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Tunable broadband terahertz absorber based on a single-layer graphene metasurface

Juzheng Han and Rushan Chen

Open Access Open Access

Abstract

In this paper, a broadband and tunable terahertz absorber based on a graphene metasurface in a sandwiched structure is introduced. A single-layered graphene patterned with hollow-out squares is applied in this design, which is continuously connected to provide convenience for electrical tuning and fabrication. Plasmonic coupling and hybridization inside the graphene pattern can significantly enhance the absorption bandwidth. Moreover, polarization-insensitive and omnidirectional performances are also guaranteed by the symmetrical design. Full wave simulations demonstrate that the absorber exhibits over 90% absorbance within 1.14∼3.31 THz with a fractional bandwidth up to 97.5%. The device reveals tunable absorbance from 14% to almost 100% by manipulating the graphene chemical potential from 0 to 0.9 eV. When the incident angle sweeps up to 55°, the absorbance remains more than 90% from 1.77 to 3.42 THz for TE polarization, while over 90% absorbance maintains around 3.3 THz for TM polarization. These superior abilities guarantee the applicability of the presented absorber in THz cloaking, tunable sensor and photovoltaic devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Since Landy [. creatively proposed a perfect absorber in microwave region [1], various kinds of absorbers established by periodic structures have been studied. Terahertz (THz) absorber, one of the most attractive research topics in THz region, has also received increasing attention [2–4] owing to the significant application prospects of detecting [5], imaging [6] and modulation [7]. However, the above structures consisting of normal metals and dielectrics show inherent drawbacks for their absorbance cannot be altered once the physical dimensions are determined. Thus, researching and developing new implementation for THz absorbers with high efficiency, as well as tunable properties would be extremely necessary.

Tunable functional metasurface with two-dimensional (2-D) materials (such as black phosphorus, vanadium dioxide, graphene, and so on) have attracted much attention [8–10]. Graphene, a 2-D material with a monolayer of carbon atoms, stands out for its excellent electromagnetic properties [11,12]. Specially, by means of external applied electric field, the conductivity of graphene can be continuously manipulated in a broad frequency range without changing the structure [13]. This electrostatic control of conductivity makes graphene a promising candidate for flexible designs of tunable devices. Hence, metasurfaces with structured graphene patterns which can induce surface plasmon polaritons (SPPs) have become one of the most promising components to realize various THz absorbers with tunable absorbance [14–16].

In the respect of broadband application, researchers have also tried multiple implementations. In order to induce broadband performance via different resonate frequencies, series of isolated graphene patterns with gradient changed size are arranged in periodic array [17,18]. However, the absorbance remains relatively low. Geometrically patterned single-layer graphene [19–21], multi-layer graphene [22,23] and hybrid metal/semimetal/dielectric-graphene structures [24–26] have provided efficient solutions to improve the bandwidth. But most of them suffer from a common practical problem for the graphene patterns are either discretely distributed in one layer or separately arranged in different layers, which would lead to great obstacle for fabrication and electrical control. Therefore, it is advantageous to further investigate new graphene-based THz absorber with simple design, broad bandwidth, flexible tunability, as well as polarization insensitivity and angular stability.

For the above reasons, we propose a simple design of a broadband tunable THz absorber based on graphene metasurface in sandwiched structure. Different with traditional structures with multi-layered graphene or hybrid materials, a single-layered graphene patterned with hollow-out squares is adopted. As the graphene is connected by slender graphene strips for electrically continuous, active tuning flexibility and fabrication convenience are guaranteed. The absorption bandwidth is significantly enhanced through the plasmonic coupling and hybridization between the outer and inner part of the hollow-out square. Polarization-insensitive and omnidirectional abilities can also be obtained due to the symmetrical geometry. According to simulations, a 97.5% fractional bandwidth is achieved for both TE and TM polarizations under normal incidence. By controlling the graphene chemical potential from 0 to 0.9 eV, the peak absorbance can be tuned from 14% to almost 100%. In addition, for up to 55° incident angle, the absorbance remains higher than 90% within 1.77 to 3.42 THz for TE polarization while the peak absorbance maintains over 90% around 3.3 THz for TM polarization. The potential applications lie in THz sensing, cloaking and photovoltaic devices.

