Graphene Multi-Frequency Broadband and Ultra-Broadband Terahertz Absorber Based on Surface Plasmon Resonance

Abstract

When surface plasmon resonance (SPR) occurs, the incident light is absorbed by the surface of the SPR structure, thus minimizing the intensity of the reflected light. Therefore, the SPR method is adopted in this paper to achieve perfect absorption of the absorbent. In this paper, we first propose a multi-frequency broadband absorber structure based on graphene SPR, which uses the continuous resonance of patterned graphene surface plasmon in the frequency spectrum to form a multi-frequency broadband absorption. In this simulation, a sandwich-stack structure was adopted, whereby the patterned graphene is situated on top of the SiO₂ layer and the metal layer. The broad-band absorption bands of the absorber were obtained as 4.14–4.38 THz, 5.78–6.36 THz, and 7.87–8.66 THz through the analog simulation of finite-difference time-domain method (FDTD) solutions. Then, based on the multi-layer resonant unit structure, through the superposition and combination of absorbing units responding to different frequency bands, the perfect absorption of ultra-wideband is achieved. The data results illustrate that the total absorption bandwidth of the absorber is 2.26 THz, and the relative absorption bandwidth B_w is equal to 28.93%. The electric field in X-Y direction of the absorber in the perfect absorption band is analyzed, respectively, and the dynamic tunability of the absorber is studied. Finally, we studied whether the absorbing structure still has efficient absorption characteristics for the two polarization modes when the incident angle is changed from 0° to 70°. The structure model proposed has potential value for application in terahertz photoelectric detection, filtering, and electromagnetic shielding.

1. Introduction

At present, the perfect metamaterial absorber (PMA) appeals to researchers’ interest due to its high-efficiency ability to absorb electromagnetic waves, which can be applied in the fields of electromagnetic shielding, photoelectric sensing, and optical stealth [1,2,3,4,5]. Perfect absorbing devices are one of the important components in many practical applications, including selective thermal emitters, high-efficiency solar cells, photoelectric detection, and electromagnetic shielding [6,7,8,9,10,11]. Moreover, contrary to the limited absorbing characteristics of narrow-band absorbers, broadband absorbers have a wider range of applications in filtering, shielding, and other fields. For example, in 2016, Hu Dan et al. designed a circular metamaterial absorber through numerical simulation [12]. The absorber achieves broadband absorption up to more than 90% of the absorption width of 1.43 THz. In 2018, Lu Yuying et al. proposed a polarization-insensitive broadband terahertz metamaterial absorber [13]. The simulation results show that the absorption bandwidth covers the broadband frequency range of 0.22–0.33 THz, and the maximum absorption rate is 99.93% at 0.303 THz. The results show that it is feasible to design the broadband terahertz absorber by introducing a multi-scale metamaterial resonant structure. However, due to the fixed structure of such absorbers, the absorption band range cannot be changed [14,15]. Moreover, the complex structure increases the processing cost, and cannot greatly improve the bandwidth.

At present, the most direct way for many college students to realize broadband wave absorption is to use the broadband wave absorber formed by the combination of multiple resonance structures. For example, Yao Gang et al. established an absorber based on a multi-layer surface plasmon resonance (SPR) structure, providing a wide absorption bandwidth [16]. The absorber exhibits > 90% absorption over a broad frequency band of 0.55–3.12 THz. Next, in 2021, Xie Tong et al. proposed a terahertz absorber using fractal technology based on different geometric resonator structures of graphene [17]. This absorber achieves a broadband range of 1.26 THz (absorption > 80%). However, these methods of forming multi-resonance are more difficult to fabricate, with a large structure period, and sensitivity to polarized incident light [18,19,20]. In fact, the broadband-tunable metamaterial filter can also be realized by using a patterned resonator structure of graphene, and broadband absorption achieved by combining continuous resonance frequencies, so that the design can be miniaturized, the manufacturing can be simplified, and the absorption bandwidth can be effectively increased.

