1. Introduction

Electromagnetic waves in terahertz (THz) frequencies have attracted increasing interest due to its potential in fields such as communications, radar, astronomy, biological detection, and security inspection [1–5]. Perfect absorption of THz wave is of great significance in terahertz detectors, sensors and cloaking [6–9]. An ideal absorber is a device that can provide adequate, controllable, and selective absorption of THz wave, by strengthening the interaction between electromagnetic waves and objects, and realizing the energy conversion of radiant energy. As a basic component of many applications, the structure of absorber should be relatively simple and easy to integrate with other devices and materials to achieve various functions. Since Landy et al. [10] proposed the first perfect absorber based on metamaterials in 2008, metamaterials have been considered one of the best choices for perfect electromagnetic wave absorption [11–16]. In order to realize dynamically tunable terahertz absorber based on metamaterials, functional materials have been incorporated into the structure. These functional materials include two-dimensional materials like graphene [17–24] and molybdenum disulfide (MoS₂) [25], phase change materials like vanadium dioxide (VO₂) [26–29] and chalcogenide GeSbTe [30], and photosensitive semiconductors like GaAs [31]. The conductivities of these functional materials can be modulated by applying voltage, heat or light, which in turn affects their optical properties, enabling the dynamically tuning of the absorption peak frequencies or absorption efficiencies of the designed absorbers. Despite these marvelous achievements, most works mentioned above either focused on narrowband absorption or broadband absorption. In order to achieve the miniaturization of modern systems, a single device integrated with multi-function is highly desirable. Interestingly, Zhang et al. [32–35] have designed THz bifunctional devices based on graphene and VO₂, in which the functionality of the devices can be switched by the conductivity of VO₂.

In this paper, we propose a dynamically switchable terahertz absorber with a relatively simple four-layered structure of metal-dielectric-graphene-dielectric. By modulating the chemical potential of graphene layer, the proposed absorber can switch between broadband absorption and triple-band absorption. The distributions of magnetic field, electric field and current density are investigated to elucidate the underlying mechanism of the absorption. Furthermore, the effects of the angle of incident and the angle of polarization on the absorption performance are also discussed.

2. Structure and simulation setup

The schematic of the proposed THz absorber is illustrated in Fig. 1, which is a four-layered structure of metal-dielectric-graphene-dielectric from bottom to top. The metal substrate is composed of a silver ground plane with silver gratings periodically arranged along x-axis on top. The graphene layer is sandwiched between polyvinylidene fluoride binary polymer (P(VDF-TrFE)). The geometrical dimensions of the unit cell are t₁ = 7 µm, t₂ = 13.5 µm, t₃ = 23 µm, t₄ = 10 µm, w₁ = 94 µm and w₂ = 53 µm, respectively. The thickness of the graphene is 3.4 nm, which is about ten times of monolayer [36].

 

Fig. 1. (a) 3D schematic view of the proposed absorber. The incident electromagnetic wave vector k is along the -z axis, the electric field component is along the x axis, and the magnetic field component is along the y axis by default. (b) Cross-sectional view of the periodic unit cell.

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The performance of the designed absorber is numerically investigated with finite element method (FEM) simulation tool. Periodical boundary conditions are applied to x and y directions, and perfectly matched layer is used in z direction. The graphene layer is defined as a boundary with thickness of 3.4 nm, and transition boundary condition is applied.

The relative permittivity of Ag in teraherz regime can be described by Drude model as following [37]: ${\varepsilon _{Ag}} = 1 - \frac{{\omega _p^2}}{{{\omega ^2} - i\gamma }}$, where ω is the angular frequency of incident wave, ω_p is the plasma frequency with a value of 1.37036×10¹⁶ rad/s and γ is the damping constant with a value of 1.71732×10¹⁶ rad/s. The thickness of the bottom Ag groud plane is set to 10 µm, which is far greater than the skin depth, to avoid any electromagnetic wave transmission. The dielectric layer P(VDF-TrFE) shows low loss at THz band and its relative permittivity is set to 2.2 [38]. The relative permittivity of graphene ε_G in teraherz regime can be calculated by ${\varepsilon _G} = 1 + \frac{{i{\sigma _G}}}{{\omega {\varepsilon _0}{t_G}}}$, where σ_G is the surface conductivy of graphene, ε₀ is vaccum dielectric constant, and t_G is the thickness of graphene layer. The surface conductivity of graphene σ_G can be derived from Kubo formula, which has intraband and interband contributions [39,40].