2. Theory and design

According to Kubo formulas, the surface conductivity σ(ω, μc, Γ, T) of graphene, which is governed by the intra-band σintra and inter-band σinter transitions [13], can be expressed by

$$\sigma ({\omega ,{\mu_c},\Gamma ,T} )= {\sigma _{intra}} + {\sigma _{inter}},$$
$${\sigma _{intra}} = \frac{{j{e^2}}}{{\pi {\hbar ^2}({\omega - j2\Gamma } )}}\int_0^\infty {\xi \left( {\frac{{\partial {f_d}({\xi ,{\mu_c},T} )}}{{\partial \xi }} - \frac{{\partial {f_d}({ - \xi ,{\mu_c},T} )}}{{\partial \xi }}} \right)d\xi } ,$$
$${\sigma _{inter}} ={-} \frac{{j{e^2}({\omega - 2\Gamma } )}}{{\pi {\hbar ^2}}}\int_0^\infty {\frac{{{f_d}({ - \xi ,{\mu_c},T} )- {f_d}({\xi ,{\mu_c},T} )}}{{{{({\omega - j2\Gamma } )}^2} - 4{{({{\xi / \hbar }} )}^2}}}d\xi } ,$$
$${f_d}({\xi ,{\mu_c},T} )= {({{e^{{{({\xi - {\mu_c}} )} / {{\kappa_B}T}}}} + 1} )^{ - 1}},$$
where ω is the radian frequency, μc is the chemical potential (i.e., Fermi level Ef), Γ=(2τ)−1 is the phenomenological scattering rate with τ stands for the relaxation time, T represents the temperature, ξ is the energy of electrons, ħ is the reduced Plank’s constant, κB is the Boltzmann’s constant, e is the electron charge, and fd (ξ, μc, T) is the Fermi-Dirac distribution. It should be mentioned that the relaxation time τ =mm·μc/(e·υf2) characterizes the plasmon decay on account of impurities, where μm denotes the carrier mobility, which can range from ∼1000 cm2/(V.s) in chemical vapor deposition synthesized graphene [27] to ∼230000 cm2/(V.s) in suspended exfoliated graphene [28]. Besides, υf is the Fermi velocity with a typical value of 106 m/s. Thus, it can be inferred that when μc is fixed, the relaxation time is determined by the carrier mobility.

In THz range and below, the intra-band transition dominates while the inter-band part is negligible. Thus, the above Kubo equation can be simplified as a Drude form, which can be expressed by

$$\sigma ({\omega ,{\mu_c},\Gamma ,T} )= \frac{{{e^2}{\kappa _B}T\tau }}{{\pi {\hbar ^2}({1 + j\omega \tau } )}}\left\{ {\frac{{{\mu_c}}}{{{\kappa_B}T}} + 2\ln \left[ {\textrm{exp} \left( { - \frac{{{\mu_c}}}{{{\kappa_B}T}}} \right) + 1} \right]} \right\}.$$

One of the advantages of graphene is that its chemical potential μc can be manipulated over a wide range through an electric field E0 via DC bias voltage Vg. The electric field modifies graphene carrier density ns and, consequently, shifts μc. The relationship between E0 and ns, as well as Vg and ns are expressed as: E0=Vg/ts=e·ns/ɛrɛ0, where ɛr is the relative permittivity of the dielectric spacer, ɛ0 is the permittivity of free space, and ts is the dielectric thickness. In addition, the carrier density ns is related with μc via [29]

$${n_s}\textrm{ = }\frac{2}{{\pi {\hbar ^2}\upsilon _\textrm{f}^2}}\int_0^\infty {\xi [{{f_d}({\xi - {\mu_c},{\mu_c},T} )- {f_d}({\xi + {\mu_c},{\mu_c},T} )} ]} d\xi .$$

Thus, for undoped, ungated graphene, μc=ns=0. It has also been argued theoretically that in reality the region near μc∼0 should not be considered ideal because of inevitable disorder presence [30]. Relationship between μc and Vg or μc and E0 is theoretically estimated by [13]

$${\mu _c} = \hbar {\upsilon _f}\sqrt {\frac{{\pi {\varepsilon _0}{\varepsilon _r}{V_g}}}{{e{t_s}}}} = \hbar {\upsilon _f}\sqrt {\frac{{\pi {\varepsilon _0}{\varepsilon _r}{E_0}}}{e}} .$$

