Active dual-tunable broadband absorber based on a hybrid graphene-vanadium dioxide metamaterial

Hui Li; Hui Li; Jiang Yu; Jiang Yu

doi:10.1364/OSAC.397243

1. Introduction

Metamaterial functional device, is an artificially engineered periodic nanostructure with the subwavelength scale unit cell. In the past decade, many researchers have been devoted to filling the “THz gap” due to great potential applications of THz functional devices [1–3]. Since then, THz functional devices have become one of the most attractive aspects of research in the modulator, biological imaging, spectroscopy, and so on [4–7]. Among all the applications, various kinds of absorbers are reported to achieve excellent absorption performance consists of single-band [8–9], multi-band [10–11], and broadband [12–14] since the perfect absorption theory is firstly proposed by Landy et al., in 2008 [8]. However, it is not easy for these traditional structures to change the working bandwidth and absorption intensity when the non-tunable materials are used. So, the tunable metamaterial absorbers emerge at a historic moment, it is a frequency (amplitude) modulator whose absorption performance can be adjusted by applying external stimuli [14–17]. One experimentally demonstrated pathway to achieve tunable property is to apply tunable materials to design, such as graphene [14–15], phase-change materials (PCMs) [16–17], and liquid crystal [11].

Among various tunable device in the THz range, graphene- or vanadium dioxide (VO₂)-based broadband metamaterial absorbers have attracted remarkable attention due to their active tunable (switchable), unique electromagnetic, and optical properties [18–22]. Huang et al., proposed a classical sandwich broadband THz absorber based on graphene, and the peak absorption can be tuned from 19% to 100% by changing the Fermi energy of graphene [23]. Zhang et al., designed a tunable and broadband metamaterial absorber in the mid-infrared region based on hybrid graphene-gold metasurface, and with the increase of graphene's Fermi energy, the resonance frequency of the absorber blue shifts [14]. Liu et al., reported a broadband tunable metamaterial absorber, based on the unique transition character of VO₂, the maximum tunable range of the proposed absorber can be realized from 5% to 100% by an external thermal excitation [24]. Furthermore, by applying both graphene and VO₂ materials in a simple sandwich structure, the tunable performance of the device can be further improved. Wang et al., propose a dual-controlled switchable broadband terahertz absorber based on a hybrid of VO₂ and graphene, using these two independent controls in tandem, it found that the state of the proposed absorber can be switched from absorption to reflection [18]. Zhang et al., proposed a terahertz bifunctional absorber is presented with broadband and narrowband absorbing properties based on hybrid graphene-VO₂ metamaterial [19]. Previous studies indicate that both graphene and VO2 materials can be used to design tunable terahertz metamaterial functional devices. But so far, there is no simple sandwich structure that can simultaneously achieve the characteristics of tunable in both absorption intensity and frequency, which is a huge challenge for researchers.

In this paper, we proposed an exquisite polarization-insensitive broadband terahertz absorber that can achieve an active tunable property in both magnitude and frequency on a simple sandwich structure. Consists of the perfect absorption peaks of the device can be tuned by adjusting the Fermi energy of graphene, which blue-shift 1.18 THz from 0.1 eV to 0.6 eV. By using external stimuli to change the conductivity of the VO₂, the absorptance of the corresponding absorption spectrum can be continuously adjusted from 28% to 99%. An excellent absorption performance over a wide range of incident angles up to 70° in the terahertz regime. It indicates that the proposed structure is beneficial to a new design method for high-performance terahertz devices.

Indeed, our results are better indicated in the recent work based on dual-control systems, both Ref. [18] and Ref. [25] have studied the polarization-dependent sandwich structure with dual-control characteristics at the THz range. When it is in the perfect broadband absorption state, the amplitude (perfect absorption peaks) of the absorption spectrum can be tuned by changing the chemical potential of graphene (Dirac semimetal) or the conductivity of VO₂. Although these works presented dual-control of the absorptance, however, our designed simple structure achieves a widened range of dynamically tunable property in both of amplitude and frequency in the THz range, simultaneously. Meanwhile, the absorber of our report shows the strong incident angle insensitive property and indicates practical operability.

