Broadband tunable graphene-based metamaterial absorber

Ying Zhang; Yan Shi; Chang-Hong Liang

doi:10.1364/OME.6.003036

1. Introduction

Graphene, which is a single atom carbon layer arranged in a honeycomb structure with two-dimensional material, exhibits several unique features including the thinnest material in the universe and the strongest ever measured. Meanwhile, graphene has the highest mobility in known materials, and its conductivity can be tuned by electrochemical potential. Hence a number of intriguing applications such as tunable cloaks [1], nonlinear optical devices [2], modulator [3], and other optoelectronic applications [4], have been proposed and experimentally demonstrated [5].

Metamaterial absorbers have attracted intense attention since Landy et al. proposed a thin and near-perfect metamaterial absorber in 2008 [6]. Since then, various metamaterial absorbers have been proposed and demonstrated from microwave to optical frequencies [7]. Graphene is optically transparent and has an absorption of 2.3% per monolayer in the optical range [8]. By designing graphene-based metamaterial absorbers, the absorption can reach nearly 100% [9]. More importantly, by controlling voltage applied to the graphene via external gate, the graphene-based absorbers can operate as tunable absorbers [10–15]. However, in the scope of our knowledge, these perfect graphene-based absorbers have very narrow absorption bands, and their capabilities of reported tuning absorption bands are very limited in the THz and optical frequencies [16, 17].

In this paper, we propose a broadband tunable, wide-angle, and polarization-insensitive graphene-based metamaterial absorber. A dual electric LC (ELC) metamaterial unit fabricated on a multilayer structure consisting of Au/BaF₂/graphene materials from the bottom to the top is designed. With the use of the ELC-graphene structure, three close resonances are simultaneously excited and thus a broadband absorption of 90% from 25.08THz to 39.56THz is generated. By varying an external gate voltage applied to the graphene, absorption band of the proposed absorber can be well tuned from 25.08THz to 44.81THz. The proposed absorber has polarization-insensitive and wide incident angle characteristics due to the approximately symmetric structure.

2. Overall structure of graphene-based metamaterial absorber

From the range of terahertz to optical frequency, graphene sheet can be modelled as a thin surface characterized by complex surface conductivity according to Kubo formula [18]:

\begin{array}{l} σ (ω, μ_{c}, Γ, Τ) = σ_{int r a} (ω, μ_{c}, Γ, Τ) + σ_{int e r} (ω, μ_{c}, Γ, Τ) = \\ - \frac{i e^{2} k_{B} T}{π ℏ^{2}} [\frac{1}{{(ω + i 2 Γ)}^{2}} \int_{0}^{\infty} d ε (\frac{\partial n_{F} (ε)}{\partial ε} - \frac{\partial n_{F} (- ε)}{\partial ε}) ε - \int_{0}^{\infty} d ε \frac{n_{F} (- ε) - n_{F} (ε)}{{(ω + i 2 Γ)}^{2} - 4 {(\frac{ε}{ℏ})}^{2}}] \end{array}

where σ_intra and σ_inter denote intra-band and inter-band conductivities, respectively, erepresents electron charge, ћ is reduced Planck’s constant, ε is carriers energy, k_B is Boltzmann constant, ω is radian frequency, Γ = 5meV is charged particle scattering rate, T = 300K is room temperature, μ_c is chemical potential of graphene, and

n_{F} (ε) = {(1 + e^{(ε - μ_{c}) / k_{B} T})}^{- 1}

is Fermi-Dirac equation distribution. In (1), σ_intra and σ_inter can be approximately evaluated in an analytical form as [18–20]:

σ_{int r a} (ω, μ_{c}, Γ, Τ) \approx i \frac{e^{2} k_{B} T}{π ℏ^{2} (ω + i 2 Γ)} [\frac{μ_{c}}{k_{B} T} + 2 \ln (e^{- \frac{μ_{c}}{k_{B} T}} + 1)]

σ_{int e r} (ω, μ_{c}, Γ, Τ) \approx i \frac{e^{2}}{4 π ℏ} \ln [\frac{2 | μ_{c} | - (ω + i 2 Γ) ℏ}{2 | μ_{c} | + (ω + i 2 Γ) ℏ}]

Note that (3) is valid when k_BT<<|μ_c | and k_BT<< ћω. The surface impedance of the graphene can be calculated as Z≈1/σ. When the graphene is externally loaded a regulated voltage V_A, its chemical potential μ_c can be estimated by using the following formula [21]:

| μ_{c} | \approx ℏ v_{F} {π a_{0} | V_{A} - V_{D i r a c} |}^{1 / 2}

where the Fermi velocity of the Dirac fermions is v_F≈9 × 10⁵ m/s, the constant estimated through a single capacitor model is a₀≈9 × 10¹⁶ m⁻²V⁻¹, and the Dirac voltage offset caused by the natural doping is V_Dirac = 0.8 V.