The schematic of the proposed tunable broadband absorber along with the external bias is illustrated in Fig. 1(a). The absorber exhibits a typical sandwiched structure composed of a top graphene layer, a middle dielectric substrate and a bottom metal plate. In order to control the conductivity, a bias voltage Vg is placed between the graphene and the metal plate. As depicted by the top view of the unit cell in Fig. 1(b), the graphene pattern is arranged in single layer and designed to be electrically continuous with hollow-out squares connected by slender graphene strips. This strategy provides a flexible electrical control method to tune the conductivity of graphene via extra bias voltage. The dielectric substrate is made of polyethylene cyclic olefin copolymer (TOPAS) with a thickness of 22 µm and a relative permittivity of 2.35. A 0.2 µm thick silver layer is selected as the ground plate which can be regarded as a dispersive medium according to Drude model [31]. The geometry parameters of the structure are as follows: p=69.5 µm, a=32 µm, b=37 µm, m=27 µm, n=22 µm and s=200 nm.

 figure: Fig. 1.

Fig. 1. The whole structure and unit cell of the proposed absorber. (a) Schematic of the proposed absorber with a DC gating voltage Vg. (b) Top view of the unit cell pattern.

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Full wave numerical simulation of the periodical arranged structure can be conducted in CST Microwave Studio, where the single-layer graphene is modeled as an equivalent 2-D surface impedance. All simulations are based on adaptive fine mesh setting. Periodic boundary conditions are set in both x- and y-directions, while floquet port is arranged in z-direction. With a plane wave impinging on the structure, corresponding transmission and reflection coefficient can be extracted based on the finite integration technique in CST. The absorbance A(ω) can be calculated by A(ω)=1−T(ω)−R(ω), where T(ω)=|S21(ω)|2 and R(ω)=|S11(ω)|2 are symbolized for the transmission coefficient and reflection coefficient, respectively. As the thickness of the bottom metal plate is much larger than the skin depth of the incident wave, transmission would be extremely suppressed and T(ω) can be treated as zero due to electromagnetic shielding. Broadband THz surface plasmon resonance and excellent absorption property can be achieved when impedance matching condition is satisfied between the metasurface and the free space.

3. Results and discussions

To evaluate the feasibility of the proposed absorber, the absorption spectra are investigated with both transverse electric (TE wave with E field along y direction) and transverse magnetic (TM wave with H field along y direction) polarizations under normal incidence. The initial values of chemical potential μc and relaxation time τ are assumed to be 0.9 eV and 0.1 ps, respectively. According to the above theoretical analysis, these values can be obtained by an electric field of 4.6 V/nm and a carrier mobility of 1100 cm2/(V.s). Recent demonstration shows that in order to avoid gate dielectric break down, the voltage bias can be significantly reduced by applying a layer of ionic gel over graphene with top gating architecture [32], which can be adapted to our design.

For the absorption property is directly related to phase-matching conditions of reflection cancellation, which is sensitive to the dielectric thickness ts, it is necessary to explain how the presented dimension is organized. Figure 2 illustrates the relation between the absorbance and the dielectric thickness ts with μc fixed as 0.9 eV under normal incident TE polarization. As ts continuously increases from 16 µm to 30 µm, the resonance exhibits a red shifting for high frequency and the absorbance enhances at lower frequency. In this way, the bandwidth of the absorber can be significantly expanded by overlapping these different resonant frequency bands. The bandwidth with over 90% absorbance reaches its maximum value at 22 µm.

 figure: Fig. 2.

Fig. 2. Absorbance under normal-incident TE polarization as a function of operating frequency and the dielectric thickness ts.

