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Abstract
A terahertz dual-tunable polarization-independent metamaterial absorber based on hybrid gold-graphene-strontium titanate (STO)-vanadium dioxide (VO2) configuration is proposed. The results show that the absorption rate of absorber can achieve 98.3% at 0.2 THz. Moreover, both the absorption frequency and absorption rate of the absorber can be dual-tuned by varying the chemical potential of graphene and temperature of STO and VO2. Additionally, the performance of the absorber is theoretically analyzed by using the coupled mode theory (CMT) and impedance matching theory (IMT). Finally, the changes in the absorber's absorption spectra are discussed when the depth of STO and VO2 layers is modified. This work provides a theoretical basis for the designs of dual-tunable absorbers and filters, and also offers a new method for switching and modulation of THz radiation.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) wave has attracted wide interest from the scientific community due to the advantages of simultaneously possessing the characteristics of microwaves and visible light waves [1–2]. As a result, in recent years, THz absorbers have become a research hotspot in many fields [3]. However, the implementation of natural materials to achieve high-performance THz absorbers is still a huge challenge due to their limitations [4]. Metamaterials are regarded as periodic composite materials with outstanding electromagnetic properties [5]. Since Landy et al. designed the first narrowband metamaterial absorber in 2008 [6], the development of THz metamaterial absorbers has attained significant progress, ranging from single-band and dual-band [7] to multi-band [8] and wide-band [9]. However, once most absorbers are produced, their spectral characteristics are difficult to be changed. Hence, their application and development are greatly limited. Therefore, the fabrication of dynamically tunable absorbers is urgently needed to fulfill the requirements of many intelligent systems.
To design absorbers with dynamic tunability, many new materials, such as semiconductors [10], doped silicon [11], germanium antimony telluride [12] and liquid water [13] have been extensively applied in absorber researches and designs. However, these materials generally suffer from various disadvantages, such as low efficiency and inconvenient operation. As a two-dimensional honeycomb structure consisting of one monolayer of carbon atoms [14], graphene has many unique electrical properties, such as dynamic tunability [15], strong localization [16], strong dispersion [17], and tight field confinement [18]. More importantly, the conductivity of graphene can be dynamically tuned by adjusting the chemical potential through chemical doping [19] or electrostatic gating [20]. In addition to graphene, strontium titanate (STO) is a ferroelectric material with relatively high dielectric constant and low dielectric loss. STO's response to terahertz wave is determined by a strongly polar soft vibration mode, and its relative dielectric constant can be modulated by the local temperature distribution [21]. Moreover, vanadium dioxide (VO2) is another important temperature-dependent material. The insulator-metal phase transition of VO2 can be induced by temperature and the response properties of VO2 can be changed based on its insulator-metal phase transition [22,23]. Due to the electrically tunable characteristics of graphene and the temperature-tunable characteristics of STO and VO2. In recent years, the development of dynamic dual-tuned absorbers using graphene, STO and VO2 has been greatly explored [24–28]. In 2020, Tian et al. [29]. presented a broadband NIR absorber based on square lattice arrangement in metallic and dielectric state VO2. Moreover, in 2021, Wu et al. [30]. proposed a dual-tunable ultra-broadband terahertz absorber based on graphene and STO. Furthermore, In 2022, Zhuo et al. [31]. designed a THz broadband and dual-channel perfect absorber based on patterned graphene and VO2. However, the metamaterial absorber based on hybrid gold - graphene - STO - VO2 configuration hasn’t been reported in published literature.
In this work, a terahertz dual-tunable polarization-independent metamaterial absorber based on hybrid gold - graphene - STO - VO2 configuration is proposed. First, the absorber achieves a 98.3% absorption rate at 0.2 THz when the chemical potential of graphene is 0.2 eV and temperature of STO and VO2 is 350 K. Second, when the chemical potential of graphene increases, the absorption rate of the absorber decreases, while the absorption frequency is almost unchanged. Meanwhile, as the temperature of STO and VO2 increases, the absorption frequency and absorption rate of the absorber also increase. Third, the performance of the absorber is theoretically analyzed by using the coupled mode theory (CMT) and impedance matching theory (IMT). Finally, the changes in the absorber's absorption spectrum are further discussed when the depth of STO and VO2 layers is modified. This work provides a theoretical basis for the design of both dual-tunable filters and absorbers in the future.
