An ultra-wideband absorber with an absorption rate of near unit is studied and numerically simulated in the terahertz frequency band. The proposed absorber is a stacked compact structure consisting of a double-layer patterned graphene embedded between two separated dielectric. Under normal incidence, the absorption rate exceeds 99% at 2.31–3.92 THz. The absorption bandwidth can reach 2.54 THz for absorptions greater than 90% (1.91–4.45 THz), and the relative bandwidth achieves 80%. Furthermore, the absorber is tunable, with absorption ranging from 14% to almost 99.9% by altering the Fermi energy of graphene from 0 to 1 eV. The phenomenon of ultra-wideband absorption is analyzed in relation to impedance matching and field distribution. Moreover, the absorber has high polarization-independence and can operate across a broad range of incidence angles. This tunable ultra-wideband absorber has promising functions in modulation, stealth, switching, and imaging technologies.

Terahertz waves are found in the electromagnetic spectrum between the infrared and microwave areas. Due to its unique advantages such as high coherence, non-ionization of terahertz radiation, broadband, safety, and spectral resolution properties,1 it has a lot of potential applications in the areas of communication, radar, astronomy, bio-detection, and security inspection. However, it is difficult for natural materials to have an electromagnetic response in the terahertz band. The development of metamaterials in recent decades has significantly changed the status of terahertz technology research. Metamaterials are artificial materials composed of subwavelength micro units and arranged in a specific order. Metamaterials can exhibit an unprecedented ability to manipulate electromagnetic waves and break the limitations of the inherent properties of natural materials. Thus, metamaterials have physical properties that natural materials do not possess, such as negative refraction, super-resolution imaging, and optical stealth.2 By using metamaterials, researchers have created a number of efficient functional terahertz devices, such as filters,3 absorbers,4 and polarization converters.5 Terahertz absorbers based on metamaterial are an important branch of functional components that are significant in terahertz detection, imaging, and sensing.6 In 2008, Landy et al. published the first metamaterial-based perfect absorber, which is formed with three layers of open resonant ring-dielectric-metal wire.7 Current flows in the contrary orientation of the electric field formed, and the dielectric constant and permeability of the absorber are regulated. Thus, the air impedance and the absorber’s surface impedance are equivalent. Subsequently, a variety of terahertz absorbers based on metamaterials have been studied. However, early metamaterial absorbers are generally based on micro–nano metal structures.8 As known, the metals have obvious inherent resistive losses, causing the metallic absorbers to have more energy dissipation. These absorbers usually achieve only a fixed absorption spectrum and have a limited operating bandwidth due to their cured material and fixed structural parameters. Therefore, the optical properties and practical applications of metal-based absorbers are greatly affected. In addition, the increasing development of electromagnetic applications requires active tunable absorbers, which can be constructed by some special materials, such as semiconductors,9 liquid crystals,10 transparent conductive oxides,11 vanadium dioxide,12 and graphene.13 The properties of such absorbers can change with different external conditions including optical pumping, external gated, and temperature control.

