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Abstract
Multi-band terahertz (THz) absorbers have recently gained attention due to their favorable application prospects in communication, imaging, detection, and other fields. However, many multi-band THz absorbers are tuned by a single method, which limits their tuning effect. To address this issue, we propose a multi-band THz absorber that can be co-modulated by thermal and electrical methods. Our proposed absorber uses vanadium dioxide (VO2) to achieve this co-modulation. When VO2 is insulating, the frequency of the absorbing peaks originating from the lateral Fabry-Pérot resonance mode can be changed by adjusting the VO2 width. When VO2 is a conductor, the quality factor of the absorbing peak based on the inductor-capacitor resonance mode can be tuned by adjusting the width of VO2. By varying the top dielectric layer thickness, the frequency of the absorbing peaks can be tuned over a wide range. For devices with two or three layers of graphene nanoribbons-dielectric stacks, a modulation effect similar to that of varying dielectric layer thickness in a single-layer graphene device can be achieved simply by applying a 1 eV Fermi energy to graphene nanoribbons in different layers. By combining thermal and electrical modulation, the two or three-layer stacked device can be dynamically switched between four or six absorbing states, and a wider range of dynamic peak frequency modulation can be realized. Furthermore, the performance of the absorber does not deteriorate significantly at an incident angle of up to 70°. Our proposed thermal-electrical switchable wide-angle multi-band THz absorber provides a reference for the design, fabrication, and application of high-performance THz absorbers in different fields.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves have frequencies ranging from 0.1 THz to 10 THz and are widely used in various fields [1–3] such as broadband communications [4], medical imaging [5], biochemical sensing [6], and nondestructive testing [7]. Graphene, due to its excellent physical properties, has been extensively researched for its applications in THz absorbers [8–16]. Over the years, researchers have reported various types of graphene-based THz absorbers, including narrow-band [8,9], broad-band [11,12], and multi-band [14,17,18] absorbers, with dynamic control functionalities. However, the dynamic tuning of many graphene absorbers is limited to single electrical tuning, which restricts the tuning range of device performance.
To improve device performance, different techniques have been introduced to modulate the device beyond electrical tuning. These techniques include the use of magnetic fields [19], micro-mechanical structures [20], and phase change materials [21]. Among these materials, vanadium dioxide ($\mathrm {VO}_{2}$) is a phase change material that can transit between insulating and conducting states at around 340 K. $\mathrm {VO}_{2}$ is an ideal material for thermally tuned graphene THz absorbers [21–28]. Researchers have employed both thermal and electrical methods to tune $\mathrm {VO}_{2}$ and graphene-based THz absorbers [22]. These absorbers can switch between different operating states such as multi-band absorption and reflection [25], dual-band and multi-band absorption [27], broadband and multi-band absorption [29], and so on.
Compared with other types of THz absorbers such as single-band, dual-band, and broadband THz absorbers, multi-band THz absorbers have unique advantages in some application fields. For example, a triple-band THz absorber based on a symmetrical dual-trident structure is designed for sensing application [30]. Thickness and refractive index of an unknown analysis layer can be detected at the same time by utilizing three variations of resonance frequencies. Besides, multi-band THz absorbers show promise in the areas of spectroscopy and THz communications.
However, many reported multi-band THz absorbers based on $\mathrm {VO}_{2}$ and graphene are complicated in structure and the device performance is difficult to predict. Therefore, in this work, we design a relatively simple THz absorber based on $\mathrm {VO}_{2}$ and graphene. The frequencies of the lateral Fabry-Pérot resonance (LFPR) mode absorption peaks can be adjusted by altering the width of the $\mathrm {VO}_{2}$ nanoribbon in the insulating state. The quality factor (Q factor) of the absorption peak based on the inductor-capacitor (LC) resonance mode can be tuned by adjusting the width of the conducting $\mathrm {VO}_{2}$ nanoribbon. Two different resistor-inductor-capacitor (RLC) equivalent circuit models are used to describe the LC resonance mode absorption peak behavior when VO2 is insulating or metallic. By adjusting the thickness of the top dielectric layer, the frequencies of the absorption peaks can be tuned over a wide range.
To enable dynamic modulation, we adopt 2 or 3 graphene-dielectric stacking structures instead of a single graphene-dielectric structure. This allows us to achieve equivalent tuning effects by applying Fermi energy to graphene at different stacking layers. The proposed single-, double- and triple-stacked absorbers all exhibit good multi-band absorption performance at incidence angles as high as 70${\circ }$, regardless of whether $\mathrm {VO}_{2}$ is insulating or conducting. This indicates that the devices have good incident angle robustness. The absorber proposed in this work serves as a reference for multi-band THz absorbers with dual thermal-electrical control.