The broadband wave absorber has a good application prospect in electromagnetic stealth, shielding, and other aspects. Compared with SPR metal, the metamaterial absorber based on SPR has more excellent characteristics, such as a great mode limitation, and high inherent loss [21,22]. In this paper, we first design a multi-frequency broadband terahertz perfect absorber, based on the graphene SPR structure. The broadband absorption frequency bands of the absorber are 4.14–4.38 THz, 5.78–6.36 THz, and 7.87–8.66 THz, and the calculated total absorption bandwidth of the absorber is 1.51 THz. Finally, on the basis of multi-frequency broadband, an ultra-wideband graphene SPR terahertz absorber is designed, using the superposition and combination of absorbers. The absorber achieved the perfect absorption of ultra-wideband in the 7.0–9.5 THz band, with the total absorption bandwidth of 2.26 THz. The multifunctional wave absorber we designed possess the peculiarity of an adjustable absorption bandwidth and an insensitive angle. The proposed absorber has many potential applications in multi-functional devices, such as modulation and electromagnetic stealth.

2. Theory and Method

The absorption principle of the metamaterial absorber can be explained using the Fabry–Pérot interference theory [23]. According to the Fabry–Pérot interference theory, the metamaterial absorber can be considered as a Fabry–Pérot interference resonant cavity, as shown in Figure 1. The graphene super surface at the roof of the structure is considered as a partial reflector, and the plate at the bottom is considered as a conduct to total reflection [24]. Due to the existence of the upper graphene structure and the lower metal layer, part of the terahertz wave transmitted from the surface of the graphene is reflected in the silicon dioxide absorption layer multiple times. This superposition of multiple reflections cancels out the direct reflection of the air from the graphene surface, achieving a high level of absorption. Therefore, all the reflection (R) coefficients of the incident light superimposed on the surface of the graphene structure can be expressed as [25,26]:

$$\begin{array}{r}\mathrm{R}={\mathrm{r}}_{12}+{\mathrm{t}}_{12}{\mathrm{t}}_{21}{{\mathrm{r}}_{23}\mathrm{e}}^{\mathrm{j}2\mathsf{\beta }}+{\mathrm{t}}_{12}{\mathrm{r}}_{21}{\mathrm{r}}_{23}{\mathrm{r}}_{23}{\mathrm{t}}_{21}{\mathrm{e}}^{\mathrm{j}4\mathsf{\beta }}+{\mathrm{t}}_{12}{\mathrm{r}}_{21}{\mathrm{r}}_{23}{\mathrm{r}}_{23}{\mathrm{r}}_{23}{\mathrm{t}}_{21}{\mathrm{e}}^{\mathrm{j}6\mathsf{\beta }}+\cdots \\ =\frac{{\mathrm{r}}_{12}-({\mathrm{t}}_{12}{\mathrm{t}}_{21}-{\mathrm{r}}_{12}{\mathrm{r}}_{21}){\mathrm{e}}^{\mathrm{j}2\mathsf{\beta }}}{1+{\mathrm{r}}_{21}{\mathrm{e}}^{\mathrm{j}2\mathsf{\beta }}}\\ ={\mathrm{r}}_{12}-\frac{{\mathrm{t}}_{12}{\mathrm{t}}_{21}{\mathrm{e}}^{\mathrm{j}2\mathsf{\beta }}}{1+{\mathrm{r}}_{21}{\mathrm{e}}^{\mathrm{j}2\mathsf{\beta }}}\end{array}$$

(1)

where $r_{12}$ is the surface reflection coefficient, and $t_{12}$ is the transmission coefficient. The reflection coefficient of the bottom metal total reflection plate is $r_{23}$ = −1. $\mathsf{\beta }=-\sqrt{{\mathsf{\epsilon }}_{\mathrm{r}}}{\mathrm{k}}_0{\mathrm{t}}_1/\mathrm{c}\mathrm{o}\mathrm{s}\left(\mathsf{\theta }\right)$ is the propagation phase, ${\mathsf{\epsilon }}_{\mathrm{r}}$ is the relative dielectric constant, k₀ is the wave vector, ${\mathrm{t}}_1$ is the thickness of the SiO₂ substrate, and $\mathsf{\theta }$ is the incident angle. Therefore, in order to achieve perfect absorption, the reflection coefficient $r_{12}$ must be reduced to a maximum degree. The results of the wave absorber simulated in this paper will be verified using this theory. The absorption (A) of the wave absorber can be computed using the following formula [27,28,29,30]:

$$A\left(\omega \right)=1-T\left(\omega \right)-\mathrm{R}\left(\mathsf{\omega }\right)=1-{\left|{\mathrm{S}}_{21}\left(\mathsf{\omega }\right)\right|}^2-{\left|{\mathrm{S}}_{11}\left(\mathsf{\omega }\right)\right|}^2$$