2. Materials
The surface conductivity of graphene is composed of intraband and interband contributions, which are expressed as ${\sigma _g} = {\sigma _{{\mathop{\rm int}} ra}} + {\sigma _{{\mathop{\rm int}} er}}$. Here, the intraband and interband contributions can be calculated through the following equations [32,33]:
As a temperature-dependent material, the dielectric constant of STO in the terahertz frequency range can be expressed as follows [35,36]:
Among these, ${\varepsilon _\infty } = 9.6$ represents the high-frequency dielectric constant, $\omega$ states the angular frequency of the incident light, and $F = 2.6 \times {10^6}\textrm{ }c{m^2}$ is the oscillator strength that is independent of the temperature. Moreover, ${\omega _0}$ and $\gamma$ denote the soft mode frequency and damping factor, respectively. Through the Cochran's Law, ${\omega _0}$ and $\gamma$ can be expressed as follows:
Figure 1 shows the variations of the dielectric constant of STO as a function of the incident light frequency under different temperatures. As can be seen in Figs. 1(a) and 1(b), when the temperature of STO remains constant, the real parts of the dielectric constant of STO slowly increase with frequency, while the imaginary parts significantly increase with frequency. Furthermore, when the temperature of STO increases, at the same frequency, both the real and imaginary parts of the dielectric constant of STO decrease.
Fig. 1. The real parts (a) and imaginary parts (b) of dielectric constant of STO under different temperatures increasing from 310 K to 370 K
As another temperature-dependent material, the relative permittivity of VO2 in the THz range can be expressed by the Drude model [37,38]:
Figure 2(a) shows the relationships between the conductivity of VO2 and temperature. As shown in the blue dotted line in Fig. 2(a), at 313 K, the conductivity is 130 S/m. At 333 K, the conductivity is 820 S/m. At 340 K, the conductivity is 21700 S/m. At 342 K, the conductivity is 158000 S/m, and at 353 K, the final conductivity is 212000 S/m [39]. Therefore, the phase transition temperature of VO2 is around $T = 340\textrm{ }K$, that is, the VO2 is in insulating phase at $T < 340\textrm{ }K$, while the metallic phase at $T > 340\textrm{ }K$.
Fig. 2. (a) The relationship between the conductivity of VO2 and temperature [39]. The real parts (b) and imaginary parts (c) of permittivitry of VO2 under different temperatures increasing from 330 K to 350 K
Figures 2(b) and (c) show the real and the imaginary parts of permittivity for VO2 with different temperatures varying from 330 K to 350 K. As shown in Fig. 2(b), the real parts of permittivity for VO2 are lower than 0 when the temperature is higher than 340 K, which also confirms that VO2 undergoes a reversible insulator-metal phase transition around $T = 340\textrm{ }K$[40].
3. Design method and coupled mode theory
The three-dimensional structure of the dynamically dual-tunable absorber based on gold - graphene - STO - VO2 configuration is schematically illustrated in Fig. 3(a). The absorber consists of four layers: the top layer is made of a cross-shaped gold nanorod resonator. The middle dielectric layer is composed of STO, and the bottom layer consists of a VO2 layer. The monolayer graphene is modeled as a 2D flat sheet, which is placed between the gold and STO layers. Furthermore, a thin layer of SU-8 photoresist is used to connect the STO and graphene layers, and a thin polysilicon layer is used to connect the STO and VO2 layers respectively. The existence of polysilicon and SU-8 will not almost affect absorption because the thicknesses of them are only 20 nm. Moreover, the top metallic pad serves as the electrodes along with the square metallic ring at the back of the SU-8 layer to tune the Fermi energy level of the graphene by applying a gate voltage. The samples of the proposed absorber can be fabricated by using the following method. The cross-shaped gold nanorod layer can be made by electron beam lithography technology. The VO2 film can be produced using pulsed laser deposition. The graphene sheet can be fabricated by chemical vapor deposition technology, and can be directly transferred onto the SU-8 layer.
Fig. 3. Schematic designs of dual-tunable absorber model, (a)Three-dimensional view, (b) Two-dimensional top view, (c)Two-dimensional side view
The initial chemical potential of graphene is ${\mu _c} = 0.2\textrm{ }eV$, and the temperature of STO and VO2 is set as $T = 350\textrm{ }K$ at first. As shown in Fig. 2, the VO2 layer is in fully metallic state at this temperature. In Fig. 3(b), the length and width of cross-shaped gold nanorod are $L = 2.6\textrm{ }um$ and $w = 0.2\textrm{ }um$. The conductivity of gold is set as $\sigma = 4.56 \times {10^7}\textrm{ }m/s$. In Fig. 3 (c), the thicknesses of the top gold layer, middle STO layer and bottom VO2 layer are ${h_1} = 0.2\textrm{ }um$, ${h_2} = 23\textrm{ }um$, and ${h_3} = 4\textrm{ }um$ respectively.
The model period is ${P_x} = {P_y} = 11\textrm{ }um$. The numerical simulation is performed by using Lumerical FDTD Solutions. Periodic boundary conditions are used in both the X and Y directions, and perfectly matched layer (PML) absorbing boundary conditions are used in the Z direction in Fig. 3(b). The incident wave is a linearly polarized wave, with the incident direction in the -Z direction and the polarization direction in the-X direction (X-polarized light).