2. Design and method
The proposed THz absorber’s schematic diagram is illustrated in Fig. 1. It consists of a parallel arrangement of monolayer graphene nanoribbon array and gold nanoribbon array separated by a TOPAS dielectric layer. The graphene nanoribbon array and the gold nanoribbon array have the same period and duty cycle. The horizontal gaps between adjacent graphene nanoribbons are aligned vertically with the middle of the corresponding gold nanoribbons and vice versa. The width of the nanoribbons is larger than the width of the horizontal gap to ensure that there are overlapping regions between graphene and gold nanoribbons. The lower TOPAS layer is sandwiched between the gold nanoribbons and the back-covered continuous gold layer. Each two neighboring gold nanoribbons are connected by a $\mathrm {VO}_{2}$ nanoribbon between them. The graphical note to Fig. 1(c) presents the detailed dimensions of the device.
Fig. 1. Schematic of the absorber at oblique incidence of THz waves, (a) when $\mathrm {VO}_{2}$ is in the insulating state, (b) when $\mathrm {VO}_{2}$ is metallic. (c) Schematic cross-sectional view of the absorber. The specific device dimensions are as follows: $p=9000\mathrm {\ nm}$, ${w}=4100\mathrm {\ nm}$, ${w}_\mathrm {s}=400\mathrm {\ nm}$, ${w'}=4100\mathrm {\ nm}$, ${w}_\mathrm {s}{'}=400\mathrm {\ nm}$, ${d}_\mathrm {1}=20\mathrm {\ nm}$, ${d}_\mathrm {2}=100\mathrm {\ nm}$, ${d}_\mathrm {3}=5200\mathrm {\ nm}$, ${d}_\mathrm {4}=500\mathrm {\ nm}$.
The relative permittivity tensor of graphene [31] is as follows:
The optical properties of $\mathrm {VO}_{2}$ in the THz band can be described by the Drude model [34] $\varepsilon _{\mathrm {VO}_2}(\omega )=\varepsilon _{\infty }-\frac {\omega _\mathrm {p}^2(\sigma )}{\omega ^2+i \gamma \omega }$ , where $\varepsilon _{\infty }=12$ is permittivity at infinite frequency, the collision frequency $\gamma =5.75 \times 10^{13} \ \mathrm {rad} / \mathrm {s}$. The plasma frequency at a conductivity of $\sigma$ can be denoted as $\omega _{\mathrm {p}}^2(\sigma )=\frac {\sigma }{\sigma _0} \omega _{\mathrm {p}}^2\left (\sigma _0\right )$, in which $\sigma _0=3 \times 10^5 \mathrm {~S} / \mathrm {m}$, $\omega _\mathrm {p}\left (\sigma _0\right )=1.5 \times 10^{15} \mathrm {~rad} / \mathrm {s}$. In our simulations, the conductivities of $\mathrm {VO}_{2}$ in the conducting and insulating states are set to $2\times 10^{5}\mathrm {~S/m}$ and $2\times 10^{2}\mathrm {~S/m}$, respectively, corresponding to temperatures of about $T=358 \mathrm {~K}$ and $T=298\mathrm {~K}$.
TOPAS has a refractive index of 1.53 [35]. Gold is set as lossy metal with a conductivity of $4.09\times 10^{7}\mathrm {~S/m}$ [36].
Finite element simulations are performed using the RF module of COMSOL Multiphysics. In the simulation, a TM-polarized THz plane wave is directed towards the absorber. Periodic boundary conditions are set along the periodic direction, and perfect matching layers are set for both boundaries in the z-direction. The back-covered reflective gold layer causes negligible transmittance, and therefore the absorptivity $A$ is equal to $1-R$, where $R$ is the reflectivity.
3. Results and discussions
Considering that the Fermi energy applied to graphene reaches 1.17 eV in the experiment [37], we simulate the cases of applying 0 eV, 0.2 eV, 0.4 eV, 0.6 eV, 0.8 eV, and 1 eV Fermi energy to graphene, respectively, when $\mathrm {VO}_{2}$ is insulating. The absorption spectra are shown in Fig. 2(a). When Fermi energy of graphene is 1 eV, the absorptivities of 4 absorption peaks at 0.760 THz, 2.995 THz, 5.565 THz, and 8.140 THz are 96.79%, 99.26%, 99.96%, and 99.55%, respectively. As the Fermi energy of graphene decreases from 1 eV to 0.2 eV, the absorption peaks show redshifts, along with significant weakening. When the Fermi energy of graphene drops to 0 eV, the absorption spectrum changes to broadband absorption with all the small absorption peaks superimposed on it disappear. Figure 2(b) shows that the field enhancement regions of the $\mathrm {M}_0$ and $\mathrm {M}_1$ modes are completely different. The elevation of the baseline of the absorption spectra at lower Fermi energy of graphene is due to the excitation of the $\mathrm {M}_0$ mode. In order to minimize the effect of the $\mathrm {M}_0$ mode on absorption spectrum, we keep the graphene Fermi energy at 1 eV in subsequent studies.
