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Abstract
We proposed a dual-controlled broadband terahertz (THz) absorber based on graphene and Dirac semimetal. Calculated results show that the absorptance over 90% is achieved in the frequency range of 4.79-8.99 THz for both transverse electric (TE) and transverse magnetic (TM) polarizations. Benefiting from the advantage of the dielectric constant of these materials varying with chemical doping or gate voltage, the simulation results exhibit that the absorbance bandwidth can be controlled independently or jointly by varying the Fermi energy of the graphene or Dirac semimetal patterns instead of redesigning the absorbers. Impedance matching theory was introduced to analyze the absorption spectra changing with EF. The bandwidth and absorptivity of the proposed absorber are almost independent of changing the incident angle θ up to 35° and 40° for TE and TM modes, respectively. It works well even at a larger incident angle. Because of the symmetry of the structure, this designed absorber is polarization insensitive and almost the same absorptivity for both polarizations. Furthermore, the physical mechanisms were further disclosed by the electric field distributions. The proposed broadband and dual-controlled absorber may have potential applications in various fields of high-performance terahertz devices.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, the terahertz band has been extensively studied for its various applications in communication, imaging, photodetector, and so on [1–3]. Terahertz absorber is an important branch due to its potential applications in these above fields [4–6]. However, most of these structures are composed of metallic materials, and the absorption bandwidths of metamaterial absorbers are usually narrow and non-adjustable absorption performance, which greatly limits their applications in practice [7]. To realize the active tunability of the bandwidth, some novel materials are urgently required [8]. Graphene, a monolayer of carbon atoms gathered in the honeycomb lattice, has shown that it is one of the ideal materials in optoelectronic devices and nanoelectronics due to its remarkable optical properties, high carrier mobility, and flexibility. Especially, the surface conductivity of graphene can be continuously tuned by using the chemical potential via external gate voltage in the terahertz range [9–13]. Therefore, many research papers about graphene-based metamaterial absorbers with bandwidth tunable absorption properties have been published [14–18].
More recently, 3D bulk Dirac semimetal (BDS), a material that can be considered “3D graphene”, has attracted great interests among many scholars for its superior properties [19]. Similar to graphene, the Fermi level and relative permittivity of BDS can also be dynamically controlled by an external gate voltage. Besides, BDS is more robust against environmental temperature than 2D graphene [20]. Up to now, many Dirac semimetal-based devices have been reported in the terahertz and infrared region [21–25]. Hence, graphene and BDS are both promising candidates for achieving dynamically tunable absorber in the THz range. However, most of graphene-based or Dirac semimetal-based devices have the disadvantage of the single tunable approach with bias voltage. Moreover, the absorbance bandwidth and center frequency cannot be controlled effectively and flexibly. Therefore, it is worthwhile to further investigate the THz absorber whose working bandwidth can be tunable, and the adjustment mode is more flexible.
In this paper, we proposed a dual-controlled broadband terahertz perfect absorber based on graphene and Dirac semimetal multilayer structures. Utilizing the properties of them, the proposed absorber shows broadband and bandwidth tunable characteristics by controlling the Fermi levels of graphene and Dirac semimetal. The simulated results show that the absorber bandwidth with over 90% absorptance reaches 4.2 THz when the Fermi energy of graphene and Dirac semimetal sheets are set as 1.7 eV and 60 meV under normal incidence. Furthermore, the tunable property of this absorber was verified, and the above 90% absorption bandwidth can be tuned from 0 to 4.2 THz. Besides, the physical mechanisms were also elucidated by the impedance matching theory and electric field analyses. To our best of knowledge, the control method of absorbers based on graphene and Dirac semimetal has not been reported. Our contribution in this paper is directed toward adjusting a narrow absorption peak to an ultra-broadband absorption spectrum with a simple method, which is very important in practical applications.