Graphene is a two-dimensional substance composed of a single sheet of carbon atoms arrayed in a honeycomb pattern. Its remarkable electrical and optical features, such as controlled plasmon attributes, high thermal conductivity, optical transparency, and high-speed operation, have garnered a lot of concern.14 Graphene has the ability to absorb terahertz waves by surface plasmon polaritons (SPPs). Graphene plasmons have lower losses and greater field confinement than metal plasmons. Therefore, graphene has been regarded as an ideal material for designing terahertz absorbers. More importantly, the graphene plasmon has a wide range of tunable electro-optical properties that can be controlled by external gate voltage. Numerous scholars have successively proposed graphene-based metamaterial perfect absorbers (MPAs), which can be obtained by horizontally and vertically integrating multiple resonant structures. Nevertheless, the majority of these established MPAs continue to have a narrow working bandwidth. In 2018, Huang et al. used complementary crossed elliptic graphene to achieve a broadband tunable metamaterial absorber (MMA),15 however, in the range of 1.2–1.8 THz, the relative bandwidth (RBW) is merely 40% when the absorption is above 80%. In 2020, Chen et al. designed a broadband tunable terahertz MMA with a single layer of complementary gamma pier-shaped graphene.16 This MMA has an RBW of 72% for absorption greater than 90%. However, the absorption remains suboptimal, causing difficulties in achieving continuous broadband absorption surpassing 99%. In 2022, Yu et al. proposed an ultra-wideband absorber with a sophisticated trilayer structure: an uppermost layer featuring a graphene motif consisting of an octagonal pattern and annular strips, an intermediate layer of dielectric material, and a metallic substrate at the bottom.17 The absorption is higher than 90%, with a BW of 62%. The absorption bandwidth is comparatively narrow and the pattern is intricate, causing significant challenges in fabrication. Despite the various metamaterial structures that have been devised to solve the aforementioned issues, the absorbers still have certain limitations, such as intricate patterns, sensitivity to polarization or incident angles, and the inability to simultaneously achieve high absorption and ultra-wide bandwidth. Therefore, further profound investigation is required to explore absorptive materials characterized by simplistic structures, convenient fabrication, high absorption efficiency, broad bandwidth, insensitivity to polarization, wide incident angles, and dynamic tunability.

In this paper, two identical graphene arrays divided by a thin insulating layer are designed to fulfill a broadband absorber. The graphene arrays are put on top as an insulating layer with a metallic substrate. The input impedance matches with free space and a high terahertz absorption is gained. The hybridization between the plasmon resonances of the two periodic hexagonal graphene layers reduces the imaginary part of the equivalent impedance, thus broadening the operating bandwidth. At different incident polarization angles, the bandwidth can reach 2.54 THz while the absorption is more than 90%, covering the spanning of 1.91–4.45 THz with an RBW of 80%. The insensitivity to the incident angle and polarization of terahertz waves is due to the symmetry of the graphene microstructure and deep subwavelength response. Finally, the operating band of the device might be effectively adjusted by modulating the Fermi energy of the graphene. To quantitatively verify the proposed absorber, the numerical simulation results are analyzed by applying impedance matching theory. Our works bring the possibility of realizing broadband tunable components in terahertz frequency domains.

The structure cell of the proposed tunable broadband terahertz MMA is shown in Fig. 1. It consists of five layers including bilayer graphene with a hexagonal pattern, two identical dielectric layers, and a metal substrate. The geometrical parameters of the structure cell are shown in Table I. The bilayer-patterned graphene is concentric in the z direction and is separated by a dielectric layer, as illustrated in Fig. 1(a). The Fermi energy of both graphene layers is set to 1 eV. The dielectric spacer layer is made of TOPAS polymer with a refractive index of 1.53 and a thickness of H1. The second layer of patterned graphene and the gold substrate (conductivity σ of 4.56 × 107 s/m and thickness of 0.2 µm) are also separated by TOPAS. To modulate the electrical conductance, a bias voltage is introduced between the graphene array and the metallic substrate. The thickness of the gold layer is substantially greater than the skin depth at 0.1–10 THz in order to suppress terahertz transmission.

FIG. 1.

(a) Schematic of unit structure with DC gating voltage Vg. (b) Top view. (c) Side view. (Ef = 1 eV.)

FIG. 1.

(a) Schematic of unit structure with DC gating voltage Vg. (b) Top view. (c) Side view. (Ef = 1 eV.)

Close modal
TABLE I.

Structural parameters of the proposed absorber.