(2)

In the formula, ${\mathrm{S}}_{21}\left(\mathsf{\omega }\right)$ and ${\mathrm{S}}_{11}\left(\mathsf{\omega }\right)$ are the transmitted and reflected amplitudes, respectively. $\mathrm{T}\left(\mathsf{\omega }\right)$ and $\mathrm{R}\left(\mathsf{\omega }\right)$ denote the transmission efficiency and reflection efficiency, respectively. Obviously, the absorption efficiency is maximal when $\mathrm{T}\left(\mathsf{\omega }\right)$ and $\mathrm{R}\left(\mathsf{\omega }\right)$ are small enough. The thickness of the metal layer is much greater than its skin depth in this design, which is enough to inhibit the transmission of all waves. Therefore, the $A\left(\omega \right)$ in this design can be derived from the following equation [31,32,33]:

$$\mathrm{A}\left(\mathsf{\omega }\right)=1-\mathrm{R}\left(\mathsf{\omega }\right)$$

(3)

That is to say, when it is close to zero, perfect absorption can be achieved. In order to calibrate the bandwidth level of the absorber, the relative absorption bandwidth B_w is calculated using Equation (4). Obviously, the relative absorption bandwidth can be expressed as the ratio of the total bandwidth to the center frequency. If the ratio is less than 1%, it is considered as narrowband. If it is within the range of 1–25%, it is considered as wideband. If it is greater than 25%, it is considered as ultra-wideband [34,35,36].

$${\mathrm{B}}_{\mathrm{w}}=2\times \frac{({\mathrm{f}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{f}}_{\mathrm{m}\mathrm{i}\mathrm{n}})}{({\mathrm{f}}_{\mathrm{m}\mathrm{a}\mathrm{x}}+{\mathrm{f}}_{\mathrm{m}\mathrm{i}\mathrm{n}})}\times 100\mathrm{\%}$$

(4)

where $f_{max}$ and $f_{min}$ are the highest and lowest frequencies, respectively. In practical applications, devices are often constructed by applying gate voltage to regulate the Fermi level, and then affecting the conductivity of the graphene. The total conductivity of graphene can be expressed as ${\mathsf{\sigma }}_{\mathrm{g}}={\mathsf{\sigma }}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}$ + ${\mathsf{\sigma }}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}$. ${\mathsf{\sigma }}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}$ and ${\mathsf{\sigma }}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}$ represent in-band and inter-band conductance, respectively. The conductivity of graphene can be considered as the following expression [37]:

$${\sigma }_{intra}=\frac{i{e}^2{K}_{B}T}{\pi {\hslash }^2(\omega +i{\tau }^{-1})}\left\{\frac{E_F}{K_{B}T}+2ln\left[exp(-\frac{E_F}{K_{B}T})+1\right]\right\}$$

(5)

$${\sigma }_{inter}=\frac{i{e}^2}{4\pi {\hslash }^2}\mathrm{l}\mathrm{n}\left[\frac{2\left|E_F\right|-\mathrm{\hslash }(\omega +i{\tau }^{-1})}{2\left|E_F\right|+\mathrm{\hslash }(\omega +i{\tau }^{-1})}\right]$$

(6)

Over here, e refers to the charge of the electron, K_B refers to the Boltzmann constant, ħ = h/2π = 1.05 × 10⁻³⁴ J·s refers to the reduced Planck constant, T refers to the ambient temperature, w refers to the angular frequency of the incident light, and E_F and τ refer to the Fermi energy and relaxation time of graphene, respectively. In the terahertz band E_F >> ħw, the inter-band conductivity of graphene is negligible, and the conductivity of graphene is dependent on the in-band conductivity. Therefore, the total conductivity $\sigma \left(\omega \right)$ of graphene can be written as [38]:

$$\sigma (\omega )=\frac{i{e}^2\left|E_F\right|}{\pi {\mathsf{ħ}}^2(\omega +i{\tau }^{-1})}$$

(7)

According to Equation (7), the optoelectronic device of graphene can be regulated by adjusting the Fermi level and the relaxation time. This indicates that graphene can control its optical conductivity by changing the Fermi level. This continuous broadband-tunable photoconductivity of graphene simplifies the design of optoelectronic devices, and improves their flexibility of use [39].