Fig. 2. (a) THz absorption spectra of the absorber at different graphene Fermi energies under vertical incidence when $\mathrm {VO}_{2}$ is insulating. (b) Schematic of device cross section and electric field intensity in the region around graphene at $\mathrm {M}_0$ and $\mathrm {M}_1$ modes. (c) Schematic of device cross section and z-component of the electric field in the region around graphene at $\mathrm {M}_1$, $\mathrm {M}_2$, $\mathrm {M}_3$, and $\mathrm {M}_4$ modes, respectively. The gray and green dashed lines represent graphene of 0 eV and 1 eV Fermi energy.
The z-component of electric fields for the $\mathrm {M}_1$, $\mathrm {M}_2$, $\mathrm {M}_3$, and $\mathrm {M}_4$ modes are plotted in Fig. 2(c). The electric field of the $\mathrm {M}_1$ mode has no nodes with 0 electric field, but the electric fields of $\mathrm {M}_2$, $\mathrm {M}_3$, and $\mathrm {M}_4$ modes have 1 node, 2 nodes, and 3 nodes, respectively. Based on the characteristics of the electric field distributions [20], we can refer to the $\mathrm {M}_1$ mode as the LC resonance mode, while the $\mathrm {M}_2$, $\mathrm {M}_3$ and $\mathrm {M}_4$ modes are 1st, 2nd, and 3rd order LFPR modes, respectively.
If we symmetrically change the width of the $\mathrm {VO}_{2}$ nanoribbons, the absorption spectra are displayed in Fig. 3(a) and Fig. 4(a) when $\mathrm {VO}_{2}$ is insulating and metallic. The $\mathrm {M}_1$ peak does not split when $\mathrm {VO}_{2}$ width is different from 400 nm, however, the $\mathrm {M}_2$, $\mathrm {M}_3$ and $\mathrm {M}_4$ peaks all split into 2 absorption peaks. We plot the electric field distributions at different absorption peak frequencies in Fig. 3(b) when $\mathrm {VO}_{2}$ width is 1200 nm. The electric field distribution of the $\mathrm {M}_1$ mode does not change significantly compared to that of Fig. 2(b). However, the electric field distributions of the $\mathrm {M}_{21}$ and $\mathrm {M}_{22}$ modes are different from that of $\mathrm {M}_{2}$ mode. The electric field enhancement of the $\mathrm {M}_{21}$ and $\mathrm {M}_{22}$ modes mainly occurs in the two overlapping regions on the left and right side of each device period.
Fig. 3. When $\mathrm {VO}_{2}$ is in the insulating state. (a) THz absorption spectra of the absorber as $w_\mathrm {s}'$ increases symmetrically from 100 nm to 1200 nm. (b) When $w_\mathrm {s}'=1200 \mathrm {~nm}$, schematic of device cross section and z-component of the electric field in the region around graphene at frequencies of the 7 absorption peaks, respectively. The green dashed lines represent graphene.
Fig. 4. When $\mathrm {VO}_{2}$ is metallic. (a) THz absorption spectra of the absorber as $w_\mathrm {s}'$ increases. (b) When $w_\mathrm {s}'=1200 \mathrm {~nm}$, schematic of device cross section and z-component of the electric field in the region around graphene at frequencies of the 4 absorption peaks, respectively. The green dashed lines represent graphene.
The frequency of an LFPR mode is inversely proportional to the width of the lateral Fabry-Pérot cavity [31], i.e., the overlapping region in this device. As $\mathrm {VO}_{2}$ width increases/decreases from 400 nm, the width of the two lateral Fabry-Perot cavities on the right side of a period decreases/increases, causing the blue-shift/red-shift. The $\mathrm {M}_1$ absorption peak shows a slight blue shift from 0.750 THz to 0.790 THz as $\mathrm {VO}_{2}$ width increases from 100 nm to 1200 nm, as shown in Fig. 5. At different $\mathrm {VO}_{2}$ widths, the absorptivities of $\mathrm {M}_1$ absorption peaks remain stable at around 96% with Q factors of about 6.9.
Fig. 5. Frequencies of the $\mathrm {M}_1$ (hollow square) and $\mathrm {M}_1'$ (solid square) absorption peaks, and Q factors of the $\mathrm {M}_1$ (hollow circle) and $\mathrm {M}_1'$ (solid circle) absorption peaks at different $\mathrm {VO}_2$ widths.
