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Abstract
In this paper, we proposed a multilayer terahertz absorber composed of hybrid graphene and vanadium dioxide (VO2). Based on electrical controlling of graphene and thermal tuning of VO2, three different switchable absorption states are achieved in one structure. When VO2 is in the metal phase and the Fermi level of graphene is set as 0eV, high-frequency broadband (bandwidth, 5.45THz) absorption from 4.5 to 9.95THz is demonstrated. While VO2 is switched to the insulator state, absorption states depend on the Fermi energy of graphene. As the Fermi level changes from 1eV to 0eV, the absorption can be switched from low-frequency broadband (bandwidth, 2.86THz) to dual-frequency absorption. The effect of geometric parameters and fabrication tolerance on the robustness of the absorption properties is explored. The proposed absorber has three switchable states through modulation of graphene and VO2, which is expected to realize potential applications in modulating, filtering, detecting, and other fields.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz waves with frequency change from 0.1THz to 10THz contain a great deal of material information, which shows potential applications such as communication and sensing. Metamaterials realize the functions of unnatural materials through artificial design with subwavelength size, becoming one of the best tools for manipulating electromagnetic waves [1,2]. Many functional devices made by metamaterials in the terahertz region have been reported, such as focusing [3], filter [4], polarization conversion [5], and absorption [6,7]. Metamaterial absorbers play a significant role in detecting, sensing, and electromagnetic shielding since they can enhance the interaction of localized electromagnetic waves with matters [8]. However, traditional metamaterial absorbers [9] composed of metals and dielectrics are usually MIM (metal-insulator-metal) three-layer structures. One obvious disadvantage is that once the structure is designed and produced, the working function and profile of the spectrum cannot be adjusted and tuned, which hinders practical applications.
It is highly demanded that metamaterials system can enable ultra-broadband absorption modulators with integrated multifunction. To increase the absorption bandwidth, various approaches have been proposed. Among them, planar stacking [10–12] and vertical multi-layer stacking structures [13,14] are proven to be quite effective, where bandwidth expansion is demonstrated through the coupling of multiple modes. Furthermore, in order to meet the needs of switchable multifunction designs, active materials such as graphene [15], liquid crystal [16], vanadium dioxide [17], and silicon [18] are introduced into the design. Among these active materials, graphene and vanadium dioxide are outstanding for their efficient and dynamic switchable features. The conductivity of graphene can be precisely controlled by applying varied chemical doping or gate voltages [19,20]. The VO2 undergoes a reversible phase transition at a specific critical temperature of 340K [21]. In 2019, Zhai et al. designed a terahertz broadband absorber based on graphene [22]. The corresponding absorption bandwidth for an absorption rate exceeding about 90% is 1.22THz. Huang et al. demonstrated a VO2-based absorber in 2020, where dual-band broadband absorption is achieved simultaneously [23]. There is only a single working state in their designed structure. Furthermore, results of combining graphene and VO2 for dynamic absorbers supporting alternative modulation (both electricity and temperature) methods show fascinating possibilities for realizing multifunctional absorbers. Liu et al. proposed a hybrid graphene-VO2 metamaterial with dual-frequency and broadband absorption bifunctional [24]. In 2021, Liu et al. proposed a dynamic switchable dual-broadband terahertz absorber, which shows a high-frequency broadband absorption of 2.25THz when VO2 is in the metal phase, and low-frequency broadband absorption of 1.2THz when VO2 is in the insulator phase [25]. Despite two switchable states, the operating bandwidth is highly limited. Although there is much great progress in terahertz absorption, wider absorption bandwidth and diversified working status are still desired.