2. Structure and methods

The schematic of the proposed broadband absorber based on hybrid graphene-VO2 metamaterials is given in Fig. 1. The absorber is composed of a symmetric E-shaped resonator array on top of a continuous monolayer graphene sheet, which is supported by a dielectric spacer backed with a reflective mirror. At the designed system, unlike most traditional metamaterial absorbers, both of the symmetric C-shaped resonator array and bottom reflective film use a common phase change material of VO₂. By controlling the insulator-to-metal transition (IMT) of VO₂, we can achieve the proposed structure to function as a unity-broadband THz metamaterial absorber. Besides, both of the thickness of the top VO₂ resonator array and ground plane are optimized as $t = 0.3\; \mu m$, it can be easily manufactured by molecular beam epitaxy in practical application [26,27]. Here, the dielectric spacer is defined as ToPaS with a complex electric permittivity ${\varepsilon _s} = 2.35\, + \,0.01i$ [23] and a thickness of ${t_s} = 20\; \mu m$. The structural dimensions of the proposed absorber are listed as follows: $P = 50\; \mu m,\; {t_1} = 2\; \mu m,\; L = 30\; \mu m,\; G = 5\; \mu m,$ and $W = 2\; \mu m$.

Fig. 1. Schematic of the unit cell of the proposed broadband absorber.

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Indeed, VO₂ has been studied for different applications based on its metal-insulator phase transition at ∼68°C [27]. Since metallic VO₂ has a high free carrier concentration, it can achieve a significant modulation depth in application [28]. Moreover, in the insulated state, it is highly transparent to electromagnetic waves below 6.7 THz [29]. The optical properties of VO₂ in the THz range can be modeled by the Drude model [18–21]

(1)$$\varepsilon (\omega )\textrm{ = }{\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + j\gamma \omega }}$$

where ${\varepsilon _\infty } = 12\; $is the dielectric permittivity at the infinite frequency, $\varepsilon (\omega )$ is defined as the permittivity at high frequency, $\gamma = 5.75 \times {10^{13}}\; rad/s\; $is the collision frequency. The plasma frequency ${\omega _p}$ can be approximately defined as $\omega _p^2 = \frac{{\sigma ({V{O_2}} )}}{{{\sigma _0}}}\omega _p^2({{\sigma_0}} )$, where ${\sigma _0} = 3 \times {10^5}\; S/m$ and ${\omega _p}({{\sigma_0}} )= 1.4 \times {10^{15}}\; S/m\; $[28]. During the IMT process, the conductivity of VO₂ can be transformed via five orders of magnitude. In the calculation process, we can apply different permittivity to describe the different phase state of VO₂, such as the conductivity of VO₂ is $2 \times {10^5}\; S/m$ is taken to describe the metal phase and $10\; S/m$ to describe the insulator phase.

In addition, the monolayer CVD graphene is molded as an equivalent 2D surface impedance layer and without thickness [26,30]. From the range of terahertz to optical frequency, the graphene’s surface conductivity ${\sigma _g}(\omega )$ can be described as ${\sigma _g}(\omega )= {\sigma _{inter}}(\omega )+ {\sigma _{intra}}(\omega )$, which consists of intra-band ${\sigma _{intra}}(\omega )$ and inter-band ${\sigma _{inter}}(\omega )$ contributions from the Kubo formula, respectively. However, according to the Pauli exclusion principle, the inter-band contribution is negligible compared to the intra-band part as the photon energy $\hbar \omega \ll {E_f}$ and ${k_B}T \ll {E_f}$ in the THz range [23]. Therefore, the surface conductivity of graphene can be simplified to ${\sigma _g}(\omega )= {\sigma _{intra}}(\omega )$ and the intra-band ${\sigma _{intra}}(\omega )$ can be defined as [31–32]:

(2)$${\sigma _{{\mathop{\rm int}} ra}}({\omega ,{E_f},\Gamma ,{\rm T}} )= j\frac{{{e^2}}}{{\pi {\hbar ^2}({\omega - j2\Gamma } )}}\int_0^\infty {\eta \left( {\frac{{\partial {f_d}({\eta ,{E_f},{\rm T}} )}}{{\partial \eta }} - \frac{{\partial {f_d}({ - \eta ,{E_f},{\rm T}} )}}{{\partial \eta }}} \right)d\eta } $$

where ${f_d}({\eta ,{E_f},T} )= {({{e^{({\eta - {E_f}} )/{k_B}T}} + 1} )^{ - 1}}$, ${E_f}$ is the Fermi energy (chemical potential) of graphene, $\mathrm{\Gamma} = 1/({2\tau } )$ is the phenomenological scattering rate and $\tau = \mu {E_f}/({ev_F^2} )$ is the relaxation time, relating to the carrier mobility $\mu = {10^4}\; c{m^2}{V^{ - 1}}{s^{ - 1}}$ and Fermi velocity ${v_F} \approx 1.1 \times {10^6}\; m/s$, $\omega $ is the radian frequency of the incident wave, ${k_B}$ is the Boltzmann constant, $\hbar $ is the reduced Planck’s constant and $\hbar = h/({2\pi } )$, e is the charge of an electron, and $T = 300\; K$ is the Kelvin temperature. Besides, the complex surface impedance of monolayer graphene can be described by ${Z_G}(\omega )= 1/{\sigma _G}(\omega )$ [33]. According to the equation above, the surface conductivity of graphene can be continuously adjusted by changing the Fermi energy of graphene. Here, the Fermi energy of graphene sheet can be controlled by Ion-gel top gating method [34]. In this work, the numerical simulation results can be obtained by the frequency domain finite element method (FEM) solver of the CST Microwave Studio, and the adaptive mesh refinement are used to improve the accuracy of numerical simulation. Moreover, unit cell boundary conditions are assigned along both the x-direction and y-direction while open boundary condition is assigned along the z-direction of the proposed absorber. Meanwhile, using the S parameters in the calculation, the absorbance $A(\omega )$ can be obtained by $\; A(\omega )= 1 - R(\omega )- T(\omega )= 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2}$, where $R(\omega )= {|{{S_{11}}} |^2}$ and $T(\omega )= {|{{S_{21}}} |^2}$ are defined as transmittance and reflectance, respectively.

3. Results and discussions

When the Fermi energy of graphene is set to 0.1 eV and the VO₂ was in a fully metallic state with conductivity of 200000 S/m, the designed system can realize broadband absorption. The absorption, reflection and transmission spectrums for the transverse-electric (TE) polarization under normal incidence are given in Fig. 1(a). There is most distinctive broad absorption spectrum, and the bandwidth with absorptance over 90% are starting from 1.7 THz to 3.4 THz. Also, it can be found that there are also two near-unity absorption peaks located at ${f_1}$=2.3 THz and ${f_2}$=3.2 THz, respectively. To further reveal the working mechanism for the proposed device, the impedance matching theory is introduced. Therefore, the absorptance and the relative impedance can be defined as [35,36]:

(3)$${Z_r} = \sqrt {\frac{{{{({1 + {S_{11}}(\omega )} )}^2} - {S_{\textrm{21}}}{{(\omega )}^\textrm{2}}}}{{{{({1 - {S_{11}}(\omega )} )}^2} - {S_{\textrm{21}}}{{(\omega )}^\textrm{2}}}}} $$

(4)$$A(\omega )= 1 - R(\omega )= 1 - {\left|{\frac{{Z - {Z_0}}}{{Z + {Z_0}}}} \right|^2} = 1 - {\left|{\frac{{{Z_r} - 1}}{{{Z_r} + 1}}} \right|^2}$$

where Z and ${Z_0}$ are the effective impedances of the proposed absorber and the free space, respectively. ${S_{11}}$ and ${S_{21}}$ are denoted as transmission coefficient and reflection coefficient. The real and imaginary parts of the relative impedance of the proposed device are displayed in Fig. 2(a), it can be seen that the real part is close to 1, and the imaginary part is close to 0 in the corresponding broad absorption spectrum. This phenomenon indicate that the impedance of the proposed absorber matches with that of the free space. Besides, as no incident light can transmit the absorber due to the metal-phase VO₂ film is on the bottom. Therefore, the incident THz lights can be absorbed to the maximum extent and it leads to high absorptance.