When $\mathrm {VO}_{2}$ is metallic, the absorption peaks do not split while changing $\mathrm {VO}_{2}$ width. The $\mathrm {M}_{2}'$, $\mathrm {M}_{3}'$ and $\mathrm {M}_{4}'$ absorption peaks show little change in Q factors, frequencies, and absorptivities, unlike the $\mathrm {M}_{1}'$ absorption peak. The electric field enhancements of all four modes are located in the two lateral Fabry-Pérot cavities on the left side of each period, as seen in Fig. 4(b). When $\mathrm {VO}_{2}$ is metallic, the LFPR modes in the right overlapping regions are not excited, unlike when $\mathrm {VO}_{2}$ is insulating. Therefore, the localized LFPR modes generating the $\mathrm {M}_{2}'$, $\mathrm {M}_{3}'$ and $\mathrm {M}_{4}'$ absorption peaks on the left side of each period are hardly affected by the change in $\mathrm {VO}_{2}$ width. The behavior of the absorption peak $\mathrm {M}_{1}'$ originating from the LC resonance mode with the width of $\mathrm {VO}_{2}$ is also different from that when $\mathrm {VO}_{2}$ is insulating. When $\mathrm {VO}_{2}$ width increases from 100 nm to 1200 nm, the frequency of $\mathrm {M}_{1}'$ absorption peak increases slightly from 0.590 THz to 0.615 THz. The Q factor of the $\mathrm {M}_{1}'$ absorption peak decreases significantly from 7.2 to 2.8, with absorptivity decreasing from 94.85% to 57.93%, as shown in Fig. 5. Thus, when $\mathrm {VO}_{2}$ width is fixed, the frequency of the LC resonance mode peak can be decreased by about 0.17 THz through temperature increase. The relative frequency change is about 22%. This means that a frequency change of more than 20% can be achieved by thermal modulation alone. At $\mathrm {VO}_{2}$ widths larger than 200 nm, the Q factor changes considerably when modulated by thermal methods. Therefore, by thermal tuning alone, both frequency and Q factor can be switched in a large range.
To further understand the characteristics of the absorption peaks produced by LC resonance modes, equivalent circuit diagrams of the LC modes are plotted in Fig. 6(a) and 6(b) for $\mathrm {VO}_{2}$ in its insulating and metallic states respectively. When $\mathrm {VO}_{2}$ is insulating, the current flows from one side of $\mathrm {VO}_{2}$ to the other side through capacitors $\mathrm {C}_\mathrm {L}'$ and $\mathrm {C}_\mathrm {R}'$ along with inductor $\mathrm {L}_{1}$ and resistor $\mathrm {R}_{1}$. On the other hand, when $\mathrm {VO}_{2}$ is metallic, the current flows directly from one side of $\mathrm {VO}_{2}$ to the other. The two points $\mathrm {N}_{1}$/$\mathrm {N}_{3}$ and $\mathrm {N}_{2}$/$\mathrm {N}_{4}$ are identical in adjacent periods. The circuit between $\mathrm {N}_{1}$/$\mathrm {N}_{3}$ and $\mathrm {N}_{2}$/$\mathrm {N}_{4}$ can be represented by a classical RLC series resonant circuit as shown in Figs. 6(c) and 6(d). For an RLC series resonant circuit, the circuit is in resonance when the complex impedance $Z=R$, and the resonant frequency at this point is $f=\frac {2\pi }{\sqrt {{L} {C}}}$. The Q factor of the RLC resonance peak can then be calculated by $Q=\frac {1}{R}\sqrt {\frac {L}{C}}$. The impedances between $\mathrm {N}_{1}\mathrm {N}_{2}$ and $\mathrm {N}_{3}\mathrm {N}_{4}$ are expressed as follows:
in which $R_\mathrm {A}=2 R_1+2 R_2$, $L_\mathrm {A}=2 L_1+2 L_2$, $C_\mathrm {A}=\left (C_\mathrm {L}^{-1}+C_\mathrm {R}^{-1}+C_\mathrm {L}^{\prime -1}+C_\mathrm {R}^{\prime -1}\right )^{-1}$, $R_\mathrm {B}=R_1+2 R_2+R_3$, $L_\mathrm {B}=L_1+2 L_2+L_3$, $C_\mathrm {B}={({C_\mathrm {L}^{-1}}+{C_\mathrm {R}^{-1}})^{-1}}$. In the above equations, $R_\mathrm {A}$/$R_\mathrm {B}$, $L_\mathrm {A}$/$L_\mathrm {B}$, and $C_\mathrm {A}$/$C_\mathrm {B}$ represent the equivalent resistance, equivalent inductance, and equivalent capacitance between the points of N1/N3 and N2/N4, respectively. The resistances of graphene nanoribbon, gold nanoribbon, and metallic state $\mathrm {VO}_{2}$ nanoribbon are represented by $R_1$, $R_2$, and $R_3$, respectively. The inductances of graphene nanoribbon, gold nanoribbon, and conducting state $\mathrm {VO}_{2}$ nanoribbon are represented by $L_1$, $L_2$, and $L_3$, respectively. The capacitances of capacitors formed by graphene nanoribbons and gold nanoribbons underneath in different overlapping regions, as shown in Fig. 6, are represented by $C_\mathrm {L}$, $C_\mathrm {R}$, $C_\mathrm {L}'$, and $C_\mathrm {R}'$.Fig. 6. (a) Equivalent RLC circuit diagram of the absorber when $\mathrm {VO}_2$ is insulator. (b) Equivalent RLC circuit diagram of the absorber when $\mathrm {VO}_2$ is metallic. (c) and (d) are simplified circuit diagram between $\mathrm {N}_1$/$\mathrm {N}_3$ and $\mathrm {N}_2$/$\mathrm {N}_4$, respectively.