The plane of incident is the xoz plane. The angle between the incident wave vector and the normal direction of the xoy plane is the incident angle θ, which is set to 0 by default. That is, the electromagnetic wave is normal incident. The amplitude of magnetic field of the incident wave is set as ${H_x} ={-} 1\ast sin\mathrm{\Phi }$, ${H_y} = 1\ast cos\mathrm{\Phi }$, ${H_z} = 0$, where Φ is the incident polarization angle. The default polarization of the electromagnetic wave is set to transverse magnetic (TM) mode, that is $\mathrm{\Phi } = 0^\circ $. By increasing Φ from 0° to 90°, the polarization direction of the incident wave rotates clockwise on the xoy plane, and the TM wave gradually changes to transverse electric (TE) wave.

The absorption efficiency A can be calculated by the following equation: $A(\omega )= 1 - {|{{S_{11}}(\omega )} |^2} - {|{{S_{21}}(\omega )} |^2}$, where S₁₁ and S₂₁ are reflection parameter and transmission parameter, respectively. As the thickness of Ag ground plane is far greater than the skin depth, ${|{{S_{21}}(\omega )} |^2}$ equals zero.

3. Results and discussion

The absorption spectra of the proposed absorber with chemical potential of graphene μ_C from 150 meV to 650 meV is shown in Fig. 2. As the chemical potential of graphene increases, the absorption spectrum splits from broadband absorption into triple-band absorption. The overall trend of the full width at half maximum of the absorption peak is narrowing with the increasing of μ_C. This may be attributed to the fact that as the chemical potential increases, the carrier concentration on the graphene layer increases significantly, and the plasmon resonance frequency brought about by it also increases, resulting in a blue shift of the absorption spectrum. Meanwhile, the increase in electrical conductivity reduces the loss and improves its quality factor, resulting in a narrowing of the absorption spectra. A wide absorption frequency range from 5.28 THz to 7.83 THz is achieved with ${\mu _C} = 150\;{meV}$, and the corresponding absorption efficiency is above 90%. When increasing μ_C to 550 meV, three absorption bands with the peak locating at 5.39 THz, 7.01 THz and 8.1 THz are obtained, and the absorption rate are 97.6%, 98.3% and 82.9%, respectively.

 

Fig. 2. (a) Absorption spectra of the proposed absorber with chemical potential of graphene μ_C from 150 meV to 650 meV. (b) Absorption curves of the proposed absorber with graphene chemical potential of 150 meV and 550 meV.

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The absorber can localize the incident electromagnetic wave at a limited position inside the device, so that the electromagnetic radiant energy can be effectively converted into other forms of energy through thermal loss of the material or the generation of carriers. Several methods can be adopted to generate localized field, like Fabry-Pérot (F-P) cavity resonance [41–43], magnetic resonance [17,25] and surface plasmon polariton [44,45], which can be used alone or jointly [46,47]. In order to elucidate the physical mechanism of the absorption spectra, the distributions of electric field, current density and magnetic field for frequencies at which absorption efficiencies reaching the local maximum values are rigorously investigated. For broadband absorption spectra with μ_C of 150 meV, five frequencies at which S₁₁ parameter reaches its local minimum values are selected according to ${S_{11}}$ spectra, as shown in Fig. 3. For frequencies of 5.52 THz, 5.78 THz and 7.67 THz, magnetic field distributions and the corresponding current density distributions are depicted in Fig. 3(a), (b), and (e). The magnetic field intensity is indicated by color, and the direction and magnitude of current density is indicated by arrows. Significant localized magnetic field enhancement can be observed in the circular currents, indicating that the main absorption mechanism is magnetic resonance at these frequencies [17]. For frequencies at 6.52 THz and 7.06 THz, the electric field distributions are plotted in Fig. 3(c) and (d), with color for intensity and arrows for directions. It can be concluded that the strong absorption at 6.52 THz originates from F-P cavity resonance between graphene layer and the raised metal, as indicated by the white dotted boxes. Besides, SPP at the upper surface of hollowed metal, with positive and negative signs indicating the direction of the localized electric field introduced by SPP, is another reason for the strong absorption. For frequency of 7.06 THz, the absorption is the joint effects of F-P cavity resonance between graphene layer and the raised metal, indicating by the white dotted boxes, and SPP at the sidewalls of the hollowed metal, indicating by positive and negative signs.