Here we report a multifunctional dynamically tunable metamaterial absorber, which exhibits alternatively switchable three absorption states by tuning different states of graphene and VO2. When vanadium dioxide is turned into the metal phase, by maintaining the Fermi level of the graphene at 0 eV, the spectrum of high-frequency broadband (bandwidth 5.45THz) absorption from 4.5THz to 9.95THz is achieved. Moreover, in the same system, by decreasing temperature to induce phase transition of VO2, absorption shift from broadband to dual-frequency is presented. Furtherly, when VO2 acts as an insulator and graphene is tuned with its Fermi energy level value at 1eV, low-frequency broadband absorption is achieved. Compared with the previously reported results, the proposed design with remarkable three switchable states presents the largest total absorption bandwidth. Due to highly structural symmetry, the proposed absorber is insensitive to the polarization of incident light. The working mechanism behind is analyzed. These results show potential applications for filtering, sensing, electromagnetic shielding, and other multi-scenarios.
2. Design of the proposed switchable absorber
One unit cell of the proposed absorber structure is schematically shown in Fig. 1(a). The period P of the unit cell is 30µm, both in the x and the y directions. A pattern layer consisting of graphene and VO2 is set at the top of the structure in Fig. 1 (b). Graphene and VO2 are patterned with a designed square and a square loop, where the four sides of the graphene square loop are etched. The parameters of the top pattern layer are optimized as g1 = 10.5µm, g2 = 9µm, g3 = 21µm, w1 = 13µm, and w2 = 26µm. A 40-nm-thick Topas gap is between graphene and VO2. The second pattern layer is composed of VO2 and Au cross-nanostructure with w3 = 0.2µm and w4 = 10µm and underneath them is another graphene square with g4 = 16µm in Fig. 1(c). The thicknesses of the two VO2 layers are set as t4 = 0.06µm and t2 = 0.5µm. The bottom layer is a 0.3-µm-thick gold ground plate with a conductivity of 4.56 × 107S/m. The spaces between the pattern layers are filled with Topas, which is considered lossless in the terahertz frequencies with t1 = 10µm and t3 = 6.5µm. The relative dielectric permittivity of Topas is set as 2.35 [26].
Fig. 1. Schematic view of one unit cell of the proposed periodic structured absorber composed of graphene and VO2. (b)Top view of the first patterned graphene-VO2 layer. (c)Top view of the second patterned layer of graphene-VO2 and Au.
The conductivity properties of VO2 in the terahertz region are expressed by the Drude model [27,28]:
Graphene is a two-dimensional material which is set as a 2D plane in the simulation. The in-plane conductivity of graphene includes two parts, the intraband transition and the interband transition, which are described by the Kubo formula [29,30]:
The Finite Difference Time Domain (FDTD) method is employed to calculate the absorption properties of the designed absorber. Periodic boundary conditions in the x and y directions and perfect matching layer (PML) in the z direction are used for the unit cell. The incident wave is polarized in the x-direction and propagates in the z-direction. The absorption spectrum of the metamaterial absorber is obtained by A = 1-R-T = 1-|S11|2-|S21|2, where S11 and S21 stand for the calculated S-parameters. Since the gold layer is thicker than the skin depth of incident terahertz waves, the transmission is almost null and can be ignored. Correspondingly, the above formula is simplified to A = 1-R = 1-|S11|2. Through optimizing the structural parameters to reduce reflection, it is possible to match the impedance of the metamaterial to the free space and maximize the absorption.
3. Results and discussions
The results in Fig. 2 show that as the collocation between different states of graphene and VO2, three switchable absorption states are obtained in one structure. When VO2 is in the metal phase and the Fermi energy level of graphene is set as 0eV, the proposed structure acts as a VO2-Topas-VO2 sandwiched structure, and ultra-broadband absorption at high-frequency region is demonstrated (see red line in Fig. 2). As VO2 transforms into insulator phase with the graphene’s Fermi energy increasing to 1eV, the graphene pattern determines the absorption performance, leading to a low-frequency broadband (bandwidth 2.86THz) absorption from 1.52THz to 4.38THz (blue line in Fig. 2). By maintaining VO2 at an insulator state, and regulating the graphene Fermi level to 0eV, the designed Au cross dominates the absorption response of the structure. Dual-frequency perfect absorption (black line in Fig. 2) is obtained. In order to understand the underlying physics of the switchable three absorption states in the proposed system, the individual absorption response of the absorber is furtherly analyzed.