2. Design and materials
A unit cell of dual-controlled metamaterial absorber is illustrated in Fig. 1(a). The structure consists of one graphene pattern and a BDS pattern supported by Al2O3 layers with a relative permittivity of 2.28 [26]. And a reflective layer of gold with conductivity $\sigma = 4.56 \times {10^7}$ S/m and the thickness of 0.6 μm is placed at the bottom. The thicknesses of double-layer insulators and BDS are set as h1 = 6.6 μm, h2 = 3.4 μm and 0.4 μm, respectively. The other detailed geometric parameters of the broadband and tunable THz absorber are optimized as l1 = 10.8 μm, l2 = 5 μm, w = 1 μm, a = 7.3 μm, b = 5.2 μm, r = 3.2 μm, W = 13.6 μm and R = 4.8 μm. Besides, we considered graphene monolayer as a two-dimensional conductive surface with zero thickness. The structure is designed to be polarized along the x-direction, and THz wave impinges on the graphene pattern from the air. The numerical calculations are conducted by using the CST microwave package. Periodic boundary conditions were adopted in the x- and y- directions and an open boundary condition in the z-direction. We define the angle θ between the E-field and the positive side of the z-axis, and angle φ between E-field and x-axis. Since the gold film thickness on the bottom is considerably larger than the skin depth. By utilizing the scattering parameters (S-parameters) from the simulation, the absorbance can be calculated by $A = 1 - {|{{S_{11}}} |^2}$.
Fig. 1. (a) Schematic diagram of the proposed terahertz absorber. (b) Simulated absorption for different conditions under TE and TM incident THz wave.
On the one hand, the surface conductivity of graphene can be calculated from the Kubo formula [27]:
Fig. 2. (a) Surface impedance Zg of graphene and (b) permittivity of BDS versus frequency for different Fermi energies.
On the other hand, within the THz range, the relative permittivity of BDS can be expressed as [28]:
3. Results and Discussion
First, we studied the absorption properties of this proposed absorber under normal TE and TM polarizations. For TE polarization, the electric field was parallel to the x-axis. However, for TM polarization, the magnetic field was along the x-axis. The Fermi energy EF of graphene was initially set to be 1.7 eV, and Fermi level $E_F^{\prime}$. of the BDS was initially set as 60 meV. As shown in Fig. 1(b), by combining graphene and BDS resonators with different sizes together to form a unit, the bandwidth is improved significantly. For these two kinds of polarizations, the graphene-BDS composite absorber has a broadband effective absorption (above 90% absorption) from 4.79 THz to 8.99 THz with a bandwidth of 4.2 THz. The center frequency fc is defined as ${f_c} = ({{f_ - } + {f_ + }} )/2\, = \,6.89$ THz, where the f- and f+ are the low- and high-frequency edges of 90% absorptance, respectively. Therefore, the ratio of the absolute bandwidth to the center frequency is about 61%. To further illustrate the novelty of ts proposed absorber, we listed the main characteristics of some published papers based on graphene or others in Table 1 for comparisons.
Table 1. Comparison of the absorber in this paper with published graphene-based or other THz absorbers.
For comparison, the simulated absorption rate for different conditions without graphene or BDS is also shown in Fig. 1(b). When the BDS pattern and its substrate are removed from the structure, it can be found that zero-absorption bandwidth of 90% is noted. Additionally, when the absorber is comprised of BDS pattern, Al2O3 and metal ground, 90% absorption of the BDS absorber is 2.92 THz, starting from 6.66 THz to 9.58 THz. Therefore, the combination of BDS and graphene are obtained resulting in improved absorption bandwidth.
Next, we investigated the relationships between the absorption properties and graphene Fermi energy. Figures 3(a) and (c) display the absorption spectrum of this proposed absorber as a function of the frequency and graphene Fermi energy EF at normal incidence with BDS Fermi energy $E_F^{\prime}$ fixed at 60 meV for TE and TM polarizations, respectively. The black dotted, blue solid, magenta short dot, red solid lines denote the results of EF = 0 eV, 0.4 eV, 0.8 eV, and 1.7 eV, respectively. An absorption above 90% can be observed in the frequency range from 4.79 to 8.99 THz when graphene Fermi energy is equal to 1.7 eV. In sharp contrast, the absorption bandwidth is relatively narrow (only from 5 to 7.44 THz) when the EF = 0 eV. Meanwhile, it should be noted that the absorption bandwidth (over 85%) tends to increase with increasing of Fermi energy EF. Furthermore, the corresponding operating bandwidth (over 80%) at the first absorption peak remains relatively constant. According to the results in Figs. 3(a) and (c), we can conclude that the Fermi energy level of graphene can effectively regulate the absorption performance of the absorber. More generally, Figs. 3(b) and (d) show the color maps of absorption versus different Fermi energy for TE and TM polarizations. It can be seen that there are some discontinuous absorption bands when EF is lower than 1.2 eV. With the increasing value of Fermi energy EF from 1.2 to 2 eV, not only the high performance can be obtained, but also a more broadband absorption region can be found in the high-EF region.