Fig. 2. (a) Reflection, transmission and absorption spectra of the proposed broadband absorber. (b) The relative impedance of the absorber.

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To better grasp the absorption mechanism in the whole broadband absorption spectrum, as shown in Fig. 3, we monitor the electric field distribution for different resonance frequencies. It can be seen that the absorptance at 0.1 THz is only 1%, it means that there is almost no electric field distribution of the device, indicating that the absorber does not interact with the incident waves. As shown in Fig. 3(a), when the frequency shift to 0.6 THz, the corresponding absorptance is varied to about 18%. It seems like a weak resonant response is generated in the symmetric C-shaped metasurface and the electric field is coupled at both corners of the arms. Next, we have monitored the electric field distributions at the strong resonance frequencies of 1.5 THz, and 2.3 THz with the absorptance above 80%, respectively. From Figs. 3(a) and 3(b), the electric energy is strongly concentrated on the whole surface of the symmetric C-shaped array, and a strong electric energy is concentrated on the interface between the dielectric and the graphene sheet. It means that the graphene surface plasmon resonances (SPR) can also enhance the absorption performance. In contrast, when the resonance frequency shifts to 3.2 THz and 3.7 THz, the coupled electric field intensity is gradually reduced, as shown in Fig. 3(a), we can obtain that the resonant response gradually disappears and the absorptance decreased. Indeed, it can be seen from Fig. 3(b) that the local magnetic resonance is caused by the coupling between the adjacent unit lattice and the metal phase grounding plane so that the electric field distribution presents a typical high-order mode. From the side view of the absorber, as the frequency increases, it can be seen that the inside electric field distribution has a tendency to strengthen. However, the power loss of electromagnetic energy in the top graphene layer gradually increases with the increasing frequency according to Ref. [14], so the absorptance will decline.

Fig. 3. (a) Physical mechanism of broadband absorption. (b) Electric field distributions of the C-shaped metasurface in the proposed absorber at different resonance frequencies.

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The surface conductivity of the graphene sheet layer can be dynamically tuned by varying its Fermi energy from 0.1 eV to 0.6 eV, thus leading to a blue-shift on the absorption spectra. The resultant frequency shift can be defined as [14,37]

(5)$$\Delta \omega \textrm{ = }({{\mathop{\rm Im}\nolimits} ({{\sigma_G}(\omega )} )- j{\rm{Re}} ({{\sigma_G}(\omega )} )} )\frac{{\int_S {{{|{{E_{xy}}} |}^2}dS} }}{{{W_0}}}$$

where ${\sigma _g}(\omega )$ is the surface conductivity of graphene, S denotes graphene sheet area of the absorber, ${E_{xy}}$ is the electric field in the plane of graphene, ${W_0}$ is the stored electromagnetic energy in an uncovered metamaterial resonator of symmetric C-shaped. Besides, $Re({{\sigma_g}(\omega )} )$ and $Im({{\sigma_g}(\omega )} )$ defined as the real and imaginary part of a complex value of surface conductivity of graphene, respectively. In fact, When the graphene layer is placed in the vicinity of the symmetric C-shaped VO₂ resonator, it will influence the performance of the resonator [14]. According to Eq. (6), by adjusting the surface conductivity of the graphene, the absorption performance can be dynamically controlled. As shown in Fig. 4(a), the broad absorption spectra occur blue-shift when the Fermi energy varies from 0.1 eV to 0.6 eV. In addition, with the Fermi energy of graphene increases, the perfect absorption peaks can be dynamically tuned, while the bandwidth with the absorptance above 90% gradually decreases. On the other hand, as shown in Fig. 6(b), the bandwidth of the absorption spectrum still keeps more than 0.9 THz when the Fermi energy of graphene shift to 0.6 eV. It can be explained by the impedance matching theory. In fact, the effective impedance Z of the proposed absorber is determined by the effective permittivity of $\varepsilon (\omega )$ and permeability of $\; \mu (\omega )$. Different coupling mode effects between the top layer of a hybrid graphene- VO₂ metasuface and metal-phase ground plane, and lead to the variation of the permeability of $\mu (\omega )$ when the surface conductivity of graphene changes. According to the equation of $Z = \sqrt {\mu (\omega )/\varepsilon (\omega )} $ [15] and ${Z_r} = Z/{Z_0}$, the excellent impedance matching between the proposed absorber and the free space will be destroy, which obtains the different absorption spectrum.