i) state 1 (high-frequency broadband absorption)
The result in Fig. 3 shows the absorption and reflection spectrum of the proposed structure when the conductivity of VO2 is 2 × 105S/m and the Fermi energy level of graphene of 0eV. The red line shows the high-frequency broadband absorption with a bandwidth of 5.45THz (from 4.5THz to 9.95THz). The ratio of the absorption bandwidth to the absorption center frequency is considered as fractional bandwidth, which reaches 96.9%. One can see that there are three absorption peaks centered at frequencies of f1 = 5.11THz, f2 = 7.74THz, and f3 = 9.45THz. Since VO2 is in the metal phase, there is nearly no incident terahertz wave transmitting through the second VO2 layer, hence the absorber acts as a MIM structure. To understand clearer the origin of the response, the corresponding electric field distributions on the surface of the first VO2 layer at three absorption peaks in Fig. 3 are shown in Figs. 4(a)–(c). The related magnetic field distributions between the Topas and the VO2 layers are shown in Figs. 4 (d)–(f). From Fig. 4 (a), one can see that the electric field is mainly concentrated on the edge of the middle VO2 square at 5.11THz. The result in Fig. 4(d) shows further detail of the features of energy localizations, where a clear localized magnetic field is seen in the Topas layer underneath the patterned layer with the VO2 square. Electric and magnetic field distribution is localized around the VO2 square which matches the performance of localized surface plasmon resonance (LSPR) mode, indicating that LSPR mode is excited at the first absorption peak position at f1 [31]. For peak 2 at the frequency of f2, from the results in Figs. 4(b) and (e), one can see that the electric field is focused at the boundary of the VO2 square loop with the magnetic field localized in the Topas layer under the square loop. The distribution of the electromagnetic field is similar to that of peak 1 at f1, where LSPR mode leads to efficient absorption at the second frequency position f2. For absorption response at peak 3, the result in Fig. 4(c) shows that there is electric field concentration around both the VO2 square and the square loop at f3. It is noted that the magnetic field is showing a broader distribution in the Topas layer. Different from peaks 1 and 2, the electromagnetic field energy below the square and the square loop is coupled for peak 3, where a propagating surface plasmon resonance (PSPR) is excited at 9.45THz [31].
Fig. 4. The x-y electric field |E| distribution on the top of first VO2 layer at (a) 5.11THz, (b) 7.74THz, (c) 9.45THz. The magnetic field |H| distribution in Topas between two VO2 layers at x-z plane at (d) 5.11THz, (e) 7.74THz, (f) 9.45THz.
Figure 5 shows the surface current distribution on the two VO2 layers at 5.11THz,7.74THz, and 9.45THz, respectively. For peak f1 at 5.11THz, the current intensity is mainly distributed in the VO2 square of the upper VO2 pattern layer, and the direction of the current is from left to right in Fig. 5(a). But the current flows to the left in the lower VO2 in Fig. 5(d). The anti-parallel current of two VO2 layers generates magnetic resonance and contributes to high absorption. For resonance at 7.74THz, the surface current has a strong localization in the four corners of the square loop of the upper VO2 layer and the horizontal sides on the lower VO2 layer where there are currents in opposite directions in two layers, as well (see Fig. 5(b) and (e)). From Figs. 5 (c) and (f), one can see that at the third resonant frequency f3, the anti-parallel current characteristic on the upper and lower VO2 pattern layers is maintained. The magnetic resonance in the MIM structure suppresses the incident electromagnetic waves resulting in high absorptivity at high-frequency regions.
Fig. 5. The surface current distribution on the upper VO2 pattern layer at (a) 5.11THz, (b)7.74TH, and (c) 9.45THz and on the lower VO2 layer at (d)5.11THz, (e)7.74THz, and (f) 9.45THz. The direction and size of the arrows represent the direction and values of the surface current.
