Abstract

In this paper, we propose a terahertz bifunctional absorber with broadband and dual-band absorbing properties based on a hybrid graphene-vanadium dioxide (VO2) metamaterial configuration. When VO2 is in the insulating state and the Fermi energy of graphene is set to 0.8 eV, the designed device behaves as a tunable perfect dual-band absorber. The operating bandwidth and magnitude of the dual-band spectrum can be continuously adjusted by changing the Fermi energy of graphene. When VO2 is changed from insulator to metal, the designed system can be regarded as a broadband absorber, it has a broad absorption band in the range of 1.45-4.37 THz, and the corresponding absorptance is more than 90%. The simulation results indicate that the absorptance can be dynamically changed from 17% to 99% by adjusting the conductivity of the VO2 when the Fermi energy of graphene is fixed at 0.01 eV. Besides, both dual absorption spectrum and broad absorption spectrum maintain a strong polarization-independent characteristic and operate well at wide incident angles. Furthermore, we have introduced the interference theory to explain the physical mechanism of the absorption from an optical method. Therefore, our designed system can be applied in many promising fields like cloaking and switch.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Metamaterials, an artificially engineered periodic nanostructure with extraordinary electromagnetic properties, could have some special and broad applications in different regions [1,2]. In recent years, the metamaterial tunable THz device has become one of the most attractive aspects due to its promising applications in some fields, such as the modulator, biological imaging, and spectroscopy [36]. Among all the applications of metamaterials, the tunable metamaterial absorbers have aroused wide concern since Landy et al. reported a single-band perfect structure in 2008 [7]. Furthermore, various kind of absorbers, such as single-band [8], multi-band [9,10], and broadband [11,12] absorbers, are proposed by researchers to realize excellent absorption performance. However, the single-performance tunable absorber can no longer meet the requests in practical application, therefore, the flexible and intelligent tunable metamaterial device is more attractive for many systems.

Due to their unique electromagnetic, and optical properties of graphene and vanadium dioxide (VO2) materials, making them considered to be a new pathway for designing tunable and switchable material absorber [1124]. Compared to other new materials, graphene is a two-dimensional crystal composed of a monolayer of carbon atoms arranged in a honeycomb lattice, and the surface conductivity of graphene can be continuously adjusted by chemical doping or applying an external bias voltage [1113]. Meanwhile, VO2 is an ideal choice for controlling devices, which can realize the reversible phase transition from insulator to metal by thermal, electrical or optical methods and lead to a dramatic change in dielectric function and optical properties, so that the absorber combined with VO2 has a wide dynamic range and high modulation depth for THz waves [1416]. To achieve excellent absorption performance, Song et al. reported a multilayer absorber with switchable functionalities based on phase-transition property of VO2, the result showed that structure be switched from a broadband absorber to a narrowband absorber [17]. Chen et al. by introducing VO2 film into a multilayer structure, the designed system can be switched from an absorber to a transparent conducting metal [18]. Wang et al. proposed a dual-controlled switchable broadband terahertz absorber based on a hybrid of VO2 and graphene, by changing the conductivity of VO2 and the Fermi energy of graphene simultaneously, it found that the state of the proposed absorber can be switched from absorption to reflection [24]. Previous works indicate that the graphene and VO2 are both hopeful choices for achieving dynamically tunable or switchable absorber in the THz range. In fact, a great challenge today is to design new structures where the change in optical properties can lead to more flexible and intelligent response.

In this paper, we propose an exquisite polarization-insensitive THz bifunctional device with excellent absorption performance over a wide range of incident angles based on hybrid graphene-VO2 metamaterial. Moreover, by controlling these two independent parameters (the conductivity of VO2 and the Fermi energy of graphene) reasonably, we can achieve the switchable and tunable property in both broadband and dual-band on the proposed multilayer structure. Besides, we can use the interference theory to explain the physical mechanism of the perfect absorption. The results indicate a new method for designing high-performance terahertz devices, such as modulator, thermal emitter, and photovoltaics device.