Fig. 3. Absorption spectra with graphene Fermi energy EF = 0 eV, 0.4 eV, 0.8 eV and 1.7 eV for (a) TE and (c) TM polarizations. Color map of the absorption with EF varying from 0 eV to 2 eV for (b) TE and (d) TM polarizations.
To elucidate the physical mechanism of the above phenomenon that the absorption spectra change with EF, we introduced the impedance matching theory [33]. When the THz wave is under normal incidence, the relative impedance of the absorber is calculated using the expression:
Fig. 4. (a) Real and (b) imaginary parts of the relative impedance Zr with different Fermi energies EF.
As the permittivity of BDS can also be controlled by the Fermi level, the absorptance could be tuned accordingly. Figure 5 presents the absorbance under different Fermi level at normal incidence with EF = 1.7 eV. We can find that the positions of absorption shift to the higher frequency as $E_F^{\prime}$ increases. When $E_F^{\prime} = 60 $ meV, the absorption bandwidth and magnitude achieve the optimal value. Besides, compared with Figs. 5(a) and (b), it can be found that the difference between the TE and TM polarizations is very small on absorption frequency points and bandwidth. This is due to the symmetry of the structural elements of the absorber. Thus, we can conclude that the absorption peaks and bandwidths can be tuned by $E_F^{\prime}$. In sum up, this proposed absorber combines the characteristics of broadband-controlled and frequency-adjusted.
Fig. 5. Absorption map with Fermi level $E_F^{\prime}$ of BDS varying from 10 to 100 meV in the case of (a) TE polarization, and (b) TM polarization.
In practical applications, polarization insensitivity is a significant property for any proposed absorber. Therefore, the independence of absorption with the incident angle and polarization was then investigated. Here, the Fermi energy EF and $E_F^{\prime}$ of graphene and BDS are fixed at 1.7 eV and 60 meV, respectively. For TE and TM polarized waves under oblique incident angle θ, the absorption maps are shown in Figs. 6(a) and (b), respectively. It can be observed that the absorbance is almost independent of changing the incident angle θ up to 35° and 40° for TE and TM modes, respectively. The absorptance even remains over 80% when the incident angle θ up to 50°for TE polarized waves. With increasing incident angle θ, the absorptance decreases gradually and the absorption frequency is slightly expanded to a higher position. Meanwhile, the absorption map occurs a blue shift with increasing incidence angles. As for TM polarized wave, the absorption amplitudes are greater than 80% for incidence angles up to 60°. However, the absorptance bandwidth starts slightly decline when θ is large than 20°. Hence, this absorber can tolerate a relatively wide incident angle for both TE and TM polarization. Figure 6(c) depicts the absorption spectra under normal incidence with different polarization angles φ. It can be observed that the absorptance spectrum is insensitive to the polarization angle, which is attributed to the symmetric property of the designed structure. Therefore, this design structure can be utilized as a polarization-insensitive and broadband terahertz absorber.
Fig. 6. (a) and (b) are absorption maps as a function of incident angles θ for TE and TM polarization, respectively. (c) is the absorption map for various polarization angles φ under normal incidence.
To further illuminate the working principle of the absorber, the electric field distributions on the x-y plane at the peak frequencies 5.19, 6.51, 7.67 and 8.75 THz which correspond to peaks I-IV (shown in Fig. 1(b)) for TE polarization are investigated and shown in Fig. 7. Figure 7(a1)–7(a4) are the two-dimension electric-field profiles of the graphene absorbing layer at the four frequencies, whilst Fig. 7(b1)- b(4) correspond to two-dimension electric fields of the BDS layer. A general trend regarding the graphene layer can be found that the intensity of the electric field first increases and then decreases as the frequency increases. As for the BDS layer, however, the electric field distribution is gradually distributed from the four sides to the left and right sides.