Based on the decoupled theory, the broadband absorption mechanism is discussed by using the multiple reflection interference model. There are two interfaces (air-metamaterial interface and TOPAS-VO2 interface) in the simplified decoupled model (see Fig. 6 (a)). When incident waves reach the first interface of the metamaterial, there is the first-order reflection coefficient ${\tilde{r}_{12}} = {r_{12}}{e^{i{\varphi _{12}}}}$ and transmission coefficient ${\tilde{t}_{12}} = {t_{12}}{e^{i{\theta _{12}}}}$ in this air-metamaterial interface. The transmission part passes through the dielectric layer to the second VO2 layer. Due to the properties of metal at this frequency range, the reflection coefficient of VO2 is considered to be -1. Electromagnetic waves propagate inversely from the dielectric layer to the air, resulting in the second-order reflection coefficient ${\tilde{r}_{21}} = {r_{21}}{e^{i{\varphi _{21}}}}$ and transmission coefficient ${\tilde{t}_{21}} = {t_{21}}{e^{i{\theta _{21}}}}$. All reflection and transmission coefficients are calculated through the FDTD simulation based on the metamaterial system without the second VO2 layer and the following parts. Therefore, the reflection of the absorber can be regarded as the superposition of multiple reflections, expressed as [32]
Fig. 6. (a) Multiple interference model for the high-frequency absorber. (b) Amplitude and (c) phase of the first and second reflection and transmission coefficients. (d) The absorption spectra calculated with two methods.
ii) state 2 (low-frequency broadband absorption)
When the temperature decreases below the critical temperature, the conductivity of VO2 changes continuously from 2 × 105S/m to 0S/m. By setting VO2 to the insulator phase and the Fermi level of graphene as 1eV, it obtains a broadband absorption of 2.86THz from 1.52THz to 4.38THz over 90% absorbance. The absorption state is insensitive to the oblique angles of incidence. Figure 7(a) shows the effect of different parts of metamaterial on absorption properties. It can be found that, compared with a monolayer of graphene (only upper graphene, pink-dashed-line; only bottom graphene, blue-dashed-line), the proposed structure with two graphene layers (green-dashed-line) is attributed to the low-frequency broadband absorption response of the whole metamaterial (red-solid-line, in Fig. 7(a)). Because graphene shows strong metallicity at 1eV, the effect of the metal cross is weakened, it slightly enhances the impedance matching between the metamaterial and the free space. The effective impedance of the absorber can be expressed as [33]
Fig. 7. (a) The absorption spectrum for low-frequency broadband absorption of solo units and the proposed structure. (b) Relative impedance of the proposed structure for low-frequency absorption.
Figure 7(b) is the relative impedance of the absorber for low-frequency absorption, where the value of real part is around 1 and the value of imaginary part is around 0, indicating impedance matching with free space.
To better understand the physics, the electric field distributions of patterned graphene at the three peaks in Fig. 7(a) are calculated and analyzed. The results in Figs. 8(a)–(c) show the electric field at the interface of the upper patterned graphene. Figures 8(d)–(f) show the electric field at the interface of the lower graphene square at 1.73THz, 3.05THz, and 3.99THz. The electric field distribution in the x-z plane is shown in Figs. 8(g)–(i). From the electric field in the x-y plane, the electric field distributions are strongly localized at the corners of the graphene pattern, which is attributed to the broadband absorption of graphene and the proposed absorber (see Fig. 7(a)). For the first peak p1 of absorption, the electric field is mainly concentrated on the vertical side of the broken graphene square loop (Fig. 8(a)) and the four corners of the lower graphene square (Fig. 8(d)). In the vertical direction, the localized effect of the electric field of the upper and lower layers is clearly seen, as shown in Fig. 8(g). For the second peak p2, the electric field is mainly distributed in the four corners of the square, and partial energy is coupled to the square loop at the upper graphene pattern interface (see Fig. 8(b)). For the lower graphene square, from Fig. 8(e), one can see that, in addition to the confined field at the four corners of graphene, the horizontal sides of the localized energy are still seen at the end of the Au cross nanostructure. Additionally, from the result in Fig. 8(h), the electric field localization intensity of the upper patterned interface is stronger than the lower patterned interface, which both contribute to the overall absorption response of the proposed absorber. At the third peak p3, there is the electric field located on the horizontal sides between upper graphene patterns (see Fig. 8(c)) and coupled resonance in the lower layer between graphene and Au cross (see Fig. 8(f)). Similar to Fig. 8(h), there is stronger localized energy on the upper graphene pattern than that of the bottom layer in Fig. 8(i). From the electric field distribution results in Fig. 8, one can see that the realization of broadband absorption at lower frequencies is formed by coupled LSP resonances of patterned graphene (also see Fig. 7(a)).