2. Design and methods

The schematic of the proposed absorber based on hybrid graphene-VO2 metamaterials is given in Fig. 1. Apparently, the structure consists of six layers, from top to bottom, they are E-shaped VO2 resonator array, ToPaS dielectric spacer, VO2 film, monolayer graphene sheet, SiO2 dielectric layer and fully metallic reflective layer. By controlling the property of insulator-to-metal transition (IMT) of VO2, we are able to switch the structure between a unity-broadband absorber and a perfect dual-band absorber. When the VO2 is in the fully metallic state, the thickness of the middle VO2 reflective film is selected as $t2 = 1\; \mu m$, which is larger than skin depth in the THz region [16]. Besides, the complex electric permittivity of ToPaS dielectric spacer (thickness $t = 15\; \mu m$) is $\varepsilon = 2.35 + 0.01i$ [25]. Meanwhile, the lower dielectric layer is 38-µm-thick SiO2 with the permittivity ${\varepsilon _s} = 3.8$ [26]. The structure dimensions of the proposed absorber by careful design are listed as follows: $P = 50\; \mu m,\; t1 = 2\; \mu m,\; R1 = 40\; \mu m,\; R2 = 38\; \mu m,\; tm = 0.5\; \mu m,\; G = 2\; \mu m$ and $W = 1\; \mu m$.

 figure: Fig. 1.

Fig. 1. The schematic of the unit cell of the proposed absorber consists of perspective, top, and side view.

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In the numerical simulation, VO2 films undergo a IMT process at a critical temperature around 68°C [27]. Since metallic VO2 has a high free carrier concentration, it can achieve a significant modulation depth in application [28]. Moreover, the insulator-state VO2 is highly transparent to electromagnetic waves below 6.7 THz [29]. The optical permittivity of VO2 in the THz range can be described by the Drude model [1619]

$$\varepsilon (\omega )= {\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + j\gamma \omega}}$$
where the ${\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. And 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.

Meanwhile, in the modeled process, the thickness of the graphene film (${t_g}$) is assumed to be a typical value of 1 nm. The monolayer graphene sheet is molded as an equivalent 2D surface impedance layer and without thickness in this paper, and it was built from a closed planar square curve extruding to a surface. [30,31]. 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 in the case of the photon energy $\hbar \omega \ll {E_f}$ and ${k_B}T \ll {E_f}$ in the low THz region. 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 [30,31]

$${\sigma _{intra}}(\omega )= j\frac{{{e^2}}}{{\pi {\hbar ^2}({\omega - j2\mathrm{\Gamma}} )}}\mathop \smallint \nolimits_0^\infty \eta \left( {\frac{{\partial {f_d}({\eta ,{E_f},T} )}}{{\partial \eta }} - \frac{{\partial {f_d}({ - \eta ,{E_f},T} )}}{{\partial \eta }}} \right)d\eta $$
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 ${Z_G}(\omega )= 1/{\sigma _G}(\omega )$ [31]. 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 is used to improve the accuracy of 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 0.01 eV and the VO2 was in a fully metallic state with conductivity of 200000 S/m, the designed system can realize broadband absorption. As shown in Fig. 2(a), there are most distinctive broad absorption band, and the bandwidth with absorptance over 90% are as wide as 2.92 THz. Besides, it is obvious that there are also two near-unity absorption peaks located at ${f_1} = 2.45$ THz and ${f_1} = 3.88$ THz, respectively. Additionally, the magnitude of the corresponding broad absorption spectrum can be continuous adjusted by a thermal control system to prompt the IMT property of VO2. It is clear that with the conductivity of VO2 changes from 10 S/m to 200000 S/m, the corresponding absorptance is adjusted from 17% to 90% for the absorption spectrum of 1.45 THz to 4.37 THz. Compared with the device when the VO2 in the insulating state, the proposed device at 2.45 THz obtains almost 9 times absorptance enhancement. It means that we can regard the proposed structure as an amplitude modulator, and we can independently set the sensitivity of the absorber to the incident wave. On the other hand, When VO2 is in the metallic state, only the upper three-layer structure realizes the absorbing properties, while the lower graphene sheet-dielectric-gold structure does not work. So, as shown in Fig. 2(c), when the Fermi energy of graphene raised from 0.2 eV to 0.8 eV, the absorption curves of the device are perfectly coincident.

 figure: Fig. 2.