According to the Coupled Mode Theory (CMT), the physical mechanism of a “perfect” absorbing system can be described by using the following equations [41,42]:
Finally, the absorptivity of the absorber can be expressed as follows:
As shown by the equation above, when $|{1/{\tau_a} - 1/{\tau_c}} |= 0$, the system reflectance reaches its minimum and the absorptivity reaches its maximum at $\omega \textrm{ = }{\omega _0}$.
4. Results discussion and impedance matching theory
Figure 4(a) presents the absorption, reflection, and transmission spectra of double-tuned metamaterial absorber when the chemical potential of graphene is ${\mu _c} = 0.2\textrm{ }eV$, and the temperature of STO and VO2 is $T = 350\textrm{ }K$. The black solid line indicates that the absorber achieves a 98.3% absorption rate at 0.2 THz. This means that electromagnetic wave with frequency of 0.2 THz is almost unable to penetrate the absorber, which is similar to the function of a band-stop filter. Meanwhile, at the same frequency, the reflectance of absorber is close to zero. Additionally, throughout the entire frequency range of the analysis, the transmissivity of the absorber also remains close to zero. This is because the bottom VO2 thin film layer is in fully metallic state, and the thickness of the VO2 is larger than the skin depth of the incident light in the terahertz range, which can effectively block all transmissive wave and act as a reflecting layer in the model.
Fig. 4. (a) Simulated absorption, reflection, transmission spectra of the designed absorber, (b) The comparison between simulated and theoretical absorption spectra. (c) Frequency dependence of absorptivity with different polarization angles.
Furthermore, the theoretical absorption spectrum of the CMT model is displayed in Fig. 4(b). The fitting parameters are set as $1/{\tau _a}\textrm{ = }0.011 \times {10^{12}}\textrm{ }Hz$, $1/{\tau _c}\textrm{ = }0.008 \times {10^{12}}\textrm{ }Hz$. By comparison, it can be found that the trend of the theoretical absorption spectrum is approximately consistent with the numerical absorption spectrum of FDTD.
In Fig. 4(c), due to the structural symmetry of the absorber, the absorption frequency and the absorption rate at the absorption peak remain almost unchanged as the polarization angle changes from $\theta = {0^ \circ }$ to $\theta = {90^ \circ }$, Therefore, the absorber exhibits polarization-independent characteristic.
Figures 5(a) and (b) show the electric field and surface current distributions of the absorber in the X-Y plane under X-polarized and Y-polarized waves at the absorption peak of 0.2 THz.
Fig. 5. The distributions of electric field and surface current distribution at frequency of 0.2 THz in the X-Y plane for (a) X-polarized wave, (b) Y-polarized wave. (c) The distributions of electric field and surface current distributionat frequency of 0.2 THz in the X-Z plane for X-polarized wave. (d) The distributions of electric field and surface current distributionat frequency of 0.2 THz in the X-Z plane for Y-polarized wave.
Particularly, as can be seen from Fig. 5(a), since only the gold nanorod in the X direction can directly interact with the incident light, the electric field is mainly distributed on the two sides of the horizontal nanorod, exhibiting a dipole mode distribution. Meanwhile, according to the surface current distribution, we can find that the positive and negative charges are also mainly distributed at the left and right sides of horizontal nanorod respectively, and the electric dipole resonance is produced [7,43]. Furthermore, by comparing Figs. 5(a) and 5(b), it can be found that the distribution of the electric field and surface current distributions under Y-polarized wave is mutually perpendicular to that under X-polarized wave, and the distribution trend is approximately consistent. The electric field is mainly distributed on the two sides of the vertical nanorod in a dipole mode.
Figures 5(c) and (d) show the electric field distribution of the absorber in the X-Z plane for X-polarized wave and in the Y-Z plane for Y-polarized wave respectively. As shown in Figs. 5(c) and (d), we can see that the electric field is also mainly distributed on the two sides of the gold nanorod.
To further analyze the physical properties of the dual-tuned absorber from a theoretical point of view, the impedance matching theory (IMT) is introduced. In this model, the relative impedance and absorptance of absorber can be defined as [20,44]:
Figure 6(a) presents the change laws of relative impedance of proposed absorber under different frequencies. We can see that the relative impedance of absorber is ${Z_r} = 1$ at the absorption frequency ${f_0} = 0.2\textrm{ }THz$, which satisfies the impedance matching condition. Therefore, the absorptivity is close to 1 at this frequency point.
Fig. 6. (a) The change laws of impedance of proposed absorber under different frequencies. (b) The variations of the absorber's absorption spectra under different chemical potentials of graphene
In order to confirm the electrically tunable characteristics of absorber, Fig. 6(b) shows the variations of the absorber's absorption spectra under different chemical potentials of graphene. As the chemical potentials increase from ${\mu _c} = 0.2\textrm{ }eV$ to ${\mu _c} = 1.0\textrm{ }eV$, the absorption rate decreases from 98.3% to 56.9% gradually, while the absorption frequency is almost unchanged.