iii) state 3 (dual-frequency narrowband absorption)
Fig. 8. The electric field |E| distribution at upper graphene interface at (a) 1.73THz, (b) 3.05THz, and (c) 3.99THz. The electric field |E| distribution at lower interface of graphene at (d) 1.73THz, (e) 3.05THz, and (f) 3.99THz. The x-z planar electric field |E| distribution from monitors at y = 7µm at (g) 1.73THz, (h) 3.05THz, and (i) 3.99THz.
By setting VO2 to the insulator and the Fermi level of graphene as 0eV, the absorber is switched to a dual-frequency absorption state (see Fig. 9) with high absorption values of 98.41% and 98.95% at 6.06THz and 7.84THz, respectively. The physical origin of perfect absorption is explored. The inset figures (i) and (iii) in Fig. 9 are the electric field |E| distribution of the gold cross at two resonance frequency points. It can be seen that the electric field is mainly localized on both sides of the horizontal arm of the cross for TE polarization incidence. Strong dipole resonances in one arm of the Au-cross along the polarization direction are excited in the insets for Fig. 9(ii) and (iv), indicating that enhanced electric field in the x-direction and induced perfect absorption are obtained. For the two peaks in the absorption spectrum, the phases of the dipole resonances are inverted. The electric dipole resonances lead to the dual-frequency perfect absorption at high-frequency range in the proposed structure. The absorption at 6.84THz also derived from the dipole resonance mode which is weak, resulting in electric field leakage and low absorption strength.
Fig. 9. The absorption spectrum of dual-frequency absorption state. The inset figures (i) and (iii) ((ii) and (iv)) are the electric field |E| distribution and the Ez distribution at 6.06THz (at 7.84THz).
Triple-switchable states are demonstrated and investigated in one designed meta-absorber nanostructure. For practical fabrications, the robustness of the absorber for varied structure parameters at high frequency (state 1) are calculated, and the results are shown in Fig. 10. In high-frequency broadband zone, the VO2 layers and the Topas gap form a resonance cycle. For the LSPR mode, the resonant frequency can be described by an equivalent circuit theory as [34]
where C and L are the equivalent capacitance and inductance and can be approximated by the plate formula. For peak f1, capacitance and inductance are described $L = {\mu _0}\frac{{{l_{eff}}{t_3}}}{{{w_{eff}}}}$ and $C = {\varepsilon _0}{\varepsilon _d}\frac{{{l_{eff}}{w_{eff}}}}{{{t_3}}}$, where µ0, ε0, εd, leff, and weff are the vacuum permeability, the vacuum dielectric constant, the dielectric constant of Topas, the effective length of the resonator, and the effective width of the resonator. For the VO2 pattern, the resonance frequency is inversely proportional to the effective length leff. While w1 increases, the resonance frequency becomes smaller and an obvious red shift of the first peak is seen in Fig. 10(a). For the second peak f2, as w2 increases, resonance area and the equivalent length of the VO2 square loop leff decrease, thus the resonant frequency is blue-shifted in Fig. 10(b). The peak f3 for state 1 is dominated by the PSPR mode, for which the resonance frequency is described by [35]Fig. 10. The absorption spectrum of high-frequency broadband varies with (a) the side length of the VO2 square w1, (b) inner side length of VO2 square loop w2, and (3) period P of unit cell.