Fig. 2. (a) Absorption spectrum of the proposed absorber with different phase of VO2. (b) The real and imaginary parts of the relative impedance of the absorber. (c) Absorption curves of the device with different Fermi energies. When VO2 is in the metal phase.

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To further understand the inherent mechanism of the proposed structure, the impedance matching theory is introduced. Therefore, the absorptance and the relative impedance can be defined as [32,33]:

$$A(\omega )= 1 - R(\omega )= 1 - {\left|{\frac{{Z - {Z_0}}}{{Z + {Z_0}}}} \right|^2} = 1 - {\left|{\frac{{{Z_r} - 1}}{{{Z_r} + 1}}} \right|^2}$$
$${Z_r} ={\pm} \sqrt {\frac{{{{({1 + {S_{11}}} )}^2} - S_{21}^2}}{{{{({1 - {S_{11}}} )}^2} - S_{21}^2}}}$$
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 absorber are displayed in Fig. 2(b). One can clearly see that the real part is close to 1, and the imaginary part is close to 0 in the corresponding broad absorption spectrum, which means the impedance of the proposed absorber matches with that of the free space. So far, the structure can be simplified as a VO2 resonator-dielectric-VO2 reflective layer, as no incident light can transmit the proposed absorber due to the metal-phase VO2 film is on the middle. It means that the transmittance of the structure is almost zero and the incident wave can be absorbed to the maximum extent.

To better grasp the absorption mechanism in the perfect absorption, we monitor the electric field distribution at 2.45 THz and 3.88 THz. As shown in Fig. 3(a) and Fig. 3(b), from the top view of the absorber, it is obvious that the electric field is mainly concentrated on both ends of the E-shaped VO2 array at the resonance frequency of 2.45 THz. Since the frequency shifts to 3.33 THz, the electric field is not only concentrated on both ends of E-shaped VO2 array but also strongly concentrated on its arm gaps. In addition, from the side view of the absorber, the electric field is mainly compressed into the upper of the structure when the middle VO2 reflective layer was in a fully metallic state. As shown in Fig. 3(c), one can clearly see that a strong electric field is concentrated on the interface between the ToPaS spacer and the fully metal-phase VO2 resonator, which means that the surface plasmon resonances (SPR) can also enhance the absorptance of the absorber [27,33]. Besides, it can be seen from Fig. 3(d) that there exists a classical magnetic resonance absorption mechanism between the top E-shaped VO2 resonator and middle VO2 reflective film [8,30].

 figure: Fig. 3.

Fig. 3. The electric field distribution of the proposed absorber at different perfect resonance frequencies (a-b) Top view; (c-d) Side view when the conductivity of VO2 is set to 200000S/m.

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In this study, we introduced the interference theory to better understand the physical mechanism of the proposed absorber when the VO2 material is in metal phase. As shown in Fig. 4(c), a modified asymmetric Fabry-Perot resonant model is displayed to indicates the incident wave multi-reflection process inside the ToPaS dielectric layer. In the calculation process, ${r_{23}} ={-} 1$, there was no incident wave transmission through the simplified structure due to the transmittance of the proposed absorber is almost 0 when the VO2 is in the metal phase. Therefore, the amplitude of all reflected THz waves from the air-VO2 metasurface interface can be modeled as [34,35]