Fig. 4. (a) Absorption spectra, (c) color map with different graphene Fermi energies ranging from 0.1 eV to 0.6 eV and (b) The function between Fermi energy and the resonance frequency of perfect absorption peaks. When the conductivity of VO₂ is set to 200000S/m.

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Next, Fig. 5(c) depict the absorption spectrums of the proposed absorber with different conductivities of VO₂ at perfect absorption of 2.3 THz when the Fermi energy of graphene is set to 0.1 eV. It is clear that with the conductivity of VO₂ increases from 10 S/m to 200000 S/m, the corresponding absorptance dynamically adjusted from 28% to 99% for the broad absorption band of 1.7 THz to 3.4 THz. It means that we can continuously modulate the amplitude on the absorption spectrum. On the other hand, as shown in Figs. 5(d) and 5(e), according to the side view of the electric field distributions, When the VO₂ is in the metallic state, a strong electric field is mainly concentrated on the interface between the dielectric spacer and the hybrid metasurface. It indicates that the graphene plasmon resonances can enhance the absorption performance, while the electric field distributions are quickly decreased to zero when VO₂ is in the insulating state. Furthermore, the variation of permittivity of VO₂ mainly decides the relevant physical mechanism of the continuous modulation of amplitude. Specifically, we can see that the real parts under different conductivities of VO₂ are much smaller and almost unchanged than that of imaginary parts, as the Figs. 5(a) and 5(b) shows, the real and imaginary parts of the permittivity of VO₂. It means that the real parts of the permittivity mainly decide the resonance frequency; however, the imaginary parts mainly decide the loss of amplitude. Therefore, the positions of two broad bands almost unchanged, while the intensity of the absorption spectra varies significantly from the proposed absorber.

Fig. 5. The (a) real parts and (b) imaginary parts of permittivity with different conductivity of VO₂. (c) Absorption spectrum of the proposed absorber with different conductivity of VO₂. (d) and (e) Side view of electric field distribution at 2.3THz. When the Fermi energy of graphene is set to 0.1 eV.

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When we changed the conductivity of VO2 in both top and bottom layers simultaneously, we introduced the impedance matching theory to clarify the internal mechanism. As shown in Fig. 6, the real and imaginary parts of the relative impedance ${Z_r}$ under different conductivity of VO₂. One can clearly see that the real part gradually approaches to 1, while the imaginary part gradually approaches to 0 with the dynamically increase conductivity of VO₂, in the broadband frequency range of 1.7 THz to 3.4 THz. It means that the impedance between the proposed absorber and the free space gradually matches when the IMT properties occurs from VO₂ of the bottom layer. Therefore, a high modulating intensity is obtained.

Fig. 6. The (a) real parts and (b) imaginary parts of the relative impedance Z_r with different conductivity of VO₂ when the Fermi energy of the graphene is set to 0.1 eV.