Fig. 7. Top view of the electric field $|{\boldsymbol E} |$ distributions, (a1)-(a4) are the Graphene layer and (b1)- (b4) are the BDS layer at corresponding frequencies within the absorption spectrum for Fig. 1(b).
For the lowest resonance frequency 5.19 THz as shown in Figs. 7(a1) and 7(b1), the incident wave excites carriers to oscillate along the x-axis and induce tangential electric fields both on graphene and BDS layers, implying that they will cause energy loss. The energy consumption inside the loss materials such as graphene, BDS and Al2O3 can be calculated by:
where ${\varepsilon ^{\prime\prime}}$ is the imaginary part of dielectric constant, V is the volume of lossy material and El is the electric field inside the lossy materials. In the range of 1-10 THz, the imaginary parts of graphene and BDS are large. Therefore, the electromagnetic energy of THz wave will be dissipated where the electric field is strong.For f = 6.51 THz and f = 7.67 THz, the electric field intensities are dramatically enhanced and concentrated in the center of the graphene layer, as shown in Figs. 7(a2) and (a3), respectively. Meanwhile, it can be seen from Figs. 7(b2)- (b3), the electric field distributions shift from all sides to the left and right and gradually reduce. This is because the resonance frequency is related to the effective width of the graphene and BDS pattern. At the frequency of 8.75 THz, the effective absorption area of graphene is smaller, and the transmitted electromagnetic wave will be mainly consumed by BDS, as shown in Figs. 7(a4) and (b4).
To see how the energy is located at the resonance frequency, we also simulated the electric field distribution in the x-z plane, which can help us to envision where absorption primarily takes place. Figures 8(b1)- (d4) show the cross-sectional view of the electric field $|{\boldsymbol E} |\; $. distributions at the locations marked by the dashed blues in Fig. 8(a). The eye signifies the direction that we are looking at the cut-plane. From Figs. 8(b1)- (d4), we can find that the electric fields are not only concentrated at different parts of graphene and BDS patterns but also trapped inside the dielectric layer, which means that graphene pattern, BDS pattern and the Al2O3 layer play an important role in absorption. However, comparing Fig. 7 and 8, we can know that the losses in graphene and BDS patterns are stronger than Al2O3 layers. The reason can be mainly attributed to the relatively larger imaginary part of the permittivity of graphene and BDS than the substrate in the frequency range. Due to the symmetry of the sucture, the situation of TM polarization is same as TE polarization.
Fig. 8. Electric field distributions in the x-z planes to illustrate the energy localization during absorption. (a) Schematic illustrating the x-z planes chosen, at f = 5.19, 6.51, 7.67, and 8.75 THz. Cross-sectional view of the electric field distributions at the locations of (b1)- (b4) c-c, (c1)- (c4) b-b and (d1)- (d4) a-a under TE polarization at normal incidence.
4. Conclusions
In this paper, we have proposed a broadband, tunable graphene-BDS- based terahertz absorber consisting of two layers structure. It can achieve a broadband absorption over 90% with a bandwidth of 4.2 THz when the Fermi levels of graphene and BDS sheets are set as 1.7 eV and 60 meV. By shifting the Fermi energy level of graphene and BDS, the absorption peaks and bandwidth of the proposed absorber can be dynamically tuned without reconstructing the structure. Besides, the proposed structure can maintain high absorptivity with an incident angle smaller than 35° and 40° for both TE and TM waves, respectively. At last, the absorption mechanism was illuminated by the electric field distributions for the four absorption peaks. Owing to its excellent performances, the proposed absorber can be useful in many highly THz chip-integrated optical circuits and devices, such as tunable THz modulators, multi-channel photodetectors, and nonlinear devices.
Funding
National Natural Science Foundation of China (61501067); Fundamental Research Funds for the Central Universities (2019CDQYTX033).
Disclosures
The authors declare no conflicts of interest.
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