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Abstract
Due to the problems of low absorptivity and the narrow bandwidth of existing broadband absorbers, a perfect broadband tunable absorber with high absorptivity based on double-layer graphene is proposed in this study with 99% high absorptivity as the reference standard, and its theoretical analysis is performed. The designed absorber consists of complete graphene, upper dielectric material, patterned graphene, lower dielectric material and the gold substrate. Through numerical calculation, the designed absorbing structure can achieve high absorption rate of more than 99% in the range of 2.54–3.70 THz, and has a continuous bandwidth of 1.16 THz. In addition, the absorption range is 52%–100% by changing the Fermi level of the graphene layer. The perfect absorber is symmetrical in rotation center and insensitive to incident angle and polarization. It can be widely used in terahertz switch, modulator design, power acquisition and other related fields.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterial [1] is a kind of artificial composite material, which is generally composed of micro nano structure unit array. According to Maxwell equations, the dielectric constant and permeability of the material determine the propagation effect of electromagnetic waves in the medium. Theoretically, metamaterials can have arbitrary permittivity and permeability by reasonably designing their structural parameters and shapes. Therefore, metamaterials have broad research significance and application prospects in electromagnetic wave manipulation.
As an important branch of metamaterials, absorbing materials have developed vigorously in the field of terahertz [2,3]. An advantage of terahertz absorbing materials is that the amplitude, phase and polarization mechanism of electromagnetic waves can be controlled by the geometry of metamaterials, which makes metamaterials simple and flexible in the field of absorbing. In 2008, Landy [4] et al. experimentally designed the first single-band perfect absorber with 88% absorption efficiency of ring resonant structure. Subsequently, narrow-band absorbers [5], multi-peak absorbers [6,7], broadband absorbers [8,9] and other kinds of absorbers with various structures and functions have been continuously proposed, which greatly enriches the types and functions of perfect absorbers.
Recently, with the emergence of new two-dimensional materials, such as graphene [10] and black phosphorus [11,12], etc. have been rapidly applied to the design of terahertz absorbers. Split ring structure [13], cruciform structure [14], disk structure [15], microstrip structure [16,17] and other structures have also been proposed, which greatly improves the adjustability, polarization insensitivity and absorptivity of the absorber. Graphene is an ideal candidate material for plasmons in the terahertz band, due to its single layer carbon atom arrangement in the lattice and unique energy band structure, which makes it possess ideal electromagnetic properties. Using applied voltage or chemical impurities to change the carrier mobility of graphene, we can dynamically control the Fermi level of graphene [18,19], and then actively control the absorption frequency of the absorber. Therefore, graphene materials have a wide application prospect in the design of terahertz wave absorber.
In this study, we propose a broadband tunable perfect absorber, which consists of complete graphene, patterned graphene, dielectric layer and the gold substrate. The patterned graphene is composed of windmill graphene located in the square ring graphene. The novelty and importance of the designed absorber is that the absorption bandwidth is about 1.16 THz in the specific range from 2.54 to 3.70 THz with a high absorption rate of 99% as the reference standard. By changing the Fermi level of graphene, the designed absorber is adjustable and insensitive to polarization angle and incident angle. In addition, there are two main traditional methods to expand the absorption spectrum. One is to use multiple resonators with adjacent resonance frequencies [20] in a single unit, that is, the cooperation of resonance brings wider bandwidth. The other is multi-layer absorber, different layers work in different frequency ranges, and the overlap of corresponding bandwidth increases the bandwidth [21]. In this article, we combine the advantages of both methods to increase the absorption bandwidth. Then, we analyze the influence of various parameters on the absorption effect and the situation of single-layer graphene, and find that it still has a good effect. Compared with the existing broadband terahertz absorbers (see Table 1), we put forward higher requirements for the absorption efficiency and bandwidth of the absorbers. We have solved the problems of narrow bandwidth and low real absorption caused by 90% low absorption reference standard implemented by most broadband absorbers. It can be widely used in all kinds of broadband absorbers, terahertz optical switch and electromagnetic stealth design.