The designed graphene-based metamaterial absorber consists of four layers: a dual ELC unit that is made of Au with a thickness of h1 set in a periodic pattern on the top, a graphene sheet with a thickness of tg, a BaF₂ material with a thickness of h2, and an Au material with a thickness of h3 on the bottom. Figure 1(a) illustrates a schematic drawing of the unit cell of the proposed metamaterial absorbing structure. The dimensions of the unit cell have been optimized to ensure that the proposed absorber could be tuned within a wide frequency band. The detailed dimensions are given in Table 1. In this paper, the graphene is considered as an equivalent medium with one atom thickness of tg = 3.4Å [22]. In order to consider dispersion response of the graphene, Drude model with complex relative permittivity of $ε_{r} = 1 + i σ / (ω ε_{0} t_{g})$ [23] is employed. In the infrared range, the Au material is regarded as a lossy material whose complex relative refractive index is $n_{A u} = 0.13767 + 3.7917 i$ [16, 24]. The BaF₂ material is a common laser optics material, which is considered to be a lossless dielectric material with the relative refractive index from 1.4 to 1.44 in the mid-infrared range. Due to the thickness of the bottom Au material larger than its largest skin depth of $δ \approx λ / [2 π Im (n_{A u})] \approx 28 n m$ in the mid-infrared frequencies, the absorption can be calculated as $A (ω) = 1 - R (ω)$ , where $R (ω) = {| S_{11} |}^{2}$ represents the reflection.

Fig. 1 Top and side views of the absorbing structure. (a) the proposed absorbing structure. (b) a square ring fabricated on a Graphene/BaF₂/Au multilayer structure. (c) a square ring fabricated on a BaF₂/Au multilayer structure.

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Table 1. Detailed dimensions of the proposed absorber

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3. Results and discussion

To demonstrate the electromagnetic absorption, we use a commercial finite-element solver Ansys HFSS to simulate absorption behaviors of the proposed metamaterial absorber. The periodic boundary conditions (PBCs) and Floquet ports are utilized to simulate the infinite periodic cells, as shown in Fig. 2(a). In the simulation, 1st-order vector basis functions are employed, and the number of iterative steps is set as 2. Figure 3 shows the absorbing spectra of the proposed absorber for the chemical potential of μ_c = 0.5eV when plane waves with transverse electric (TE, electric filed perpendicular to the incident plane) and transverse magnetic (TM, magnetic field perpendicular to the incident plane) polarizations are normally incident on the proposed absorber, respectively. It can be seen that for the TE polarization, there are three close resonant frequencies, e.g., 25THz, 31THz, and 38THz, thus leading to a wide absorption characteristic of 90% with a 41.12% fractional bandwidth from 27.78 THz to 42.16THz. Similar to the TE mode, the absorbing band for the TM polarization covers from 26.78THz to 40.06THz with a 39.74% fractional bandwidth. Here 15610 tetrahedrons are used to mesh the computational domain for the simulation of the proposed absorber.

Fig. 2 The unit cell and whole structure of the proposed absorber. (a) infinite periodic simulation model with periodic boundary conditions (PBC) around the unit cell. (b). a tunable gate voltage applied to the proposed absorber.

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Fig. 3 Simulated absorptivity of the proposed absorber with μc = 0.5eV for TE and TM polarizations.