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The simulated coefficients of transmission T, reflection R and absorbance A are plotted in Fig. 3(a). As is clearly shown, the T, R and A spectra under TE incidence are in perfect accordance with those of TM incidence. This polarization-insensitive property is originated from the symmetrical structure design. An effective absorption band (the frequency band which exhibits absorbance over 90%) from 1.14 THz to 3.31 THz can be obtained, which indicates an absolute bandwidth of 2.17 THz and a fractional bandwidth up to 97.5%. In addition, the peak absorption approaches almost 100% at 3 THz for both polarizations, which means near-perfect absorption can be obtained. Impedance matching theory is used to gain insight into the physics of the proposed device. As a post-processing step, S-parameter retrieval gives the relative impedance as

$$Z ={\pm} \sqrt {\frac{{{{({1 + {S_{11}}} )}^2} - S_{21}^2}}{{{{({1 - {S_{11}}} )}^2} - S_{21}^2}}} ,$$
where Z is the normalized equivalent surface impedance of the absorber (with respect to the impedance of free space Z0=377 Ω). Both real part Re(Z) and imaginary part Im(Z) are given in Fig. 3(b). It is revealed that when Re(Z) is close to 1 and Im(Z) approaches 0, high absorbance would be achieved in the corresponding frequency band. This can be attributed to the impedance matching between the absorber and the free space. Small reflection, suppressed transmission and high absorbance are all achieved under such circumstance.

 figure: Fig. 3.

Fig. 3. (a) The simulated transmission T, reflection R and absorbance A of the proposed absorber under normal incident TE and TM polarizations. (b) Real part Re(Z) and imaginary part Im(Z) of the normalized impedance Z.

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As is given by the schematic diagram in Fig. 1, the single-layer graphene pattern in each unit cell can be regarded as a combination of two parts, the first part is an outer hollow-out square with four right-triangles remained in the corner and the other part is an inner square with 45° rotation which is pierced by a square ring. As mentioned above, the outer and inner parts are connected by graphene strips for electrical continuity. In order to further explore the physical mechanism of the broadband absorption behavior, absorption spectra and electric field distributions of the outer pattern, inner pattern as well as the whole graphene pattern (x-y plane, z=0) are investigated separately. As the absorption curves are almost similar for TE and TM polarizations under normal incidence, we take TE as an example for this discussion.

The simulation results are displayed in Fig. 4. As demonstrated in Fig. 4(a), an 80% absorbance band is revealed from 0.99 THz to 2.84 THz for the outer pattern. Two absorption peaks occur at 1.15 THz and 2.5 THz, respectively. Figure 4(d) displays its normalized E-field distribution on the graphene plane at 2.13 THz. Fields confinement is observed around the graphene, leading to THz trapping and absorption. According to Fig. 4(b), only one absorption peak at 2.13 THz is observed and the absorbance approaches almost 100% for the inner pattern. Correspondingly in Fig. 4(e), the inner pattern is strongly excited by the incident wave. Even through a near-perfect absorbance is obtained, the bandwidth is quite narrow with only one resonance. The absorption property of the whole graphene pattern is presented in Figs. 4(c) and 4(f). The dash, dash-dot and solid line in Fig. 4(c) denote the results of the outer, inner and the whole pattern, respectively. A broadband absorption over 90% within the frequency range 1.14∼3.31 THz is obtained. Comparing Figs. 4(a)–4(f), we can find that stronger wave trapping, higher absorbance as well as broader bandwidth are achieved by combining the outer and the inner pattern. This could be attributed to the mutual coupling effect between the outer and inner pattern of the graphene.

 figure: Fig. 4.

Fig. 4. The absorption spectra for (a) outer pattern, (b) inner pattern and (c) whole pattern, (d), (e) and (f) are their normalized E-field distributions, respectively.

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The electric field distributions of the presented absorber at different frequencies are given in Fig. 5. Four frequency points are chosen, namely, 0.5 THz, 1.14 THz, 2.23 THz and 3.31 THz, among which the first one is characterized with rather low absorbance, the second and the last are the boundary frequencies of the absorption band (with absorbance >90%) and the third one is the center frequency. As labeled from left to right in Fig. 5(a), the electric field distribution under TE incidence at the above four frequencies are displayed, respectively. Obviously, quite weak electric confinement is observed in the structure at 0.5 THz, which corresponds with a rather low absorbance of 10%. Differently, a much stronger electric field is excited at 1.14 THz, which mainly concentrates between the gaps of the hollow-out patterns. When it comes to the latter two graphs in Fig. 5(a), the electric field spreads from the gap to almost the entire graphene pattern. It can be inferred that the localized surface plasmon resonance is stimulated by the incident THz wave at these two frequencies. Comparing the results at 2.23 THz and 3.31 THz with those at 0.5 THz and 1.14 THz, we can find that a more uniform electric field distribution is observed with the increase of the frequency, which indicates a stronger field confinement as a whole and agrees well the absorption spectra given above. Figure 5(b) gives the corresponding results in TM mode, which are same as those in Fig. 5(a) with 90° rotation.

 figure: Fig. 5.