Based on the above equations, we can write the following equations for the frequencies and Q factors of the absorption peaks from the $\mathrm {M}_{1}$ and $\mathrm {M}_{1}'$ modes:
It can be observed from Fig. 5 that the frequency of the $\mathrm {M}_1$ absorption peak increases as the width of $\mathrm {VO}_2$ increases when $\mathrm {VO}_2$ is insulating. This is because the reduction in the overlapping area between graphene nanoribbons and gold nanoribbons connected to $\mathrm {VO}_2$ makes ${C}_\mathrm {L}'$ and ${C}_\mathrm {R}'$ smaller. Meanwhile, $L_2$ becomes smaller with the decrease of gold nanoribbon width. As a result, the frequency of the M1 absorption peak becomes larger according to Eq. (6).
Furthermore, it can also be seen from Fig. 5 that the frequency of the $\mathrm {M}_1'$ absorption peak also increases as the width of $\mathrm {VO}_2$ increases when $\mathrm {VO}_2$ is metallic. This indicates that ${L}_\mathrm {B}$ becomes smaller with the increase of $\mathrm {VO}_2$ width, as the capacitances ${C}_\mathrm {L}$ and ${C}_\mathrm {R}$ remain unchanged in the process.
In addition, the Q factor of the $\mathrm {M}_1$ absorption peak increases and then decreases with the increase of $\mathrm {VO}_2$ width when $\mathrm {VO}_2$ is insulating. This occurs because the increase in $\mathrm {VO}_2$ width causes ${C}_\mathrm {L}'$, ${C}_\mathrm {R}'$, ${L}_2$, and ${R}_2$ to decrease, leading to a decrease in ${C}_\mathrm {A}$, ${L}_\mathrm {A}$, and ${R}_\mathrm {A}$. Under the combined impact of these three factors, $Q_{\mathrm {M}_1}$ in Eq. (8) undergoes a process of increasing and then decreasing. The overall Q factor change is not significant.
On the other hand, when $\mathrm {VO}_2$ is metallic, the Q factor $Q_{\mathrm {M}_1}'$ of the $\mathrm {M}_1'$ absorption peak undergoes a significant decrease with the increase of $\mathrm {VO}_2$ width. As discussed earlier, when the width of $\mathrm {VO}_2$ increases, ${C}_\mathrm {B}$ remains unchanged while LB becomes slightly smaller, but RB increases considerably. This is because the resistivity of conducting $\mathrm {VO}_2$ is much larger than that of gold. As a result, the increase in ${R}_3$ far exceeds the decrease in 2${R}_2$, making ${R}_\mathrm {B}$ significantly larger and causing $Q_{\mathrm {M}_1}'$ in Eq. (9) to decrease remarkably. This allows us to adjust the width of metallic $\mathrm {VO}_2$ to tune the Q factor of the absorption peak over a wide range.
In addition to the effect of $\mathrm {VO}_2$ width on device performance, we also investigate the effect of varying top dielectric layer thickness on device performance when the $\mathrm {VO}_2$ width is fixed at 400 nm. Our findings are shown in 7(a) and 7(b). As the thickness of the top dielectric layer increases, all absorption peaks undergo significant blue shifts. The blue shift of the $\mathrm {M}_1$ and $\mathrm {M}_1'$ absorption peaks, which originate from the LC resonant modes, can be explained by the equivalent RLC circuit model. In other words, all capacitance values in Figs. 6(a) and 6(b) are inversely proportional to the dielectric layer thickness, causing the equivalent capacitances ${C}_\mathrm {A}$ and ${C}_\mathrm {B}$ to become smaller and the $\mathrm {M}_1$ and $\mathrm {M}_1'$ frequencies to increase. During the thickness variation, ${C}_\mathrm {A}$ and ${C}_\mathrm {B}$ are inversely proportional to the dielectric layer thickness ${d}_1$. Assuming that ${L}_\mathrm {A}$ and ${L}_\mathrm {B}$ do not change much as ${d}_1$ varies, according to Eq. (6) and Eq. (7), the resonance frequencies $f_{\mathrm {M}_1}$ and $f_{\mathrm {M}_1'}$ should be proportional to the square root of ${d}_1$.