 

Fig. 3. The distributions of electric field, magnetic field and current density at five frequencies at which ${S_{11}}$ parameter reaches its local minimum values for broadband absorption with ${\mu _C} = 150\;{meV}$. (a), (b) and (e) are magnetic field and current density distributions for frequencies of 5.52 THz, 5.78 THz and 7.67 THz respectively, with color for intensity and arrows for current density. (c) and (d) are electric field distributions for frequencies of 6.52 THz and 7.06 THz respectively, with color for intensity and arrows for directions of the electric field.

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The electric field distribution for triple-band absorption with μ_C of 550 meV is depicted in Fig. 4, with color for intensity and arrows for directions. For the first absorption peak at 5.39 THz, the electric field is mainly confined in the cavity between graphene layer and hollowed metal, forming F-P cavity resonance. Weak SPP can also be observed at the graphene layer above the raised metal. For the second peak, which locates at 7.01 THz, the electric field distribution shows that the absorption mechanism is primarily F-P cavity resonance between graphene layer and raised metal, and secondarily SPPs at the upper surface of graphene layer and hollowed metal surface. As shown in Fig. 4(c), the third absorption peak at 8.1 THz should originate from both F-P cavity resonance between graphene layer and hollowed metal and SPPs at raised metal surface.

 

Fig. 4. Electric field distributions at the absorption peaks for triple-band absorption with ${\mu _C} = 550\;{meV}$. The frequencies of incident electromagnetic wave are (a) 5.39 THz, (b) 7.01 THz and (c) 8.1 THz, respectively. White dotted boxes are regions of F-P cavity resonance, and the positive and negative signs indicate the directions of localized electric field induced by SPP.

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The influence of the polarization of incident wave on the performance of the proposed absorber is also studied. Figure 5(a) and (b) show the broadband absorption and triple-band absorption spectra as a function of the incident polarization angle, respectively. As the incident wave changes from TM polarization to TE polarization, the central frequencies show very slightly blueshift and the absorption efficiencies present small variation for both conditions. It can be concluded that both broadband absorption and triple-band absorption can be considered as polarization-independent though the structure of the proposed absorber is not rotationally symmetric.

 

Fig. 5. Absorption spectra of the proposed absorber with different polarization angles Φ under normal incidence for (a) broadband absorption with ${\mu _C} = 150\;{meV}$ and (b) triple-band absorption with ${\mu _C} = 550\;{meV}$.

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To further investigate the influence of incident angles on the performance of the absorber under TM polarization, the absorption spectra with different incident angles are plotted in Fig. 6. The proposed absorber is sensitive to the incident angle of electromagnetic wave. When the incident angle is less than 15 degrees, the broadband absorption maintains stable. As the incident angle increases, the broadband absorption spectra are gradually blue-shifted, and the absorption peak efficiency fluctuates greatly, as shown in Fig. 6(a). For triple-band absorption, the absorption spectra show obvious distortion once the incident angle is larger than 10 degrees, as depicted in Fig. 6(b). Hence the absorber can maintain proper function under small incident angles less than 10 degrees.

 

Fig. 6. Absorption spectra of the proposed absorber with different incident angles θ under TM polarization for (a) broadband absorption with ${\mu _C} = 150\;{meV}$ and (b) triple-band absorption with ${\mu _C} = 550\;{meV}$.

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4. Conclusion

We have proposed and demonstrated a THz absorber which can simultaneously achieve broadband absorption and triple-band absorption, depending on the chemical potential of graphene. The absorber consists of a simple four-layered structure, from bottom to top are the patterned metal substrate, a flexible dielectric layer, a graphene layer and a flexible dielectric layer. When the chemical potential of graphene is 150 meV, the design serves as a broadband absorber, with absorption efficiency over 90% from 5.28 THz to 7.86 THz. The electric and magnetic field distributions indicate that the broadband absorption arises from the combination of magnetic resonance, F-P cavity resonance and SPP. By increasing the chemical potential of graphene to 550 meV, the broadband absorption can be switched to triple-band absorption, with the absorption peaks locating at 5.39 THz, 7.01 THz and 8.1 THz, respectively. Detailed investigation shows that the triple-band absorption should originate from F-P cavity resonance and SPP. Besides, the absorption characteristics of broadband and narrowband are almost unaffected by the polarization of incident light, but sensitive to the incident angles larger than 10 degrees.