Fig. 5. Electric field distribution of the proposed absorber at different frequencies. (a) TE mode. (b) TM mode.

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In order to reveal the dynamic tunable property of the presented absorber, the chemical potential μc is changed from 0 to 0.9 eV in the simulation. The varied absorption properties under different chemical potential are presented in Fig. 6. When μc=0 eV, the absorbance is lower than 14%, which means most of the incident wave is reflected by the structure. However, as μc increases, both increased absorbance amplitude and broadened bandwidth are obtained. It is found that, for μc=0.7 eV, near-perfect absorption is obtained at 2.8 THz, but the 90% absorbance bandwidth still needs to be enhanced. When μc=0.9 eV, most of the electric field are trapped and dissipated by the structure, absorbance higher than 90% is achieved in the frequency band from 1.14 THz to 3.31 THz. Meantime, obvious blue-shifting of the resonance can be seen with the increase of μc. This is consistent with the changing tendency of the effective refractive index and the plasmon resonance frequency with respect to μc. Deeper reasons can be found that with the increase of μc, equivalent inductance of the structure decreases, resulting in an increased resonance frequency [33]. Based on the above discussion, one can choose a suitable chemical potential according to the application scenario.

 figure: Fig. 6.

Fig. 6. Absorption spectra under different chemical potential.

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In order to fully demonstrate the polarization-insensitive property of the absorber, the azimuthal angle ϕ is scanned from 0° to 90°, where 0° represents an incident electric field along x-axis while 90° represents an incident electric field along y-axis. The simulated result, illustrated in Fig. 7(a), shows that the absorbance remains nearly unchanged with the variation of ϕ. Thus, we can conclude that the presented absorber is highly polarization independent. The above discussions are all investigated under normal incidence. However, the tolerance of wide incident angles is essential for practical application. Thus, to examine the robustness of the presented absorber to oblique incident angles, the absorbance is simulated as functions of frequency and incident angle θ for both TE and TM polarizations. For TE polarization depicted in Fig. 7(b), broadband absorption property can be maintained well and the absorbance remains more than 90% within 1.77 to 3.42 THz when the incident angle sweeps up to 55°. For TM polarization in Fig. 7(c), the peak absorbance is higher than 90% around 3.3 THz at the same angle and keeps over 90% around 4 THz when the incident angle sweeps up to 70°. Although blue shifting is observed for both polarizations, which is mainly due to the parasitic resonances occurred at large incident angle, the proposed structure can maintain its performance for both polarizations with oblique incidence. It is also observed that the absorbance decreases as the incident angle increases, this overall reduction is inevitable for the interactions between incident wave and the graphene get weaker as the incident angle increases. Meanwhile, the peak absorbance of TM polarization decreases faster than that of TE. This is due to fact that the orientation of the electric field for the electric dipole resonance in the patterned graphene changes for TM polarization, while remains for TE polarization when the incident angle is varied.

 figure: Fig. 7.

Fig. 7. The absorption characteristics for (a) different azimuthal angle. (b) different incident angle for TE polarization. (c) different incident angle for TM polarization.

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To confirm the advantage of the designed absorber, comparisons are made between our results and other recent published broadband absorbers which are mainly based on single-layered graphene pattern, multi-layered graphene pattern and hybrid structures with graphene and other materials (see Table 1, where λc represents the wavelength of the center frequency, in free space). Compared with the given references, the absorber in this paper, which is based on continuous graphene pattern arranged in single layer, achieves a relative high fractional bandwidth of 97.5%. The structure in [24] which is based on Snowflake Koch Fractal dielectric loaded on graphene demonstrates an ultra-wideband of 161%. However, its enhancement of operating band is more attributed to the design of the dielectric structure, not the graphene itself. Moreover, as compared, our design is characterized by much smaller thickness. To conclude, our presented structure is relatively simple which can bring great convenience for flexible tuning and practical fabrication. Other advantages, such as polarization-insensitive and omnidirectional abilities are also preserved. These superior performances guarantee the applicability of the designed structure for various THz applications.