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In order to understand absorbing behaviors of the proposed absorber, two different absorbers are constructed according to the proposed absorber, as shown in Figs. 1(b) and 1(c). The first one is a square ring unit fabricated on a BaF₂/Au multilayer structure, and the second one is a square ring unit fabricated on a graphene/BaF₂/Au multilayer structure. Figure 4 demonstrates the absorption performance of three absorbers. According to Fig. 4, it can be seen that for the ring/BaF₂/Au absorbing structure, there is only an absorption peak at 36THz, which corresponds to inherent resonance of the square ring structure. By comparison, for ring/graphene/BaF₂/Au absorbing structure, two absorption peaks occur at 32.5THz and 40.5THz, respectively. This is because the interaction between the square ring unit and the graphene sheet results in the second resonance except the inherent resonance. Further, with capacitance load to the square ring by using two stubs outside the ring and two dual branches inside the ring, two above absorption peaks become increasingly close to each other and what is more an extra resonance occurs at 25THz, thus leading to a wide absorbing band of the proposed structure.

Fig. 4 Absorption comparison of three absorbers.

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In order to explore the physical mechanism of the proposed absorber, surface current distributions at three resonant frequencies, i.e., 25THz, 31THz, and 38THz are calculated, as shown in Fig. 5. We can observe from Figs. 5(a)-5(c) that at 25THz, the surface currents on the dual ELC unit and the graphene sheet flow in the same direction, while the current on the ground flows in an opposite direction. The surface currents flowing in opposite directions induce the magnetic flux which is equivalent to an inductance (L). The equivalent capacitance (C) caused by the dual ELC unit on the multilayer structure cooperates with the equivalent inductance to generate a LC resonant mode. According to Figs. 5(g)-5(i), one can find that they exhibit a similar trend at 38THz to that at 25THz due to the higher-order resonant mode. Different from two above resonant modes, at 31THz the surface current on the dual ELC unit flows in a same direction as that on the ground, and in an opposite direction to that on the graphene sheet, as shown in Figs. 5(d)-5(f). The resultant equivalent inductance combined with the equivalent capacitance of the absorbing structure results in the second LC resonant mode.

Fig. 5 Current distributions of the graphene-based metamaterial absorber. (a) on the dual ELC unit at 25THz. (b) on surface of graphene at 25THz. (c) on the ground plane at 25THz. (d) on the dual ELC unit at 31THz. (e) on surface of graphene at 31THz. (f) on the ground plane at 31THz. (g) on the dual ELC unit at 38THz. (h) on surface of graphene at 38THz. (i) on the ground plane at 38THz.

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In the following, we investigate the absorption as functions of the geometric parameters for the chemical potential of μ_c = 0.5eV. Figure 6 shows the absorption variation of the proposed absorber with geometric parameters. As shown in Fig. 6(a), with the increase of the line width of the dual ELC unit w, three resonant modes become increasingly strong. This is because the interaction between the unit cell and the graphene sheet gradually strengthen as w increases. Figure 6(b) shows the variation of the absorption spectrum with the relative position between two dual branches inside the ring m. It can be seen that when two dual branches go away from each other, the coupling between them weakens, thus leading to the blue shift of the third resonance wavelength. According to Fig. 6(c), it is evident that the third resonance wavelength becomes blue-shifting due to weaker coupling between two dual branches, when the length of the shorter branch d1 decreases. It can be seen from Fig. 6(d) that with the increase of the sub, which means the decrease of the geometric parameter t, the first two resonant wavelengths become clearly red-shifting, while the last resonant wavelength is blue-shifting, thus resulting in a wider absorbing band.

Fig. 6 Variation of simulated absorption with the geometric parameters. (a) w. (b) m. (c) d1. (d) t.

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Next, the polarization and angular dependences of the proposed absorber are discussed. Figure 7 illustrates the absorbing performance of the proposed absorber with μ_c = 0.5eV at different incident angle ranging from 0° to 70° for both TE and TM polarizations. It can be seen that the absorption is nearly independent of the incident angle below 50°, and as the incident angle increases further, the absorption becomes weaker. When the incident angle reaches 60°, the absorptions for the TE and TM polarizations still remain above 80% in the operating band. Further, Fig. 8 shows the dependence of the absorption on the polarization. Due to approximate symmetry of the designed absorber by introducing two dual branches, the absorption is nearly independent of the polarization.

Fig. 7 Simulated absorption performance at different incidence angles. (a) TM mode. (b) TE mode.

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Fig. 8 Simulated variation of absorption with frequencies for different azimuth angles. (a) TM mode. (b) TE mode.