Figure 2 shows the preparation process of the single-layer graphene SPR absorption structure. In the preparation process, the dielectric structure is grown on the metal base using physical vapor deposition (PVD). Then, the graphene layer is grown on the copper catalyst by chemical vapor deposition, and the isolation layer, transferred to silica using the wet method, is prepared by chemical vapor deposition (CVD) [40,41]. The single-layer patterned graphene structure is realized by electron beam lithography and oxygen plasmon etching (OPE). Finally, the photoresist is stripped, to obtain the final pattern of the graphene SPR absorption structure.

3. Design of the Multi-Frequency Broadband Model

In order to improve the absorption rate and the absorption bandwidth of the graphene to the terahertz wave, by designing a reasonable single-layer graphene structure, relatively strong continuous terahertz surface plasmons can be excited within a broadband range, so that perfect broadband absorption to the terahertz wave is achieved. Figure 3a,b show the structural diagram of the multi-frequency broadband graphene SPR absorber. A single layer of patterned graphene is situated on the roof of a silicon dioxide (SiO₂) layer and a metal (Au) layer. The SiO₂ refractive index n₁ = 1.85, the relative dielectric constant ε_d = 3.4225, and the thickness T₁ = 25 µm were selected. The bottom metal layer constitutes lossy Au with the conductivity σ = 5.25 × 10⁷ S/m and T₂ = 0.5 µm, which can effectively prevent the transmission of terahertz wave. The overall period of the structure P = P_X = P_Y = 25 µm. During the simulation, the optimal parameters of the patterned graphene layer were as follows: L₁ = 5 µm, L₂ = 8.5 µm, R₁ = 9 µm, and R₂ = 12 µm. The E_F and τ of the patterned graphene layer were 0.15 eV and 0.15 Ps, respectively.

The absorption of the patterned graphene absorption structure in the 3.5–9.0 THz band is shown in Figure 4. It can be seen that the absorber realizes multi-frequency broadband absorption. In the frequency bands with the absorption rate greater than 80%, there are 4.14–4.38 THz (0.24 THz), 5.78–6.36 THz (0.48 THz), and 7.87–8.66 THz (0.79 THz). The center frequencies of the three broadband absorptions are 4.21 THz, 6.14 THz, and 8.35 THz, respectively. According to Equation (4), the relative absorption bandwidths B_w of the three absorption frequency bands are calculated to be 5.63%, 7.91%, and 9.55%, respectively. They are all within the range of 1–25%; i.e., multi-frequency broadband absorption is achieved [42], and the total absorption bandwidth is 1.51 THz. Notably, the absorber achieves more than 98% perfect absorption at 4.15–4.28 THz, 6.11–6.25 THz, and 8.07–8.66 THz, respectively. The theoretical curve is based on the calculation method of the reflection coefficient described in Formula 1, and the parameters simulated by the model are substituted to calculate the reflection efficiency in the frequency range of 3.5–9.0 THz, and then the absorption efficiency is calculated by Equation (3). The simulation results of FDTD Solutions have little deviation from the results verified by the Fabry–Pérot resonance theory. The reason for the deviation between the simulated absorption and the theoretical absorption is that the absorber is lossless. The absorber has a wide absorption bandwidth and a simple structure, and provides a new method for the broadband graphene absorber.

In order to understand the internal physical mechanism of the broadband absorption, the electric fields at different peaks were calculated, as shown in Figure 5a–d. It could be seen that the electric fields at 4.22 THz were mainly concentrated on the upper and lower parts of the ring, as well as on the inner side of the central square ring; the local electric fields at 6.21 THz were mainly concentrated on the upper and lower sides; and the electric fields at 8.07 THz and 8.45 THz were all concentrated on the outer side of the central square ring. The combined patterned graphene local absorption could result in stronger light absorption. It can be noted that the surface local electric field modes at 8.07 THz and 8.45 THz are similar, and this similar resonance mode achieves high-efficiency absorption at continuous frequencies, thus generating wider absorption [43,44,45]. In summary, high-efficiency absorption is the result of local surface plasmon resonance between the electromagnetic wave and the structure surface, and the absorbed resonance frequency is closely related to the structure of the resonant unit. It is shown that the method of expanding high-efficiency absorption bandwidth by the mutual fusion of adjacent resonance modes is effective.