Table 1. Comparison between the designed absorber and the existing absorber
2. Design and simulation
The unit structure of this perfect absorber is shown in Fig. 1(a), and the unit structure period is set as P. From top to bottom, there are complete graphene, upper SiO2 with thickness of h2, patterned graphene, lower SiO2 with thickness of h1 and the gold substrate. It is worth mentioning that the patterned graphene is composed of a windmill like structure and a square ring. The windmill structure is composed of four identical semicircles with a diameter of D, which are located in the center of the unit structure, and the angles between the semicircles are all 90°. The outer diameter of the square ring is L1 and the inner diameter is L2, which is just tangent to the four semicircles of the windmill structure. The gate voltage is supplied by an external bias circuit as shown in Fig. 1(b). By adjusting the resistance (R1, R2), we can apply different voltages to each graphene layer, so as to independently control the Fermi level of each graphene layer in the simulation.
Fig. 1. (a) The unit cell structure diagram of the proposed absorber. (b) The schematic of the external bias circuit.
Although the simulation research is conducted, and we also consider its feasibility in experimental manufacturing [22,23]. First, a gold layer is deposited by thermal evaporation technology as opaque background [24]. Then, the underlying SiO2 can be deposited on the gold substrate by low pressure chemical vapor deposition (LPCVD) [25]. Next, a plasma-enhanced chemical vapor deposition system (PECVD) is used to grow graphene films on the dielectric material SiO2. Then, the polymethyl methacrylate positive resist is spin-coated and baked. The intermediate layer graphene is obtained by using electron beam lithography and reactive ion etching systems [26]. After that, LPCVD technology is used again to form a SiO2 insulating layer on the sample. Finally, a complete layer of graphene is formed on the top by PECVD technology.
The perfect absorber proposed in this study is analyzed and simulated by using the frequency domain solver in the commercial software CST Studio Suite 2019. In this simulation, floquet port is applied in the z direction, and periodic boundary conditions are applied in the x and y directions. For the graphene layer, we set it as a two-dimensional plane, and the thickness of the single graphene layer is 0.34 nm. In Fig. 2, we describe the real and imaginary parts of graphene conductivity. Obviously, the real and imaginary parts of graphene conductivity vary with frequency. We use the Kubo formula to describe this change [27]:
Fig. 2. The relation diagrams correspond to the real part (a) and imaginary part (b) of graphene conductivity.
Since the designed high absorbency broadband adjustable perfect absorber works in the terahertz frequency band, the above Kubo formula can be simplified into the Drude model [28,29]:
In this study, we choose gold as the substrate, and J. R. Piper and S. Fan [30] have shown that the Drude model is suitable for measuring metals without adjustable parameters. The dielectric constant of metal can be given by ${{\cal E}} = {{{\cal E}}_\infty } - \frac{{\omega _P^2}}{{{\omega ^2} + i\omega \gamma }}$, where ${\varepsilon _\infty } = 1$, plasma frequency ${\omega _P} = 1.37 \times {10^{16}}\; {s^{ - 1}}$, $\gamma = 1.23 \times {10^{14}}\; {s^{ - 1}}$. Therefore, we choose the thickness of the metal plate as 0.2 um, which is far greater than the skin depth of the incident electromagnetic wave, so that the electromagnetic wave can not pass through the absorber, that is, the transmission of the electromagnetic wave is zero. The formula for calculating the absorptivity of the absorber is as follows:
3. Results and discussions
Based on the principle of impedance matching, we analyze the absorption mechanism of the designed absorber to achieve broadband and high absorption. From the second part, we can see that for the absorption rate of the absorber, we only need to consider the reflectivity, that is, when the reflectivity is 0, the absorption rate reaches 100%, which proves that the structure impedance of the absorber (Z) matches the impedance of free space (Z0) perfectly. However, the absorber is in free space, so we can only measure its relative impedance. The relative impedance can be described as ${Z_r} = Z/{Z_0} = 1$. Here, the impedance of free space is about 377 Ω. The structural impedance of the absorber can be obtained from the formula [31]:
As shown in Fig. 3, this absorber achieves more than 90% absorption in the range of 2.10−4.06 THz, and has more than 99% absorption in the range of 2.54–3.70 THz. In this paper, through parameter scanning and simulation optimization, these structural parameters are calculated in CST, and finally designed. When the corresponding geometric parameters are set as P = 71 µm, h1 = 15.5 µm, h2 = 8 µm, D = 25 µm, L1 = 70 µm, L2 = 50 µm, the optimal absorption of the proposed absorber is obtained. The dielectric constant of the insulating material SiO2 used is set to 2.25 [32], The Fermi level of the middle layer graphene is set to EF1 = 0.9 eV, and the Fermi level of the top graphene layer is set to EF2 = 0.1 eV. It can be seen from Fig. 4 that in the range of 2.54 - 3.70 THz, the real part of the relative impedance of the absorber is close to 1, and the imaginary part is close to 0, that is, the relative impedance Zr is close to 1. This is consistent with the actual simulation results, which further confirms the accuracy of the above results.