Table 1 shows the fitting parameters of CMT for the proposed absorber under different chemical potentials. It can be seen that when the chemical potential increases from ${\mu _c} = 0.2\textrm{ }eV$ to ${\mu _c} = 1.0\textrm{ }eV$, the $1/{\tau _a}$ increases from $0.011 \times {10^{12}}\textrm{ }Hz$ to $0.017 \times {10^{12}}\textrm{ }Hz$ and the $1/{\tau _c}$ decreases from $0.008 \times {10^{12}}\textrm{ }Hz$ to $0.003 \times {10^{12}}\textrm{ }Hz$.Hence, the decreasement of absorption rate can be attributed to the increasement of dissipative loss in absorber and the decreasement of the strength of the coupling between the incident wave and resonator.
Table 1. The fitting parameters of CMT under different chemical potentials
For the purpose of verifying the temperature-tunable characteristics of the absorber, Fig. 7 presents the variations of the absorber's absorption spectra under different temperatures of STO and VO2.
As shown in Fig. 7(a), the absorption rate is near to 0 when the temperatures vary from $T = 310\textrm{ }K$ to $T = 330\textrm{ }K$. As discussed above, the VO2 undergoes a reversible insulator-metal phase transition around $T = 340\textrm{ }K$. Hence, the low absorption rate is resulted from the insulating state of VO2.
In the Fig. 7(b), as the temperatures increase from $T = 335\textrm{ }K$ to $T = 345\textrm{ }K$, the state of VO2 will change from insulating state to metallic state. Therefore, the absorption rate of absorber also increases from 10% to 97% gradually.
Finally, as shown in Fig. 7(c), when the temperatures are higher than $T = 350\textrm{ }K$, the VO2 is in fully metallic state, and can act as a reflecting layer. Furthermore, as shown in Fig. 1, when the temperature of STO increases, both the real and imaginary parts of the STO permittivity decrease. Nevertheless, the real parts are much larger than the imaginary parts. To our knowledge, the loss generated by the model is mainly determined by the imaginary parts, and the absorption frequency of absorber is mainly determined by the real parts. Therefore, as the temperature of STO increases, the absorption frequency of the absorber will also increase, while the absorption rate remains almost unchanged [13].Hence, in Fig. 7(c), as the STO temperatures increase from $T = 350\textrm{ }K$ to $T = 370\textrm{ }K$, the absorption frequency of the absorber increases gradually and exhibits a blue shift. The absorption rate remains above 98% throughout.
Finally, Fig. 8 illustrates the variations of the absorption spectra of the absorber as the thicknesses of the VO2 and STO layers are changed.
Fig. 8. Frequency dependence of absorptivity as (a) VO2 thickness increases, (b) STO thickness increases
In Fig. 8(a), as the VO2 thickness increases, the absorptance of the absorber also gradually increases. When the thickness is ${h_3} \ge 4\textrm{ }\mu m$, the absorptance of the absorption peak reaches the maximum value because the thickness of the bottom VO2 layer is larger than the skin depth in the THz range, and therefore the transmission of the absorber is very close to zero.
As the gold layer, graphene layer, STO layer, and VO2 layer in the model construct an equivalent F–P resonator, the STO layer has a significant impact on the interaction between the BDS layer and the incident wave [45]. According to Fig. 8(b), as the thickness of the STO layer increases, the absorption frequency of the absorber gradually decreases, resulting in a red-shift. At the same time, as the thickness of the STO layer changes, the absorption rate at the absorption peak remains essentially unchanged.
5. Conclusions
A terahertz dual-tunable polarization-independent metamaterial absorber based on hybrid gold - graphene - STO - VO2 configuration is systematically examined in this work. The absorption rate of the absorber can achieve 98.3% at 0.2 THz when the chemical potential of graphene is 0.2 eV and temperature of STO and VO2 is 350 K. As the chemical potential of graphene increases, the absorption rate of the absorber decreases while the absorption frequency is almost unchanged. Meanwhile, as the temperature of STO and VO2 increases, the absorption frequency and absorption rate of the absorber also increase. Moreover, the performance of the absorber is theoretically analyzed by the CMT and IMT. Finally, the changes in the absorber's absorption spectrum are further discussed when the depth of STO and VO2 is modified. Our work provides a theoretical basis for the design of both dual-tunable filters and absorbers in the future.
Funding
Yunnan Province Basic Research Project (202301AT070495); Yunnan Provincial Department of Science and Technology Agricultural Joint Special Project (202101BD070001-064); National Natural Science Foundation of China (11564044, 61461052, 61863035).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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