ParameterNumerical value
Symbol(µm)Physical meaning
P 33 Cell structure period 
L 13 Side length of hexagonal graphene 
H1 Thickness of TOPAS between two layers of graphene 
H 16 Thickness of TOPAS between the first layer of graphene and gold 
H2 14 Thickness of TOPAS between the second layer of graphene and gold 
ParameterNumerical value
Symbol(µm)Physical meaning
P 33 Cell structure period 
L 13 Side length of hexagonal graphene 
H1 Thickness of TOPAS between two layers of graphene 
H 16 Thickness of TOPAS between the first layer of graphene and gold 
H2 14 Thickness of TOPAS between the second layer of graphene and gold 
Full-wave numerical simulations of the proposed MMA are performed using FDTD solutions, which is a commercial software. In the simulations, plane waves are used as light sources, which incidents the top of the graphene array. Periodic boundary conditions are utilized in the x and y directions. Perfectly matched layers (PML) are used in the z direction. To improve the precision of the patterned region and ensure that the simulation results converge effectively, a mesh grid of 5 nm in the x, y, and z axes is set. The Kubo formula describes the surface conductivity of graphene σgra in the terahertz frequency, which is as follows:18,
σgra=σintra+σinter=2e2kBTπ2iω+iτ1ln2coshEf2kBT+e24212+1πarctanω2Ef2kBTi2πlnω+2Ef2ω2Ef2+4kBT2,
(1)
where σintra and σinter are the interband and intraband contributions, respectively; Ef is the Fermi energy of graphene; e is the charge of an electron and is the reduced Planck’s constant; ω is the radian frequency; KB is Boltzmann’s constant; T is the absolute temperature of the environment; and τ=μEf/eVf2 is the relaxation rate when the electron mobility μ = 104 cm2/Vs and the Fermi velocity Vf ≈ 106 m/s. The σgra can be changed by setting Vg to freely modulate the Fermi energy between 0 and 1 eV. By taking into account room temperature and THz waves, the Fermi energy in graphene is far greater than half of the photon energy. Therefore, the conductivity of graphene is largely affected by the intraband transition, while the effect of the interband transition can be negligible.19 The process of intraband electron-photon scattering produces a Drude-like dispersion, and σgra can be expressed as follows:
σgra=e2Efπ2iω+iτ1.
(2)
From formula (2), it can be seen that the σgra is connected to the Fermi energy Ef.20 The Ef depends on the input Vg,
|Ef|=Vfπ|a0Vg|.
(3)

The a0=ε0εhed is the capacitance of structure model, ɛ0 is the vacuum intermediary electric constant, ɛh is the medium dielectric constant, and d is the dielectric layer thickness.

In this paper, the absolute temperature T = 300 K and Ef = 1 eV. The absorption can be expressed as A(ω) = 1 − R(ω) − T(ω), where R(ω) = |S11|2 and T(ω) = |S21|2 denote reflection and transmission, respectively. Among them, S21 and S11 are the complex transmission and reflection coefficients, respectively. T(ω) = 0 because the 0.2 µm of the bottom metal’s thickness is higher than the skin depth. Thus, A(ω) = 1 − R(ω) = 1 − |S11|2 is used to compute absorption A(ω). When the Fermi energy of graphene is fixed, the real and imaginary parts of the conductivity are frequency-dependent. The displacement of the resonance peak is governed by the imaginary component of the conductivity, while the magnitude modulation of the resonance peak is influenced by the real component. Therefore, the absorption of the absorber can be adjusted by controlling the Fermi energy.21 

To understand the mechanism of broadband absorption of the absorber, the absorption effects of absorbers with different graphene layers are studied and compared in Fig. 2(a). Only the upper hexagonal graphene is incapable of strong absorption. However, when bilayer hexagonal patterned graphene is introduced, the absorption band widens and the absorption rate increases. In the frequency range of 2.31–3.92 THz, the absorption is more than 99% with an RBW of 52%. In the frequency range of 1.91–4.45 THz, the absorption is more than 90% with an RBW of 80%. The improvement of the absorption performance and bandwidth expansion is partly attributed to the overlap of the upper and lower layers of patterned graphene, and partly attributed to the interaction of adjacent resonances. When the equivalent input impedance matches the free-space impedance, the absorption will reach its maximum value, as shown by the red curve in Fig. 2(a), at which point S11 = 0 and S21 = 0. The normalized equivalent impedance Z can be described as follows:
Z=(1+S11)2S212(1S11)2S212.
(4)
FIG. 2.

(a) Absorption spectra of single and bilayer graphene. (b) Real and imaginary parts of the impedance.

FIG. 2.

(a) Absorption spectra of single and bilayer graphene. (b) Real and imaginary parts of the impedance.