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To demonstrate the absorptance of the absorber can achieve an active tunability of wide range with the control of the special VO₂ phase change material. From Figs. 7(a)–7(f), we further monitor the electric field distribution for the heating process with different conductivity of the VO₂ at the perfect absorption of 2.3 THz. It can be seen that there is almost no electric field distribution of the symmetric C-shaped array at the conductivity $\sigma ({V{O_2} = 10\; S/m} )$. It means that the incident THz waves completely penetrate the proposed structure due to the insulation properties of VO₂. Therefore, one can clearly see that as the VO₂ material is gradually transformed from the insulation-phase to full metal-phase under normal incidence, the electric field distributions are mainly concentrated on the concerns of the symmetric C-shaped VO₂ arms and gradually diffused to the whole and the cross area of the arm, when the conductivity of VO₂ raise from 100 S/m to 200000 S/m. The reflection of the symmetric C-shaped resonant structure and the metal-phase VO₂ reflective plane are enhanced synchronously, which causes an intense increase in the absorptance. Besides, it can be seen that the electric field distributions are almost the same in both $\sigma ({V{O_2} = 40000\; S/m} )$ and $\sigma ({V{O_2} = 200000\; S/m} )$. Due to the VO₂ material is completely transformed into its metal-phase, thus the resonant induced by the symmetric C-shaped VO₂ structure will not be further changed with the increasing conductivity. Therefore, the proposed structure can achieve the alternation between the full transmission and the broadband absorption in the THz region based on external stimuli.

Fig. 7. (a-f) Top view of the electric field distribution corresponding to the perfect absorption at 2.3 THz of the proposed absorber for the heating process at different conductivity of VO₂.

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To further evaluate the importance geometrical parameters of the effect on performance, we also investigated the absorption spectra with different geometric parameters under normal incidence, keeping other structural parameters unchanged of the unit cell. As shown in Fig. 8(a), where the influence of the absorptance on the width W is simulated. One can clearly see that with the increasing width W from 2 μm to 14 μm, the broad absorption spectra is disappeared and gradually splits into two narrow bands. As shown in Fig. 8(b), The influence of the length of arm L on absorption performance is also investigated. It can be seen that the absorption spectrum is broadened gradually and the absorptance is also enhanced when the arm length changing from 20 μm to 30 μm. The symmetric C-shaped resonant properties are mainly thanks to the electric field coupled to the arms. On the other hand, it can be explained by the impedance matching theory. The excellent impedance matching between the absorber and free space is broken with the arm length decreasing. Besides, as shown in Fig. 8(c), it can be seen that the absorption curves of different gap width are perfectly coincident. To better understand the physical mechanism of the absorption spectrum, the results of analyzing the electric field distributions of the gap width of G fixed at 2 μm, 5 μm, and 8 μm, respectively at the resonance frequency of 2.3 THz are displayed in Fig. 8(d). Although the gap width of G has changed, the graphene surface plasmon resonance is stably excited, which is the key to keep the absorption performance stable. Therefore, this may have great operability in practical applications.

Fig. 8. Effects of the unit cell on broadband absorption performance. (a) with different arm widths of W, (b) with different arm lengths of L, and (c) with different gap widths of G. (d) Electric field distributions corresponding to the perfect absorption frequencies of 2.3 THz.

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When VO₂ is in the metallic state, it is indispensable to explain the main contribution to THz absorption performance of each part in the designed sandwich structure. So, the influences of dielectric loss (tagδ=0.1) in the middle spacer on absorption performance are investigated. As we can see from Fig. 9(a), it confirms that there is no evident change in the broad absorption spectrum, the dielectrics have a limited influence on the THz absorption. The insensitivity of dielectric spacers in the proposed absorber can be property applicable in many areas due to the existence deviation in practical fabricate, such as tunable modulators [36]. As shown in Fig. 9(b), one can clearly see that the achieved maximum absorption without VO2 film dielectric in the corresponding spectrum is only 28%, much smaller than that with the VO2 plane. Besides, from Fig. 9(c), absorbers based on the single C-shaped resonator are also studied. It can be seen that the two broad absorption bands are perfectly coincident due to the symmetry of the proposed device. In addition, although both of the two absorbers based on a single C-shaped resonator exhibit limited absorptance and the narrow spectrum bandwidth. However, it can be seen that absorbers based on the symmetric C-shaped can enhance the resonant and lead to strong broad absorption. Indeed, we purposely utilize the coupling effect between the two C-shaped resonant to achieve the excellent performance of the absorber. Then, we consider the effect of the proposed absorber with and without symmetric C-shaped VO2 resonant structures on the absorption performance. We found that the addition of the symmetric C-shaped resonance structure on the proposed absorber can enhance the absorptance and effectively expands the impedance matching bandwidth from the Fig. 9(d). Thus, based on the previous analysis, it can be confirmed that the energy of incident THz waves is mainly concentrated on the hybrid symmetric C-shaped VO2 resonance metasurface.