In order to demonstrate the tunability of the multi-frequency broadband absorber, as shown in Figure 6a, the absorption curves of the absorber are studied when the E_F is increasing from 0.10 eV to 0.30 eV. As the Fermi level increases from 0.10 eV to 0.30 eV, there is a slight blue shift in the resonance frequency from 4.08–4.32 THz on the left side, and the absorption efficiency remains unchanged. The absorption band at the middle 5.90–6.38 THz shows a weak blue shift, and the absorption peak can be increased from 85.68% to 99.53% with perfect absorption. The absorption band from 7.87–8.66 THz on the right remains unchanged, and the peak of the absorber can be adjusted from 65.54% to 99.65% perfect absorption. With the increase in the Fermi level of the graphene, the resonance frequency of SPR tends toward a high frequency. However, multi-frequency broadband absorption is caused by continuous terahertz surface plasmon resonance, and the mode of high-frequency resonance will change faster, while the mode of low-frequency resonance will change slower, so mode-splitting will occur at a high frequency. The absorption efficiency augments first, and then decreases, while the resonance of SPR reaches the maximum with the increase in the Fermi level. Nonetheless, when E_F increases again, the interface becomes supersaturated, and the absorption decreases [46].

The absorption curve of the absorber when the refractive index n₁ of SiO₂ is increased from 1.79 to 1.91, is shown in Figure 6b. It can be seen from the figure that with the increase in the refractive index n₁ of SiO₂, the absorption efficiency and absorption bandwidth of the absorber are almost unchanged, and a certain red shift in the central resonance frequency of the multi-frequency broadband absorber is observed. The center frequency achieves modulation from 4.08–4.39 THz, 5.96–6.36 THz, and 8.07–8.64 THz. This is because the path phase ${\phi }_P$ of the terahertz wave, when propagating in the dielectric layer, can be expressed as [47,48]:

$${\phi }_P=\frac{4t\sqrt{{\epsilon }_r-{sin}^2\theta }}{\lambda }$$

(8)

where $t$ and ${\epsilon }_r$ are the thickness and dielectric constant of the dielectric lay, respectively. $\lambda$ is the wavelength of the incident light. When the incident light is perpendicularly incident, ${\phi }_P$ and $\theta$ can be regarded as fixed values. Thus, the center frequency is inversely proportional to the dielectric constant of the dielectric layer. When the refractive index n₁ increases, the dielectric constant ${\epsilon }_r$ increases, resulting in a red shift in the center frequency. In summary, the proposed multi-frequency broadband graphene SPR absorber has excellent modulation characteristics. The absorber can be applied to terahertz broadband attenuators, filters, or spatial modulators [49,50].

Figure 7a,b show the effect of the incident light angle from 0° to 70° on the absorption of the multi-frequency broadband absorber with TE and TM polarization. It can be clearly seen that the multi-frequency broadband absorber still has relatively stable absorption characteristics, along with the variation in the incident angle. Moreover, when the incident angle is 0°, the absorption spectra of TE and TM polarization are the same. Therefore, the absorber has the characteristic of symmetrical structure, and is not sensitive to the polarized incident angle. In the process of the small incident angle from 0 to 40, the wave absorber maintains excellent angular stability. This is because the surface structure of graphene has a certain function of focusing light beams, which can ensure the stability of the light source under a small angle incidence. In TE mode, when the angle exceeds 50°, the peak in the intermediate broadband decreases slightly, while the absorption peak intensities in the other frequency broadband remain basically unchanged. Obviously, the resonant absorption in the incident TM mode decreases much faster than that in the TE mode. This is because the tangential component of the electric field of the electromagnetic wave in the multi-frequency broadband absorber is changed in TM mode, while the tangential component in TE mode remains unchanged. In addition, the blue shift in resonance frequency can be observed in TE and TM modes at large incident angles, which is due to the parasitic resonance of the graphene surface. However, the broadband and high absorption levels remain constant even at large angles of incidence, with absorbance in both modes remaining above 60% at 4.08–4.32 THz, 5.90–6.38 THz, and 7.87–8.66 THz. This polarization insensitivity, and wide-angle broadband absorption, make it ideal for detection, sensing, and other optoelectronic applications in the terahertz region.

Table 1. Performance Comparison of Similar multi-frequency broadband Absorbers.