Fig. 3. (a) The absorption spectrum of the proposed absorber under the normal incidence of electromagnetic wave (b) An enlarged view of the part of the absorption spectrum with an absorption rate greater than 90% shown in Fig. 3(a).
Fig. 4. When EF1 = 0.9 eV and EF2 = 0.1 eV, the real part and imaginary part of the relative impedance of the absorber.
To further understand the mechanism of the proposed absorber, we observe the distribution of the electromagnetic fields at a specific frequency. As shown in Fig. 5, it is the electromagnetic field distribution diagram of the absorber under the x incident polarized wave. The corresponding frequency values are f1 = 2.10, f2 = 2.54, f3 = 2.72, f4 = 3.35, f5 = 3.70 and f6 = 4.06 THz, respectively. It can be seen from the figure that the electric fields of the absorber are mainly concentrated in the patterned graphene layer. This phenomenon is mainly due to the coupling effect between the outer square ring and the inner windmill of graphene, which makes the typical hybridization of the two kinds of surface plasmon oscillators [33–35]. As the inner windmill graphene and the outer square ring graphene are close to each other, their dipole modes interact to form a hybrid plasma mode, which greatly improves the absorption efficiency and widens the absorption bandwidth of the absorber.
Fig. 5. The spatial electric field distributions and the magnetic field distributions of patterned graphene position. The corresponding values are 2.10, 2.54, 2.72, 3.35, 3.70 and 4.06 THz, where (a1) - (f1) are the electric field distributions of the corresponding frequency. (z direction) (a2) - (f2) are the spatial magnetic field distributions (y direction) at the corresponding frequency, the incident wave is x-polarized wave.
Specifically, at lower frequencies (points f1, f2, f3), the magnetic fields are mainly concentrated in the lower SiO2 (Figs. 5(a2, b2, c2)). When the absorption rate is 90% (point f1), it can be observed from Fig. 5 (a1) that the local surface plasmon (LSP) [36,37] is excited, resulting in a strong coupling between graphene and the dielectric. Many electric fields are limited to the top of the fan blades of windmill graphene, and the LSP achieves 90% strong absorption. Then, as the absorption frequency increases (point f2), the electric field (Fig. 5(b1)) develops toward a more uniform distribution. This absorption reaches its extreme at point f3, thus forming the first absorption peak. By observing the electric field distribution at point f3 (Fig. 5(c1)), we find that the electric field is mainly concentrated on the boundary of the inner windmill-shaped graphene and the inner and outer boundaries of the outer square ring. This phenomenon shows that the first absorption peak is the co-excitation of the localized surface plasmon and the magnetic coupling resonance to promote strong absorption.
For the absorption peak at point f4, we use multilayer theory [38] to explain. By observing the electric field distribution (Fig. 5(d1)) and magnetic field distribution (Fig. 5(d2)) in the x direction of this point, it can be found that such resonance absorption is found in the upper and lower layers of SiO2. It can be seen that the absorption peak is caused by the interaction of the patterned graphene, the bottom gold substrate and the complete graphene layer. Therefore, resonance can be regarded as a mixed mode of two strong coupling magnetopolarons.
Next, we observe the distribution of the electric and magnetic fields at high frequencies (points f5, f6). It can be seen from Figs. 5(e2) and (f2) that the magnetic fields of the absorber are mainly concentrated in the upper SiO2. Figures 5(e1) and (f1) show that the electric field distributions spread from the gaps concentrated in the windmill-shaped graphene to the entire graphene pattern, which are caused by the electric dipole coupling between the top graphene and the middle graphene. Through reasonable design of the thickness of this structure, we finally achieve a high absorption bandwidth of 1.16 THz.