Fig. 9. Effects of the unit cell on broadband absorption performance. (a) With loss or loss-free dielectric layers, (b) with and without metal-phase VO₂ mirror, (c) with single or double C-shaped structure, and (d) with and without C-shaped structure.

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As shown in Fig. 10(a), it is obvious that the absorption curves under different polarization angles have completely coincided when the bottom layer in metal-phase, which indicates that the proposed absorber could work well with different polarization modes. Indeed, the symmetric unit cell is the inherent reason for the perfect polarization-independent. On the other hand, the incident electric energy is stably excited, which is the key to keep the absorptance stable are displayed in Figs. 10(b)–10(e).

Fig. 10. (a) Absorption spectra of the absorber when utilized different polarization angles. (b-e) The results of the electric field distributions at 2.3 THz for θ = 0°, 15°, 30°, and 45°.

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The influences of different incident angles on the absorption performance in both the TE and TM modes are also investigated in Fig. 11. For TE polarization, the broad absorption band exhibit excellent absorption performance with incidence angles vary from 0° to 80°. The absorption peaks remain more than 80% until the incident angle exceeds 70°. It is found that the absorption frequency range is almost constant as the incident angle increases for the absorption spectrum and some parasitic resonances that occurred at the larger incident angle from the Fig. 11(a) [18]. For TM polarization, the results are similar to TE mode apart from that the absorption peaks split to two for large incidence angles and there is a slightly blue-shift for the absorption spectrum are displayed in Fig. 11(b). In addition, both of the two absorptances peaks decrease significantly as the incident angle is further increased up to 75°. On the other hand, the propagation constant ${k_z}$ along z-direction is molded by ${k_z} = {k_p}({1 - si{n^2}\xi } )$ [38,39], where ${k_p}$ is the wave number in dielectric layer. We can find that the phase-matching condition is not satisfied on the graphene surface since ${k_z}$ increases with the incident angel, it means that the excellent impedance matching is destroyed, which will weaken the absorption performance for the proposed absorber.

Fig. 11. Absorption contour map of the absorber as a function of incidence angles and frequency under oblique incident angles (a) for the TE mode, and (b) for the TM mode when the graphene’s Fermi energy E_f= 0.1 eV and VO₂ conductivity σ(VO₂) = 200000 S/m.

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4. Conclusion

In the conclusion, we proposed and demonstrated an active tunable broadband metamaterial absorber based on hybrid graphene-vanadium dioxide, polarization-insensitive properties are achieved in the absorber. The broadband absorption of the absorber maintains excellent absorption performance over a wide range of incident angles up to 80°. Apparently, by applying an external bias voltage to adjust the Fermi energy of graphene, the perfect absorption peaks frequency of the absorber occurs blue shifts, which shift 1.18 THz from 0.1 eV to 0.6 eV. Numerical simulation results indicate that the absorptance of the proposed absorber can be dynamically adjusted from 28% to 99% for the broad absorption band of 1.7 THz to 3.4 THz by adjusting the conductivity of the VO₂ due to its unique IMT properties. The impedance matching theory is introduced to explain the inherent physical mechanism. Thus, we can achieve the tunable property in both frequency and amplitude through an external stimulus on a simple structure. Following the electric field distribution can explain the absorption mechanism of the absorber. Therefore, we present a new design method for high-performance terahertz devices.

Funding

National Natural Science Foundation of China (61162004).

Acknowledgments

Thanks, due to Wenhui Xu for valuable discussion.

Disclosures

The authors declare no conflicts of interest.

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Active dual-tunable broadband absorber based on a hybrid graphene-vanadium dioxide metamaterial

Abstract

1. Introduction

2. Structure and methods

3. Results and discussions

4. Conclusion

Funding

Acknowledgments

Disclosures

References

Cited By

Figures (11)

Equations (5)

OSA Continuum