References	Bandwidth	Tunability	Polarization	Angular Sensitivity
[51]	0.5 THz, 0.6 THz	Yes	Sensitive	0–50°
[52]	0.76 THz	Yes	Insensitive	0–60°
[53]	0.93 THz, 0.83 THz	No	Sensitive	0–70°
[54]	0.95 THz,0.74 THz	Yes	Insensitive	0–60°
Present	0.24 THz, 0.48 THz, 0.79 THz	Yes	Insensitive	0–70°

shows the performance comparison of the multi-frequency broadband absorber proposed in this chapter with other similar absorbers [51,52,53,54]. The results show that the absorbing device has more absorption bands, and is insensitive to the incidence angle of the incident electromagnetic wave.

4. Design of Ultra-Wideband Wave Absorbing Model

Figure 8a shows a three-dimensional array diagram of the ultra-wideband graphene terahertz absorber. On the basis of the multi-frequency broadband absorber, the optimized complementary model and absorber units with different resonance responses are combined, to achieve the perfect absorption of ultra-wideband, and the structure is absolutely symmetrical. The specific structures are a metal reflecting layer, a SiO₂ layer, a graphene pattern layer, a SiO₂ layer, and a complementary graphene layer, respectively, from bottom to top. On the basis of multi-frequency broadband, the SiO₂ waveguide layer is added upward, with the refractive index $n_2$ = 1.95, and thickness $T_4$ = 5 μm. The structure of the top-layer patterned graphene is shown in Figure 7b. The optimal structural parameters are as follows: edge length $L_1$ = 2.5 μm, $L_2$ = 3.0 μm, and radius $R$ = 6.5 μm. When the E_F and the τ of the top-layer patterned graphene are 0.24 eV and 0.24 Ps, respectively, the optimal absorption in the frequency band of 7.0–9.5 THz is achieved. The structure period of the ultra-wideband absorber is P = 25 μm, and the total height is H = 35.501 μm.

The absorption spectra of the bilayer graphene absorber at 7.0–9.5 THz are shown in Figure 9. The calculation shows that the frequency band with the absorption efficiency greater than 80% is in the range of 7.12–9.38 THz, and the total absorption bandwidth is 2.26 THz. According to Equation (4), the relative absorption bandwidth B_w = 28.93% > 25% is calculated, and the high-efficiency absorption of ultra-wideband is achieved [55]. Moreover, the total absorption bandwidth of the absorber is 1.98 THz at an absorption efficiency exceeding 95% near-perfect absorption. After comparing the solid line obtained using the simulation with the dotted line calculated by the Fabry–Pérot theory, we can find that they are basically similar, but the simulation results are less effective than the theoretical results. This is because the influence of the inherent loss of materials is not considered in the theoretical calculation, and the electromagnetic parameters of the simulated materials are introduced into the software simulation, which has certain loss. Therefore, the theoretical calculation is better than the simulation results.

The proposed ultra-wideband absorber is mainly based on the multi-layer graphene structure SPR, to achieve perfect absorption. To explore the internal physical mechanism of perfect absorption, the electric field distributions of the graphene layer in the perfect absorption bands of 7.5 THz, 8.5 THz, and 9.0 THz were studied in this paper, as shown in Figure 10. As shown in Figure 10a–c, the local electric field of the top graphene structure is mainly distributed at the openings at the left and right ends of the sector, and with the increase in the incident electromagnetic frequency, the local electric field is gradually transferred to the upper and lower openings. The local electric field distributions of the central graphene structure, with frequency variation, are shown in Figure 10d–f. It can be found that the local electric field is firstly distributed inside the square ring when the electromagnetic wave frequency is 7.5 THz. Then, as the frequency of the electromagnetic wave increases to 8.5 THz, the local electric field diverges outward, and is distributed at the four corners of the square ring, and within the ring. When the electromagnetic wave frequency is 9.0 THz, the local electric field is tightened to the inner side of the square ring, and a more local perfect absorption is formed. Obviously, in the perfect absorption band, the natural frequencies of electromagnetic waves, and the patterned structure, are coupled with each other, resulting in surface plasma oscillation [56,57]. A local electric field is caused, and the ultra-wideband perfect absorption in the frequency band range is realized.