$$\tilde{r} = {\tilde{r}_{12}} - \frac{{{{\tilde{t}}_{12}}{{\tilde{t}}_{21}}{e^{i2\tilde{\beta }}}}}{{1 + {{\tilde{r}}_{21}}{e^{i2\tilde{\beta }}}}}$$
where the accumulated phase reflected by the middle VO2 film can be described by the formula (6):
$$\tilde{\beta } = {\beta _r} + i{\beta _i} = \sqrt {{{\tilde{\varepsilon }}_t}} {k_0}t$$
and ${\tilde{r}_{12}} = {r_{12}}{e^{\phi 12}}$ is the reflection coefficient of the incident terahertz wave propagating from the air to the E-shaped VO2 film layer and then reflected back to the air. And ${\tilde{t}_{12}} = {t_{12}}{e^{\phi 12}}$ is the transmission coefficient of the incident THz wave transmitting from air to E-shaped VO2 film and then transmitted back into air. Similarly, ${\tilde{r}_{21}} = {r_{21}}{e^{\varphi 21}}$ and ${\tilde{t}_{21}} = {t_{21}}{e^{\varphi 21}}$ are the reflection and transmission coefficients of the incident waves transmitting from air into the top E-shaped VO2 film and ToPaS and reflected back into air again, respectively. Besides, ${\beta _r}$ is the propagation phase of the structure, and ${\beta _i}$ is related to the absorption of the dielectric layer, ${k_0}$ is the wave vector of the free space, and d is the thickness of the ToPaS spacer. Additionally, according to Eq. (6) as above, the absorptance of the absorber can be closed to 1 when $|{{{\tilde{r}}_{12}}} |= |{{{\tilde{t}}_{12}}{{\tilde{t}}_{21}} - {{\tilde{r}}_{12}}{{\tilde{r}}_{21}}} |$ and $\tilde{\beta } = 2n\pi ,\; ({n = 0,\; \pm 1,\; \pm 2 \ldots } )$ are synchronously realized in the same band.

 figure: Fig. 4.

Fig. 4. The (a) magnitudes and (b) phases of the transmission and reflection coefficients calculated by the interference theory. (c) Schematic of the multiple reflection and interference model. (d) Comparison of the absorption spectra calculated by interference theory and the absorption spectra simulated by CST.

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Figures 4(a) and 4(b) show the magnitude and phase of the transmission and reflection coefficients calculated by the Fabry-Perot resonant model. It can be seen that the incident THz waves have the same magnitude and phase, and almost existing a Pi phase shift before and after the resonant frequency in the reflectance spectrum [35]. Apparently, from the Fig. 4(d) we can see that the absorptance spectra simulated by CST is almost consistent with that calculated by interference theory.

When the conductivity of VO2 was fixed at 200000 S/m and the period of the unit cell was unchanged, we performed simulations with different geometric parameters. As shown in Fig. 5(a), the absorption intensity of the absorber can be continuously adjusted with the increasing width of W from 1 µm to 7 µm. From the Fig. 5(b), one can clearly see that with the increasing radius of $R1$ from 38 µm to 42 µm, VO2 patches are getting bigger, and spectra width becomes to broaden. In fact, the effective impedance Z of the absorber is determined by the effective permittivity of $\varepsilon (\omega )$ and permeability of $\mu (\omega )$. Different coupling mode effects between the E-shaped VO2 resonator and middle metal-phase plane lead to the variation of the permeability $\mu (\omega )$. According to the equation $Z = \sqrt {\mu (\omega )/\varepsilon (\omega )} $ [32] and ${Z_r} = Z/{Z_0}$, the excellent impedance matching between the absorber and the free space will be destroyed, which causing the different spectrum. Therefore, we choose the radius of 38 µm for design. Meanwhile, from Fig. 5(c), it can be observed that the absorption curves of different gap width G have a high overlap ratio. As shown in Figs. 5(d)–5(f), although the gap width of G has changed, the incident electric energy is still excited steadily, which is the key to keep the absorption stable, and this may have great operability in actual production. Therefore, from the discussion above, we illustrate the optimization process of the structure.

 figure: Fig. 5.