Close modal

Figure 2(b) shows the real part Re(Z) and imaginary part Im(Z) of the equivalent impedance. The results revealed that Re(Z) is very close to 1 and Im(Z) nearly approaches zero in the scope of 1.91–4.45 THz. Therefore, the impedance matching is achieved, and an efficient broadband absorption is obtained.

Figure 3 investigates the absorption spectra of different Ef. As Ef changes from 0 to 1 eV, the maximum absorption increases from 14% to near 100%, and the corresponding bandwidth is widened. This is because an increase in the Fermi energy leads to an increase in the conductivity of graphene, and at the same time, the carrier density also increases, as shown in formula (2). When Ef increases to a certain extent, graphene exhibits a highly conductive metal-like property. In this case, the incident terahertz wave can excite plasma resonance in graphene, leading to broadband and high absorption. Therefore, by adjusting Ef, the operating frequency and performance of the device can be dynamically adjusted.

FIG. 3.

Absorption spectra of different Ef.

FIG. 3.

Absorption spectra of different Ef.

Close modal

Meanwhile, the electromagnetic field distribution of the absorber at 2.31, 3.18, and 3.92 THz is analyzed to interpret the broadband absorption mechanism further. Figure 4 shows the electromagnetic field distribution of the absorber in TE mode at different frequencies of 2.31, 3.18, and 3.92 THz. It can be seen in Figs. 4(a)4(c) that the electric field is mainly concentrated between up-layer and down-layer patterned graphene in the vertical direction, and the upper and lower edges of bilayer patterned graphene at 2.31 THz. At 2.31 THz, bilayer-patterned graphene sheets show electrical resonance properties. The electrical resonance corresponds to the dipole plasmon mode’s discharge, which is strongly confined to the graphene sheet. The largest electric fields at 3.18 THz and 3.92 THz are centered at the upper and bottom margins of bilayer patterned graphene, respectively, while the second strongest electric fields are found throughout the whole graphene sheets. As the frequency increases, the electric field starts to spread out from the margins of bilayer patterned graphene to the whole pattern graphene. The electric field of bilayer patterned graphene is more uniform and robust, and a broadband absorption close to 100% is obtained. Figure 4(c) shows the electric field distribution in the yz plane. It can be seen the electric field is mainly located between the graphene cells, indicating that the localized surface plasmon (LSP) mode is excited in the absorber. The electric field is highly restricted to the interphase between the graphene and the dielectric medium, which indicates that the propagating surface plasmon (PSP) mode is excited. Two different resonance modes can also be recognized from the magnetic field distribution in Fig. 4(d). Thus, the LSP mode predominates the absorption at 2.31 THz, the two modes coexist at 3.18 THz, and the PSP mode controls the absorption at 3.92 THz. When the patterned graphene interacts with the terahertz wave, the plasmon excitations are resonantly excited in bilayer-patterned graphene. In the overlapping zone, these two resonances produce an integrated effect, where a broadening of the absorption band and a further increase in the absorption rate can be seen.

FIG. 4.

Electromagnetic field (TE mode). (a) Top layer graphene electric field distribution. (b) Bottom layer graphene electric field. (c) The y-z plane electric field distribution. (d) The y-z plane magnetic field distribution.

FIG. 4.

Electromagnetic field (TE mode). (a) Top layer graphene electric field distribution. (b) Bottom layer graphene electric field. (c) The y-z plane electric field distribution. (d) The y-z plane magnetic field distribution.