As shown in Fig. 6, we analyze the influence of the geometry size of the proposed absorber on the absorption efficiency. It can be seen from Fig. 6(a) that the overall absorption efficiency decreases slightly with the increase of period P. Through the analysis of the electric field distribution of each frequency in Fig. 5, we find that there is a part of the charge distribution mainly concentrated on the outside of the square ring graphene. Because the opposite charges gather on both sides of the square ring, the electric dipole of two square rings close to each other will produce resonance, and the antiparallel surface current can be obtained on the graphene layer and the bottom metal layer, which forms a magnetopolaron and causes a strong magnetic resonance. Due to the increase in period P, the effect of this magnetic resonance is reduced, so a slight decrease in the absorption efficiency is caused by the decrease in interaction in adjacent unit cells [39]. For the diameter D of the four semicircles in the windmill, with the decrease in D, the coupling effect between the windmill graphene and the square ring graphene decreases, resulting in the decrease of the absorption efficiency, as shown in Fig. 6(b). Based on the above analysis, let us look at the changes of the outer diameter (Fig. 6(c)) and inner diameter (Fig. 6(d)) of the square ring. With the decrease of the outer diameter, the absorptivity decreases, which is the same principle as the decrease of the absorptivity caused by the decrease of the interaction in the adjacent cell due to the increase in the period P. The increase of inner diameter leads to the decrease of absorption, which is also caused by the decrease in coupling effect between windmill graphene and square ring graphene. For the fluctuations of the curve in the figure, we think it may be caused by Rabi splitting [40,41]. When the electromagnetic wave enters the absorber, the particles will exchange energy, and the Rabi splitting is caused by the coupling between the particles and the optical cavity. In addition, the absorption rate of the high-frequency part of each graph in Fig. 6 drops faster, indicating that the high-frequency part is more sensitive to the above-mentioned coupling effect.
Fig. 6. The proposed broadband tunable absorber has (a) different periods P (b) different diameters of the four semicircles of the windmill D (c) different outer diameters of the square rings L1 (d) different inner diameters of the square rings L2.
As shown in Fig. 7, we study the influence of physical parameters (h1, ɛ) of the dielectric material on the absorber absorption rate, while keeping other parameters unchanged. Figures 7(a) and (b) show the phenomenon of red shift in the perfect absorption band with the increase in thickness h1 and dielectric constant ɛ, which can be qualitatively described by the following formula [42]:
where ${\varepsilon _{eff\; }}$ is the effective dielectric constant, ${\omega _P}\; $ is the plasma frequency of graphene, which is related to its conductivity, ${\omega _{PSP}}$ is the absorption frequency of the plasmon on the transmission surface. The increase in h1 and ɛ results in the effective permittivity of the resonant mode (${\varepsilon _{eff\; }}$) increases. Therefore, ${\omega _{PSP\; }}$ becomes smaller, that is, the perfect absorption band is red shifted. It can be seen from Fig. 7 that with the increase in h1 and ɛ, the change of high frequency absorption is more obvious. Therefore, we infer that the transmission surface plasmons have a greater influence on the perfect absorption of the high-frequency part and a smaller influence on the low-frequency part.Fig. 7. The proposed broadband tunable absorber has (a) different thickness h1 of the bottom medium material (b) different dielectric constant ɛ of dielectric materials.
Figure 8 shows the effect of the Fermi level change of the patterned graphene layer on the absorptivity of the absorber. When EF2 = 0.1 eV remains unchanged, with the increase of Fermi level EF1, the absorption peak shifts blue. This phenomenon can be explained by the theory of equivalent inductance [43]:
First, the resonant frequency of the absorber structure can be roughly described as
where L and C are the total inductance and capacitance of the absorber, respectively. In addition, the total inductance L = Lk + Lg, Lk is the kinetic inductance, Lg is the usual inductance. For the absorber with the fixed structure, Lg is a certain value. The kinetic inductance Lk can be estimated as according to this relation, α is the electron mass, e is the electron charge and Nd is the carrier concentration. With the increase of graphene Fermi level EF1, the carrier concentration Nd increases and the kinetic inductance Lk decreases, which leads to the decrease of total inductance L and the increase in resonance frequency ω. Therefore, the blue shift occurs. With the decrease of Fermi level, the surface plasmon resonance of graphene will become weaker in this frequency band (0 - 6 THz), and the absorptivity corresponding to each frequency will also become smaller. Therefore, the bandwidth will become narrower in general. It can be seen from Fig. 8 that the absorber designed has an absorption range of 52% - 100%.In Fig. 9, we study the influence of different incident angles of electromagnetic waves on the absorptivity. With the increase of incident angle α, the optimal absorption frequency band is blue shifted (Fig. 9(a)), which can be explained according to the Fabry-Perot resonator mode [44]:
Fig. 9. (a) The absorption spectrum corresponds to changing the incident angle α of electromagnetic wave. (b) Absorption contour maps of the absorber as a function of incident angle and frequency.