Fig. 7. Absorption spectra as $d_1$ increases from 10 nm to 80 nm, (a) when $\mathrm {VO}_2$ is in the insulating state, (b) when $\mathrm {VO}_2$ is in the metallic state.
In Fig. 8, the $\mathrm {M}_1$ mode frequencies at different dielectric thicknesses and the $\mathrm {M}_1'$ mode frequencies are shown. Both sets of frequencies are fit with square root functions, and the resulting curves are in good agreement with simulations. This suggests that the $\mathrm {M}_1$ and $\mathrm {M}_1'$ frequencies are proportional to the square root of $\mathrm {d}_1$, providing a theoretical basis for frequency tuning.
Fig. 8. Frequencies of $\mathrm {M}_1$ peak (hollow square) and $\mathrm {M}_1'$ peak (solid square) as top dielectric layer thickness increases from 10 nm to 80 nm. The dashed lines are the fittings of peak frequencies.
If the value of dielectric layer thickness is fixed and $\mathrm {VO}_2$ transitions from insulating state to metallic state, the frequency switching characteristics are demonstrated in Table 1. As $\mathrm {VO}_2$ switches from insulating to metallic state, the absorption peak frequencies all become smaller. We define relative frequency change as the reduction of frequency divided by the original value. For different dielectric layer thicknesses, the relative frequency changes of the $\mathrm {M}_1$/$\mathrm {M}_1'$ absorption peaks are between 22% and 23%, while those of the $\mathrm {M}_2$/$\mathrm {M}_2'$ absorption peaks are less than 7%, and the relative frequency changes of the $\mathrm {M}_3$/$\mathrm {M}_3'$ absorption peaks are even below 3.5%. When $\mathrm {VO}_2$ switches states, the relative frequency changes of the LC mode-based peaks are much larger than those of the LFPR-based peaks. This is because an LFPR mode is a highly localized mode inside the lateral Fabry-Pérot cavity, and the frequency of an LFPR mode is strongly influenced by geometry and material parameters [31], and is less affected by the changes outside the cavity.
Table 1. Frequency thermal switching characteristics.
The dynamic modulation range of LFPR frequencies would increase significantly if the thickness of the dielectric layer can be dynamically varied. However, in practice, it is challenging to modify the thickness of the dielectric layer. Therefore, an alternative method can be used, which involves modifying the structure of the device to a bilayer graphene nanoribbon array-dielectric layer stacked structure with identical graphene positions, as schematically shown in Fig. 9(b). The thickness of both dielectric layers in the double-stacked structure is 20 nm. In this structure, one layer of the graphene nanoribbon array is set to a Fermi energy of 1 eV, while the Fermi energy level of the other layer is kept at 0 eV. Considering that a graphene mobility of about $30,000\mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ at room temperature is already achievable in the experiments [38], we add $20,000\mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ and $5,000\mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ graphene mobility in addition to $10,000\mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ in our simulations for comparison. The corresponding relaxation times are 2 ps and 0.5 ps, respectively.
Fig. 9. (a) Absorption spectra of the double-stacked absorber when 1 eV Fermi energy level is applied to the lower and upper graphene layer and when $\mathrm {VO}_2$ is in insulating and metallic states, respectively. The dashed, solid, and dotted lines represent the mobility of graphene at $5000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ , $10000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$, and $20000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$, respectively. (b) Schematic of device cross section when $\mathrm {VO}_2$ is in the insulating and metallic states, respectively, and z-component of the electric field in the region around graphene at frequencies of the 8 absorption peaks, respectively. The green and gray dashed lines represent graphene with $1 \mathrm {~eV}$ and $0 \mathrm {~eV}$ Fermi energy.
Figures 9(a) and 9(b) show the performance and electric field distributions of a double-stacked device. The subscripts A and B indicate the application of 1 eV Fermi energy to the lower and upper graphene nanoribbon arrays, respectively. In Fig. 9(b), the field enhancements of the $\mathrm {M}_\mathrm {A}$ modes are distributed between the lower graphene and gold layer, while the field enhancements of the $\mathrm {M}_\mathrm {B}$ modes are located between the upper graphene and gold layer. This implies that the double-stacked device is equivalent to the single-stack graphene-dielectric device discussed earlier, with an equivalent dielectric layer thickness of 20 nm and 40 nm for subscripts A and B respectively. Table 2 lists the absorption peak frequencies of the double-stacked device ($\mu =10000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$), which are found to be almost identical to the corresponding values in Table 1. This suggests that electrically switching the Fermi energy of graphene is equivalent to dielectric thickness variation. Under thermal-electrical dual modulation, the double-stacked device can be switched between four states, with the minimum frequency of $\mathrm {M}_1$ being 0.590 THz ($\mathrm {M}_\mathrm {A1}'$) and the maximum frequency of $\mathrm {M}_1$ being 1.060 THz ($\mathrm {M}_\mathrm {B1}$). Therefore, the relative frequency change of $\mathrm {M}_1$ can be calculated to be 44.3%. Similarly, the relative frequency change of $\mathrm {M}_2$ is 30%. These two values are considerably larger than the 22.6% and 5.4% frequency changes observed in the 40-nm-thick dielectric layer device with single thermal modulation in Table 1. This shows the advantage of thermal-electrical modulation.