Close modal
The resonant wavelength λ0 in free space is linked to the thickness of the dielectric spacer d by the following equation in the interference cancellation theory:22 
d=λ04n=λ04ε,
(5)
where n and ɛ are the refractive index and dielectric constant of TOPAS, respectively. In free space, the center frequency 3.18 THz corresponds to a wavelength of about 94.3 μm, and the dielectric spacer layer’s comparable thickness d is 15.4 μm. The actual thickness of the intermediate dielectric spacer H (16 μm) is almost equal to d, which satisfies the interference cancellation condition.
Because the characteristics of metamaterials can be affected by their structures, it is critical to investigate the impact of geometrical factors on the design of absorbers. Figure 5 shows the variation of the absorption spectrum with structural parameters when Ef is 1 eV. In Fig. 5(a), the absorption bandwidth and intensity increase as the edge length L increases from 9 to 13 μm. As the effective area of graphene increases, the surface plasmon resonance region expands, and the enhanced resonance intensity increases the overall absorption bandwidth and absorption rate. Figure 5(b) shows the absorption spectra by varying H2. It can be seen that the center frequency of the absorption band is red-shifted with the increase in the value of H2. Meanwhile, the absorption bandwidth decreases as the value of H2 increases. The center frequency of the absorbers is contributed by the thickness of the dielectric spacer H2,
ωLSP=πδLeqvnsp
(6)
where ωLSP denotes the LSP-mode resonant angular frequency, δ denotes the phase change, Leqv is the equivalent resonance length in the y direction, and nSP is the effective refractive index of the SPPs, which depends strongly on Leqv.23 Under TE polarization, the LSP mode is a local plasmon resonance generated along the y direction of the hexagonal graphene. As shown in Fig. 5(a), the effect of nSP on the LSP resonance modes in the structure is small. In this work, the equivalent lengths in the x and y directions are the same, so the SPP resonance in the x direction cannot be neglected. The resonant frequency in the x direction decreases as L decreases, and the resonant frequency may be blue-shifted.24 Thus, the LSP-dominated peak can be found in Eq. (6) with a blue shift as Leqv decreases.25 At the same time, with a constant period, the decrease in L makes the coupling between the hexagonal graphene unit weaker and reduces the effective resonance area, resulting in narrower bandwidth and lower absorption rate,
ωPSP=ωp1+εeff,
(7)
where ωP is the plasma frequency of graphene, which is connected to σgra. The increase in H2 and P leads to the PSP-dominated peak red shift due to the rise in the effective dielectric constant of the absorber caused by the growth in H2 or P,26 and Eq. (7) can qualitatively explain this change. The LSP-dominated peak shift is relatively small compared to the PSP-dominated peak in Fig. 5(b). This implies that in the suggested MMA, the dielectric constant of the substrate has a major influence on the PSP. The absorption variation in Fig. 5(b) is an outcome of the Fabry–Perot effect in the second insulator layer of thickness H2. For H2 of 14 μm, the effective impedance of the absorber matches the effective impedance of the free space at the resonant frequency so that all reflections from the structure disappear and the whole incident wave is absorbed in the structure.
FIG. 5.

Absorption spectra with different geometrical parameters. (a) Different L. (b) Different H2. (c) Different H1. (d) Different P.

FIG. 5.

Absorption spectra with different geometrical parameters. (a) Different L. (b) Different H2. (c) Different H1. (d) Different P.

Close modal

As shown in Figs. 5(c) and 5(d), when other parameters were held constant, the position of the absorption peak rarely altered. This is mostly because the thickness of the insulator H1 is substantially lower than the device’s operating wavelength, preventing the Fabry–Perot effect associated with the top insulating layer.27 When H1 is 0, the two layers of graphene coincide and the waveform is almost the same as if only the upper layer of graphene were used. This is because the graphene used is a two-dimensional material, and when the two layers of graphene are seamlessly bonded together, the increased thickness has almost no effect on the experimental results.

For the absorber, the sensitivity of the absorption spectra to polarization is studied and plotted in Fig. 6. Under normal incidence, the absorption spectrum with transverse electric (TE) and transverse magnetic (TM) polarizations is given in Fig. 6(a). It is observed that the two absorption curves almost overlap and the absorption rates remain highly consistent. The impact of varying polarization angles from 0° to 90° on the absorption was simulated to better illustrate the polarization insensitivity. It is obvious that the absorption is almost constant when the polarization angle is varied, as shown in Fig. 6(b). This insensitivity to polarization is due to the centrosymmetric structure. The polarization-independent property can enhance the usability of the proposed broadband absorber in many areas.

FIG. 6.

(a) Absorption spectra in TE and TM modes. (b) Absorption contour plots for different polarization angles.

FIG. 6.

(a) Absorption spectra in TE and TM modes. (b) Absorption contour plots for different polarization angles.