By observing Fig. 9(b), we find that with the increase of the incident angle, the absorptivity inevitably decreases due to the smaller interaction between the incident wave and the absorber. However, the absorptivity is still very high when the incident angle is in the range of 0 - 50°. Therefore, it is ideal to keep the absorptivity stable when the incident angle is adjusted [45]. Additionally, because the absorber has the characteristic of rotation center symmetry, it is almost the same in TE and TM direction, so it has the characteristic of polarization-insensitive. Based on the above discussion, we come to the conclusion that the designed broadband tunable absorber with high absorptivity based on double-layer graphene has the characteristics of wide angle absorption, which greatly reduces the limitation of its use. Based on Table 1, we compare the designed absorber with other absorbers to confirm the characteristics of high absorption and wide band.
Finally, considering that the preparation of double-layer graphene is not easy, we also study the case of one layer graphene. In Fig. 10, we compare the case of double-layer graphene (red), only removing the top graphene (blue), and only patterned graphene absorber (black). In order to obtain the best absorption, the thickness of SiO2 used in the absorber with only patterned graphene is 18 µm and the Fermi level of graphene is 0.7 eV. Other parameters are consistent with the above. It can be seen from the figure that more than 99% of their absorption bandwidths are 1.16, 0.75 and 0.78 THz, and the relative bandwidths are 37.2%, 25.1% and 24.5% respectively. The absorption bandwidth of the double-layer graphene absorber is about 50% higher than that of the other two absorbers. In addition, the Fermi level of complete graphene is low, which is generally close to the dielectric state. This is why the red and blue parts are close in Fig. 10(a). However, our absorber aims to study the bandwidth of high absorptivity and is sensitive to the regulation of graphene, so we can't ignore the important role of top graphene. From Fig. 10(b), we can find that the red part produces a new absorption peak compared with the blue part, which confirms the coupling between the top graphene and the patterned graphene, and the magnetic field in Fig. 5 (d2) also confirms this. For only patterned graphene absorber (black), its bandwidth is much worse than that of the double-layer graphene absorber (red), and their absorptivity is similar. Considering the accuracy of software simulation and the absorptivity has reached more than 99%, it is of little significance to use simulation to further improve the absorptivity. Therefore, this paper mainly studies the double-layer graphene absorber.
Fig. 10. Absorption spectrum (a) and enlarged diagram (b) of the absorber with different layers. (Among them, red represents double-layer graphene. Blue indicates that only the top layer of complete graphene is removed. Black indicates only patterned graphene absorber.)
4. Conclusion
In conclusion, we propose a broadband tunable absorber with high absorption rate based on double-layer graphene in this study. The proposed absorber works in the 0 - 6 THz band, and has a high absorptivity of more than 99% in the range of 2.54 - 3.70 THz, reaching a bandwidth of 1.16 THz. Compared with the previous absorber, it has higher absorptivity and larger bandwidth, and the effect is more marked. Moreover, the absorber in this study uses less graphene layers, which is easy to integrate. At the same time, due to the symmetrical rotation center of the structure, it has the characteristics of insensitive to polarization, and has low restrictions on the angle of incident light. By changing the Fermi level of graphene, the absorptivity can be adjusted from 52% to 100%. The designed absorber can provide a design idea for various absorbers with terahertz, infrared and microwave frequencies. The absorber may have good application prospects in the terahertz switch, modulator design, power acquisition, etc.
Funding
National Key Research and Development Program of China (2019YFB2203904); National Natural Science Foundation of China (62075047, 61965006, 61975038, 6194005,62065006); Natural Science Foundation of Guangxi Province (2020GXNSFDA297019, 2020GXNSFAA238040, 2021GXNSFAA075012, 2019GXNSFAA245024, 2020GXNSFBA159059, 2018GXNSFAA281272); Science and Technology Project of Guangxi (AD19245064); Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ20107, YQ19108); the Innovation Project of GUET Graduate Education (2020YCXS089).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available from the corresponding author upon a reasonable request.
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