Table 2. Thermal-electrical switching characteristics of double-stacked device.
A larger or smaller graphene mobility implies a larger or smaller relaxation time, which corresponds to a better or worse graphene crystal quality. Compared to graphene with a mobility of $10000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$, the absorption peak is wider when the graphene mobility is $5000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$, and the absorption peak is narrower with a larger Q factor when the graphene mobility is $20000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$. For sensor applications where a large Q factor is required, it is necessary to use high-quality graphene with higher mobility and longer relaxation time. The intensity of the absorption peaks also changes at different mobilities, but the frequencies of the absorption peaks are little affected.
The device’s switchable states can be increased by changing the double-stacked structure to three stacks. To enable easy comparison of device performance, a new layer of identical graphene nanoribbon array is inserted in the middle of the two layers of graphene nanoribbon array in the double-stacked device, as shown in Fig. 10(b). This creates a thickness of 10 nm, 10 nm, and 20 nm for the top, middle, and bottom dielectric layers respectively. Through electrical control, one graphene nanoribbon array is set to 1 eV Fermi energy, while the other two layers are set to 0 eV Fermi energy. Also, we add $20,000\mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ and $5,000\mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ graphene mobility in addition to $10,000\mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$ in our simulations for comparison.
Fig. 10. (a) Absorption spectra of the triple-stacked absorber when 1 eV Fermi energy level is applied to the lower, middle, and upper graphene layer, and when $\mathrm {VO}_2$ is in insulating and conducting states, respectively. The dashed, solid, and dotted lines represent the mobility of graphene at $5000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$, $10000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$, and $20000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$, respectively. (b) Schematic of device cross section when $\mathrm {VO}_2$ is in the insulating and conducting states, respectively, and z-component of the electric field in the region around graphene at frequencies of the 12 absorption peaks, respectively. The green and gray dashed lines represent graphene with $1 \mathrm {~eV}$ and $0 \mathrm {~eV}$ Fermi energy.
The six states of the device and the corresponding electric field distributions of absorption peaks are shown in Figs. 10(a) and 10(b) respectively. The subscripts a, b, and c denote applying 1 eV Fermi energy to the lower, middle, and upper graphene nanoribbon arrays respectively. As shown in Fig. 10(b), for the $\mathrm {M}_\mathrm {a}$ ($\mathrm {M}_\mathrm {a}'$), $\mathrm {M}_\mathrm {b}$ ($\mathrm {M}_\mathrm {b}'$), and $\mathrm {M}_\mathrm {c}$ ($\mathrm {M}_\mathrm {c}'$) modes, the electric field is mainly located between the lower, middle, or upper graphene and the gold layer, with equivalent dielectric layer thicknesses of 20 nm, 30 nm, and 40 nm, respectively. The absorption peak frequencies of the triple-stacked device are listed in Table 3. A comparison with Table 1 reveals that the corresponding frequencies are either equal or very close. Higher graphene mobility results in narrower absorption peaks, corresponding to higher Q factors.
Table 3. Thermal-electrical switching characteristics of triple-stacked device.
The triple-stacked device has an advantage over the double-stacked device since each mode can have six switchable states instead of four by thermal-electrical modulation, allowing finer tuning of frequency. By comparing Figs. 10(a), 9(a) and Fig. 7, some of the absorption peaks ($\mathrm {M}_\mathrm {a3}'$ and $\mathrm {M}_\mathrm {a4}'$ for example) show a certain amount of reduction compared to the 2-layer or single-layer devices. This is assumed to be caused by the graphene nanoribbons located above with a Fermi energy of 0 eV already reflecting a part of the incident light in advance. Therefore, although it’s possible to use more than 3-stacked device structures to obtain more device switching states in theory, the number of stacked layers should not be exceeded considering the absorption peak weakening with the increase of stacking number.
In this study, we also investigate how well single-, double-, and triple-stacked absorbers perform at different $\mathrm {VO}_2$ states when hit by THz waves at angles ranging from 0$^\circ$ to 85$^\circ$. The mobility of graphene is fixed at $10000 \mathrm {~cm}^2 \mathrm {V}^{-1} \mathrm {s}^{-1}$. As shown in Fig. 11, the absorbers work best when the angle of incidence is less than 70$^\circ$, with absorption peaks slightly blue-shift as the angle increased. Even at 70$^\circ$, the absorbers maintained high absorptivities. When the angle of incidence exceeds 70$^\circ$, the absorption peaks weakened significantly.