For low-frequency broadband absorption (state 2), variations of graphene parameters are investigated. The upper and lower layers of graphene can be respectively equivalent to an RLC branch, and the entire absorber can be simplified into an equivalent circuit model. Since the proposed structure has fourfold symmetry, the upper layer can be equivalent to a graphene square. Its equivalent resistance and capacitance are similar to a circular graphene sheet [37]. According to Eq. (8), the resonance frequency is only related to the side length of the equivalent square. Changing g1 has the greatest impact on the second peak p2 owing to the strong electric field concentration on the upper graphene square. The increase of g1 leads to the increase of the effective length of the equivalent square leff, resulting in a red shift for LSPR mode in Fig. 11(a). Figure 11(b) shows that g2 severely affects the first peak p1. The decrease in g2 results in the increase of the filling factor of the upper layer graphene and leff, which leads to a redshift similar to Fig. 11(a). For Fig. 11(c), the increase of g3 causes a redshift of p2 and p3. Since the graphene square couples with the square loop in Figs. 8(b) and 8(c), g2 and g3 have the same influence on the effective length of the upper graphene pattern. Therefore, when g3 increases, p2 and p3 move towards low resonant frequencies. As the electric field is concentrated at the edge of the underlying graphene at peak p1, the increase of g4 causes a red shift in Fig. 11(d). It is noted that for the third peak p3, due to strong electric field localization on the gold cross, the deviation of g4 has little effect on the resonance frequency. To sum up, the absorption performance is robust in the proposed meta-absorber structure.
Fig. 11. The absorption spectrum of low-frequency broadband varies with (a) the side length of the upper square g1, (b) etching width of upper square graphene loop g2, (3) inner side length of upper square graphene loop g3, and (d) the side length of the lower square g4.
Typical results of absorption performance reported in recent years are briefly listed in Table 1. Compared with them, the designed absorber creatively realizes the three-state absorption function based on switchable graphene and VO2, including dual broadband absorption and dual-frequency absorption. Especially for broadband absorption, the absorber achieves ultra-broadband absorption at high and low frequencies and the corresponding fractional bandwidths are 96.9% and 75.4%. Dual-frequency perfect absorption is also obtained in the narrow-band absorption (state 3). Due to the different states of graphene and VO2, the absorption modulation range can be continuously changed from 15% to 100% (see Fig. 2). Compared with absorbers in Table 1, the proposed design presents great progress in absorption bandwidth and switchable performance.
Table 1. Comparing the proposed design with the related metamaterial absorber designs
4. Conclusion
In conclusion, a dynamically switchable triple-states multifunctional terahertz absorption modulator based on multilayer graphene and vanadium dioxide is elaborately designed and investigated. When VO2 is in a metal state and graphene is set at 0eV, high-frequency broadband absorption exceeding 90% absorption efficiency is demonstrated with a broad bandwidth of 5.45THz from 4.5THz to 9.95THz. The proposed VO2-Topas-VO2 (similar to MIM structure) design plays a significant role in broadband absorption attributed to the excitation of LSPR mode and PSPR mode. As the temperature decreases, VO2 transforms into a dielectric state and the Fermi energy level of graphene is set as 1eV, broadband absorption from 1.52THz to 4.38THz is presented. When VO2 is in the insulator phase, the absorption spectrum turns to a dual-band state with the Fermi energy of graphene at 0eV. The proposed metamaterial absorber with efficiently switchable three states shows great potential to be used as tunable filters, detectors, sensors and modulators.
Funding
National Key Research and Development Program of China (No. 2020YFB2206103); National Natural Science Foundation of China (No. 12075244); National Natural Science Foundation of China (No. 61835011); The Strategic Priority Research Program of Chinese Academy of Sciences (No. XDB43010000).
Disclosures
The authors declare no conflicts of interest.
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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