Tables Icon

Table 1. Comparisons between the proposed structure and other publications.

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4. Conclusion

We have proposed a tunable THz absorber based on a single-layered graphene metasurface in this paper. The fractional bandwidth of absorption rate above 90% can reach up to 97.5% due to the coupling between the designed hollow-out squares in the single-layered graphene. By changing the graphene chemical potential through external bias voltage, the absorbance can be tuned from 14% to near-perfect absorption. Polarization-insensitivity and omni-directionality are also demonstrated. Compared to conventional single/multi-layered structures or those with hybrid materials, this single-layered graphene structure which is electrically continuous can greatly simplify the electrostatic gating and fabrication. Benefitting from the above promising properties, the presented absorber may have various promising applications in THz smart sensing, clocking and photovoltaic devices.

Funding

Fundamental Research Funds for the Central Universities (30919011276); National Natural Science Foundation of China (61801224).

Disclosures

The authors declare no conflicts of interest.

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Figures (7)
Fig. 1.
Fig. 1. The whole structure and unit cell of the proposed absorber. (a) Schematic of the proposed absorber with a DC gating voltage Vg. (b) Top view of the unit cell pattern.

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Fig. 2.
Fig. 2. Absorbance under normal-incident TE polarization as a function of operating frequency and the dielectric thickness ts.

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Fig. 3.
Fig. 3. (a) The simulated transmission T, reflection R and absorbance A of the proposed absorber under normal incident TE and TM polarizations. (b) Real part Re(Z) and imaginary part Im(Z) of the normalized impedance Z.

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Fig. 4.
Fig. 4. The absorption spectra for (a) outer pattern, (b) inner pattern and (c) whole pattern, (d), (e) and (f) are their normalized E-field distributions, respectively.

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Fig. 5.
Fig. 5. Electric field distribution of the proposed absorber at different frequencies. (a) TE mode. (b) TM mode.

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Fig. 6.
Fig. 6. Absorption spectra under different chemical potential.

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Fig. 7.
Fig. 7. The absorption characteristics for (a) different azimuthal angle. (b) different incident angle for TE polarization. (c) different incident angle for TM polarization.

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Tables (1)

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Table 1. Comparisons between the proposed structure and other publications.

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Equations (8)

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σ ( ω , μ c , Γ , T ) = σ i n t r a + σ i n t e r ,
σ i n t r a = j e 2 π ℏ 2 ( ω − j 2 Γ ) ∫ 0 ∞ ξ ( ∂ f d ( ξ , μ c , T ) ∂ ξ − ∂ f d ( − ξ , μ c , T ) ∂ ξ ) d ξ ,
σ i n t e r = − j e 2 ( ω − 2 Γ ) π ℏ 2 ∫ 0 ∞ f d ( − ξ , μ c , T ) − f d ( ξ , μ c , T ) ( ω − j 2 Γ ) 2 − 4 ( ξ / ℏ ) 2 d ξ ,
f d ( ξ , μ c , T ) = ( e ( ξ − μ c ) / κ B T + 1 ) − 1 ,
σ ( ω , μ c , Γ , T ) = e 2 κ B T τ π ℏ 2 ( 1 + j ω τ ) { μ c κ B T + 2 ln ⁡ [ exp ( − μ c κ B T ) + 1 ] } .
n s  =  2 π ℏ 2 υ f 2 ∫ 0 ∞ ξ [ f d ( ξ − μ c , μ c , T ) − f d ( ξ + μ c , μ c , T ) ] d ξ .
μ c = ℏ υ f π ε 0 ε r V g e t s = ℏ υ f π ε 0 ε r E 0 e .
Z = ± ( 1 + S 11 ) 2 − S 21 2 ( 1 − S 11 ) 2 − S 21 2 ,
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