Fig. 11. Frequency-incidence angle absorption spectra of (a) single-layer absorber of insulating $\mathrm {VO}_2$, (b) single-layer absorber of metallic $\mathrm {VO}_2$, (c) double-stacked absorber of insulating $\mathrm {VO}_2$, (d) double-stacked absorber of metallic $\mathrm {VO}_2$, (e) triple-stacked absorber of insulating $\mathrm {VO}_2$, (f) triple-stacked absorber of metallic $\mathrm {VO}_2$. In (c), (d), (e) and (f), the 1 eV Fermi energy all apply to the upper graphene layer.
Taking the triple-stacked device as an example, considering that different bias voltages are to be applied to different layers of graphene nanoribbons in practical situations, we design the edges of the device as a kind of step-profile structure, as shown in Fig. 12. The three parallel gold electrodes are in contact with different layers of graphene nanoribbons, which can be set to different Fermi energies by setting different bias voltages between them and the back-covered gold layer.
Fig. 12. (a) Top view schematic of the triple-stacked device. (b) The cross-section schematic of the triple-stacked device at the dashed line and zoom-in schematic of bias voltages applying to different layers of graphene nanoribbons.
A possible fabrication procedure for the triple-stacked device is described as follows. (1) A layer of gold is sputtered on a silicon wafer. (2) A TOPAS layer is spin-coated on the gold layer. (3) A gold nanoribbon array is formed by photolithography, sputtering, and lift-off process. (4) $\mathrm {VO}_2$ is deposited using magnetron sputtering, then patterned and etched by photolithography and reactive ion etching. (5) Spin-coating of TOPAS layer. (6) Using wet transfer technology to transfer a graphene sheet on the TOPAS layer and using oxygen plasma and photolithography to define the graphene nanoribbon array. Then repeat steps (5) and (6) two times to form the triple-stacked structure. Finally, gold electrodes are formed using photolithography, sputtering, and lift-off technology.
A comparison of the performance of 5 multi-band THz absorbers proposed within the past year is presented in Table 4. Although different materials and structures are used to create multi-frequency THz absorbers, they all utilize graphene, whose Fermi energy can be electrically modulated. Most of the absorbers use the changing of graphene Fermi energy to tune the absorption peaks. Some studies also use temperature to switch $\mathrm {VO}_2$ states and tune device performance, but they tend to implement multi-band to broadband conversion. However, in our study, the state change of $\mathrm {VO}_2$ is used to modulate device performance such as absorption peak frequencies and Q factors. Our devices have the advantage of achieving more than 40% relative frequency change through thermal and electrical tuning, which is about 4 times larger than existing results. Our proposed absorber also has the best incidence angle robustness among these absorbers. Furthermore, unlike many multi-band THz absorbers with complicated structures, the absorber in our work has a relatively simple structure with more predictable performance.
Table 4. Comparison of absorption performance of some published multi-band THz absorbers within the past year.
4. Conclusions
We have proposed and examined a multi-band THz absorber that utilizes graphene nanoribbon array and $\mathrm {VO}_2$. With a Fermi energy of 1 eV applied to the graphene nanoribbon array, the absorber produces four absorption peaks in the THz band. One of these peaks originates from the LC resonance mode, while the remaining three come from the LFPR mode. By altering the width of the $\mathrm {VO}_2$ when it’s insulating at room temperature, we can split the three LFPR mode-originated absorption peaks, and the total peak number increases to seven. Additionally, when $\mathrm {VO}_2$ is conductive at a temperature of 358 K, by adjusting the width of $\mathrm {VO}_2$ from 100 nm to 1200 nm, we can significantly decrease the Q factor of the LC mode absorption peak from 7.2 to 2.8, while the remaining three LFPR mode-originated absorption peaks remain almost unaffected. We employ the equivalent RLC circuit model and related equations to investigate the performance of LC mode absorption peaks under different $\mathrm {VO}_2$ widths and states. The frequency of the LC mode absorption peak changes with dielectric thickness variation with a law proportional to the square root of thickness. The LFPR mode absorption peaks also undergo significant blue shifts with the increase of dielectric layer thickness. Through the design of double and triple stacking of graphene nanoribbon array-dielectric layers, the device can be thermally and electrically switched between four states and six states, respectively, with relative frequency changes of up to 44.3% for LC resonance-mode and up to 30% for LFPR-mode absorption peaks. The single-, double-, and triple-stacked devices all show promising multi-band absorption performance at incident angles as high as $70^\circ$, demonstrating good incident angle robustness. The thermal electrical switchable wide-angle multi-band THz absorber proposed in this paper provides a reference for the applications of THz absorbers in the fields of communication, imaging, detection, and so on.
Funding
National Natural Science Foundation of China (11664020, 61665004); Natural Science Foundation of Jiangxi Province (20202BABL201020); Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi (2024KY0874,2022KY0851).
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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