Since the E_F of the graphene material can be controlled by changing the grid voltage $V_f$, we investigated the tunability when the E_F of the top-layer graphene is increased from 0.04 eV to 0.22 eV, as shown in Figure 11a. Here, as the ultra-wideband absorber in this paper adopts the double-layer patterned graphene structure, considering that the applied voltage of the central patterned graphene is relatively complex in the actual manufacturing process, the E_F of the central patterned graphene is fixed. The E_F and τ are 0.15 eV, and 0.15 Ps, respectively, as the parameters of the multi-frequency broadband absorber. Therefore, the change in the E_F of the top-layer graphene can regulate the bandwidth of the absorber. The absorption bandwidth with the absorption efficiency higher than 80% is regulated within the range of 1.85–2.26 THz. In the process of increasing the Fermi level of graphene, the bandwidth increases first, and then decreases, reflecting the process of surface plasmon resonance generated by the absorber from unsaturated, to critical saturated and, finally, supersaturated. The relaxation time of graphene can be regulated by changing the carrier mobility in graphene through weakly doping the graphene structure [58]. For this reason, we studied the absorption curve when the τ of the graphene increased from 0.24 Ps to 2.00 Ps, as shown in Figure 11b. Obviously, with the increase in the τ of the top-layer graphene, the absorption bandwidth of the ultra-wide band absorber hardly changes. The relaxation time has little effect on it, but the absorption efficiency tends to decrease gradually. When the relaxation time $\tau$ = 0.24 Ps, the absorption is best. Therefore, in the actual application process, the efficiency of the ultra-wideband absorber can be changed by changing the graphene relaxation time without affecting the absorption bandwidth.

In actual application, the incident light angle will be changed, so the characteristics of the polarization angle, and the large angle incidence of the incident wave, have great research needs. In this paper, by changing the polarization of the incident light source in the simulation process using FDTD Solutions, we studied the absorption of the absorber under the TE and TM polarization when the incident angle increased from 0° to 70°, as shown in Figure 12a,b. Obviously, when the incident angles are all 0°, the absorption efficiency of TE and TM is the same, because the designed ultra-wideband perfect absorber has the characteristics of absolute symmetry of structure, and is not sensitive to incident light sources of different polarizations [59]. Besides, it can be seen that the bandwidth of the ultra-wideband hardly changes with the increase in the incident angle. The absorption spectra at both polarizations achieve greater than 80% good absorption in the range of 7.12–9.38 THz, with better absorption efficiency with increasing angle. When the angle of incidence is 70°, the near-perfect absorption of more than 90% is achieved in the absorption spectrum of 7.12–9.38 THz for the two polarization modes. The comparison of the ultra-wideband absorber proposed in this paper with other similar absorbers is shown in

Table 2. Performance Comparison of Similar ultra-wideband Absorbers.

References	Bandwidth	Tunability	Polarization	Angular Sensitivity
[60]	0.46 THz	Yes	sensitive	0–60°
[61]	1.6 THz	Yes	sensitive	0–60°
[62]	0.8 THz	Yes	insensitive	0–50°
[63]	2.2 THz	Yes	sensitive	0–60°
[64]	1.38 THz	No	insensitive	NA
Present	2.26 THz	Yes	insensitive	0–70°

below [60,61,62,63,64]. Obviously, the ultra-wideband absorber proposed has the characteristics of an ultra-wide absorption bandwidth, dynamic tunability, polarization independence, and large angle insensitivity, meaning the ultra-wideband absorber has more effects in practical applications.

5. Conclusions

To summarize, in this paper, based on the graphene SPR structure, two optimized tunable absorbers in the THz band are designed, which achieve perfect absorption in multi-frequency and ultra-wideband, respectively. The results are verified by the FDTD method calculation model, and Fabry–Pérot resonance theory. The multi-frequency broadband graphene terahertz wave absorber has a simple structure, and high-efficiency absorption, with wide multi-frequency, is realized in a 3.5–9.0 THz frequency band. The designed ultra-wideband graphene SPR terahertz absorber adopts a double-layer graphene SPR structure. Based on the multi-frequency broadband structure, the SiO₂ waveguide layer, and the top-layer patterned graphene, were added. The combination of the two realizes the ultra-wideband absorption in the 7.0–9.5 THz frequency band. The designed absorber has the property of adjustable bandwidth, and is not sensitive to the polarization and incidence angle of the incident terahertz. Compared with similar wave absorbers, it has more excellent characteristics, and more plasticity. This paper will lay an important theoretical and technical foundation for the development of THz-absorbing devices, which can be widely used in the fields of THz filtering, electromagnetic shielding, and optical attenuation, and has important practical value.