Close modal

The absorption characteristics of the proposed absorber with obliquely incident under TE and TM polarization modes are investigated and shown in Figs. 7(a) and 7(b), respectively. For the TE mode, the broadband absorption exceeds 90% when the incidence angle is between 0° and 55°. As the incidence angle increases, the absorption bandwidth becomes narrower, the absorption rate becomes lower, and new additional peaks begin to appear. This is because the component of the magnetic field in the y direction becomes smaller as the incidence angle increases. Finally, it becomes hard to maintain the magnetic resonance with insufficient magnetic flux. When the electrical resonance and magnetic resonance do not coincide, the high absorption rate becomes difficult to maintain. On the other hand, with the increase in incidence angle, the parasitic resonance of some parts of the structure is sharply enhanced and new peaks are generated. For the TM mode, the absorption is more than 90% when the incident angle is less than 70°. As the incidence angle increases, the absorption rate decreases. This can be explained by the decrease in the electric field component parallel to the absorber surface. The resonant currents on the front and rear metal plates cannot be excited effectively leading to weak absorption.

FIG. 7.

Absorption spectra at different incidence angles under different polarization. (a) TE polarization. (b) TM polarization.

FIG. 7.

Absorption spectra at different incidence angles under different polarization. (a) TE polarization. (b) TM polarization.

Close modal

Table II compares our work to other literature on the modification of absorption frequency band, relative bandwidth, and absorption rate, demonstrating that the proposed absorber has the advantages of ultrawideband and tunability.

Table II.

Comparison between the proposed device and similar works.

ReferenceBW > 90% (THz)Relative BW (%)BW > 99% (THz)BW>99%BW>90%Tunable range (%)
4  1.05–2.35 76 1.45–2.00 42% 5–100 
26  1.10–1.86 51 1.23–1.68 59% 1–100 
28  0.53–1.05 66 18–100 
29  1.27–2.59 68 14–98 
30  1.38–3.40 85 18–100 
This work 1.91–4.45 80 2.31–3.92 63% 14–100 
ReferenceBW > 90% (THz)Relative BW (%)BW > 99% (THz)BW>99%BW>90%Tunable range (%)
4  1.05–2.35 76 1.45–2.00 42% 5–100 
26  1.10–1.86 51 1.23–1.68 59% 1–100 
28  0.53–1.05 66 18–100 
29  1.27–2.59 68 14–98 
30  1.38–3.40 85 18–100 
This work 1.91–4.45 80 2.31–3.92 63% 14–100 

In summary, a broadband terahertz absorber based on double-layer patterned graphene is designed and discussed. The simulation results verify that the designed absorber exhibits broadband absorption in the 1.91–4.45 THz range and can be actively tuned by adjusting the Fermi energy without changing the structural geometrical parameters. In particular, it is insensitive to polarization and can achieve broadband absorption for TE and TM polarizations over wide incidence angles up to 60°. There is also an analysis concerning which structural parameters affect the absorption. Based on impedance matching theory and interference cancellation theory, the physical process of ultrawideband absorption is addressed. This tunable broadband absorber provides a new approach for active stealth systems, photodetectors, terahertz imaging, energy harvesting, and dynamic modulators.

This work was supported by the National Natural Science Foundation of China (Grant No. 61805072), Research Foundation for University Key Teacher of Henan Province (Grant No.2020GGJS084), Research Foundation for Key Teacher of Henan University of Technology, and the Innovative Funds Plan of Henan University of Technology (Grant No. 2022ZKCJ15).

The authors have no conflicts to disclose.

This manuscript was written by M. F. (Maixia Fu) and N. X. (Na Xia). The simulation was carried out by N. X. (Na Xia). The analyses and discussions of these obtained results were carried out by Y. D. (Yule Duan), F. Z. (Fei Zhou), Y. L. (Yinsheng Li) and M. F. (Maixia Fu).

Maixia Fu: Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Na Xia: Data curation (equal); Methodology (equal); Software (equal); Writing – original draft (equal). Yule Duan: Formal analysis (equal); Methodology (equal). Fei Zhou: Formal analysis (equal); Methodology (equal). Yinsheng Li: Formal analysis (equal); Methodology (equal).

All data that support the findings of this study are included within the article.

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