption is also related to the phase-matching conditions of reflection cancellation, which is sensitive to the thickness of the SiO₂ spacer and propagation constant for both TE and TM polarizations. According to transmission line theory [40], the propagation constant $k_{z p}$ along z-direction is decided by $k_{z p} = k_{p}^{} (1 - \sin^{2} θ)$ , where $k_{p}$ is the wave number in SiO₂. When $k_{z p}$ varies with incident angle, the phase-match condition is no longer satisfied on graphene surface, which will also weaken the absorption performance. We can conclude that the proposed absorber is insensitive to polarization angles and remains high absorption at large incident angles. These characteristics may have great potential applications in terahertz sensing, detecting, and optoelectronic devices.

Fig. 7 Simulated absorption spectrums of the proposed absorber as a function of operating frequency and incidence angle with the graphene chemical potential $E_{f}$ = 0.5 eV for (a) TM polarization and (b) TE polarization. The absorber exhibits excellent performances with relatively stable absorbance and bandwidth over a wide range of oblique incidence angles for both polarizations. Its peak absorbance remains more than 70% with a sufficient broadband of 0.5 THz over a wide range of incident angle up to 60° for both polarizations.

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4. Conclusion

In conclusion, in this contribution we have proposed and investigated a dual broadband absorber based on graphene metamaterial in THz range. The distributions of electric field and surface current are used to explore the absorption mechanism. The numerical simulation results show that the proposed absorber possesses dual operating frequency range and broadband absorption characteristics due to the specific design. There are two broad absorption bands (absorption is larger than 0.95 and bandwidth is about 0.5THz) with the central frequencies of 1.6 THz and 4.75 THz respectively and the amplitude of absorption peaks can be regulated by chemical potential via electrostatic bias from more than 95% to less than 10%. In addition, we also discussed the sensitivity of absorptance to incident angles and it is found that the proposed absorber has a good tolerance of polarization angles and exhibits excellent performances with relatively stable absorbance and bandwidth over a wide range of oblique incidence angles for both TE and TM polarizations. Generally, the special design of the absorber and utility of graphene provide a new perspective to broadband absorber design. The flexible tunability and brilliant absorptance make the MA show promising prospects in dynamic modulators, sensors, switchers and other THz components.

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Dual broadband absorber based on graphene metamaterial in the terahertz range

Abstract

1. Introduction

2. Design and simulation methods

3. Results and discussion

3.1 Simulation results and mechanism analysis

3.2 Frequency tunability and robustness of broadband absorber

4. Conclusion

References

Cited By

Figures (7)

Equations (5)

Optical Materials Express