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The surface conductivity of the graphene can be tuned by varying its chemical potential via electrostatic biasing, thus leading to a blue shift. The resultant frequency shift can be determined as [25]

Δ ω = (Im (σ_{} (ω)) - i Re (σ_{} (ω))) \frac{\int_{S} {| E_{x y} |}^{2} d S}{W_{0}}

By adjusting the surface conductivity of the graphene, the absorption can be controlled accordingly. A possible implementation is to introduce an Au plate as a positive electrode, and use the ground as a negative electrode, as shown in Fig. 2(b). When a variable gate voltage is applied between two electrodes, the chemical potential in the graphene sheet is changed accordingly. Figure 9 demonstrates absorption variation of the proposed absorber with the chemical potential of the graphene. For the TE polarization, the fractional absorbing band of the absorption of 90% with μ_c = 0.2eV is 44.8% from 25.08THz to 39.56THz. With the increase of the chemical potential, the absorption curve has a blue shift accompanied by an approximately unchanged fractional band. By adjusting the chemical potential from 0.2eV to 0.8eV, the absorbing band covers from 25.08THz to 44.81THz. By comparison, for the TM polarization, the fractional absorbing bandwidth firstly increases and then decreases as the chemical potential increases. With the variation of the chemical potential from 0.2eV to 0.8eV, the absorbing band of the absorption of 90% covers from 25.74THz to 40.06THz. When μ_c = 0.5eV, the maximal fractional absorbing band reaches 39.74%. A detailed description of the absorption performance for different chemical potentials of the graphene is given in Table 2.

Fig. 9 Variation of the absorption with the chemical potential $μ_{c}$ . (a) TE mode. (b) TM mode.

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Table 2. Absorption for different chemical potentials

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4. Conclusion

In this work, we have designed a novel graphene-based tunable broadband absorber. The proposed absorber has three close resonances generated by the interaction between the dual ELC metamaterial unit and the graphene sheet. By analyzing surface current distributions, the proposed absorber operates as the LC resonance at three resonant frequencies. With the adjustment of the external gate voltage applied to the graphene to control surface conductivity, a broadband from 25.08THz to 44.81THz with the absorption of 90% is achieved. Numerical results demonstrate the tunable, broadband, polarization-insensitive, and wide-angle properties of the proposed absorber.

Funding

Program for the New Scientific and Technological Star of Shaanxi Province (No.2013KJXX-66, No. BD11015020008); Technology Innovation Research Project of the CETC; Fundamental Research Funds for the Central Universities (No. SPSZ031410).

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Parameters	Value/μm	Parameters	Value/ μm
p	2	d1	0.4
w	0.16	d2	0.2
b	1.6	h1	0.1
s	0.2	h2	0.24
t	0.12	h3	0.5
m	0.1

chemical potential μ_c	TE mode		TM mode
chemical potential μ_c	f_max-f_min (THz)	Δf/f₀ (%)	f_max-f_min (THz)	Δf/f₀ (%)
0.2eV	39.56-25.08	44.8	30.27-27.81	8.47
0.4eV	41.27-27.01	41.77	37.83-25.74	38.04
0.5eV	42.16-27.78	41.12	40.06-26.78	39.74
0.6eV	44.50-27.88	45.92	33.92-27.85	19.65
0.8eV	44.81-29.86	40.04	35.15-29.78	16.51

Parameters	Value/μm	Parameters	Value/ μm
p	2	d1	0.4
w	0.16	d2	0.2
b	1.6	h1	0.1
s	0.2	h2	0.24
t	0.12	h3	0.5
m	0.1

chemical potential μ_c	TE mode		TM mode
chemical potential μ_c	f_max-f_min (THz)	Δf/f₀ (%)	f_max-f_min (THz)	Δf/f₀ (%)
0.2eV	39.56-25.08	44.8	30.27-27.81	8.47
0.4eV	41.27-27.01	41.77	37.83-25.74	38.04
0.5eV	42.16-27.78	41.12	40.06-26.78	39.74
0.6eV	44.50-27.88	45.92	33.92-27.85	19.65
0.8eV	44.81-29.86	40.04	35.15-29.78	16.51

Broadband tunable graphene-based metamaterial absorber

Abstract

1. Introduction

2. Overall structure of graphene-based metamaterial absorber

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (9)

Tables (2)

Equations (5)

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