Fig. 5. Effects of different parameters on broadband absorption performance. (a) different arm widths of W, (b) different outside diameter of the circle R1, and (c) different gap widths of G. (d) Electric field distributions resonance frequencies of 2.45 THz when VO2 is in the metal phase.

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Moreover, by using thermal or electric stimulation to prompt the IMT property of VO2 in both top and bottom layers simultaneously, the influences of different conductivity of VO2 on the absorption performance are further investigated. As shown in Figs. 6(a)–6(h), when the Fermi energy of the graphene is set to 0.8 eV [36,37], the proposed hybrid metamaterial absorber can achieve dual-band absorption performance by decreasing the conductivity of VO2 from 200000 S/m to 10 S/m in the THz range. From Fig. 7(a), we can find that there are two perfect absorption peaks (above 93%) at the frequencies of 0.81 THz and 3.17 THz when the VO2 is in the insulating state. So far, the proposed bifunctional device can be considered as a four-layer structure of dielectric-graphene-dielectric-gold. In this state, the amplitude of the absorption spectrum can be continually tuned by changing the Fermi energy when the conductivity of VO2 is fixed at 10 S/m. As shown in Fig. 7(a) and Fig. 7(b), due to the existence of the bottom gold reflective layer, we are able to switch the proposed structure between absorber and reflector in a wide frequency range, from 1 THz to 4 THz. On the other hand, we investigate the influence of the thickness of SiO2 layer on the absorptance spectrum. From Fig. 7(c), it is obvious that when the thickness of SiO2 increases from 36 µm to 40 µm, the dual absorption bands occur red-shift and the peak absorptance of the spectrum keeps stable since the changes of the thickness of SiO2 influence the relative impedance of the device. And it indicates that the thickness of SiO2 designed as 38um is better to achieve high absorption performance for the whole structure. So far, the detailed parameters settings are given in Table 1. It can be seen that we can realize different absorption performance by applying the parameters in both $\sigma ({V{O_2}} )$ and ${E_f}$ reasonably.

 figure: Fig. 6.

Fig. 6. (a-h) The calculated absorption spectrum of the absorber with different conductivity of VO2.

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 figure: Fig. 7.

Fig. 7. The absorption and reflection spectrum (a) and contour map (b) of the proposed absorber with different Fermi energy, and the absorption spectrum with different thickness of SiO2 spacer (c) when the conductivity of VO2 is set to 10 S/m.

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Tables Icon

Table 1. Comparison of properties using different parameters.

To better investigate the influences of the proposed absorber on the incident energy loss, it is indispensable to explain the main contribution to THz absorption of each part in the designed structure. In the analysis above, we realized that the proposed device can be regarded as a dual-band absorber for THz waves when VO2 is in the insulating state and the Fermi energy of graphene is fived at 0.8 eV. As shown in Fig. 8(a), the reflection and transmission spectrums of the SiO2 spacer are simulated. And there are two distinctive reflection peaks located at 1 THz and 3 THz, and the frequency interval is $\Delta f = 2$ THz. Likewise, we can see from Fig. 8(c) that when a gold reflective layer is added to the bottom, it still has two absorption peaks with similar absorptance but lower amplitudes at 1.03 THz and 3.03 THz. The inherent reason for this phenomenon can be also explained by the Fabry-Perot resonance model. Indeed, the dielectric of SiO2 is modeled to be the finite thickness in simulation to realize Fabry-Perot resonance [3840]. Thus, the frequency interval between adjacent peaks can be defined as [38]

$$\Delta f = \frac{c}{{2n{t_d}\cos \xi }}$$
where $\xi $ is the incident angle of the THz wave, c is the velocity of light in vacuum, n and ${t_d}$ are the refractive index and the thickness of the SiO2 layer, respectively. According to the Eq. (7), the calculated frequency interval is $\Delta f = 2$ THz, which is in correspondence with the simulation results. Moreover, as shown in Fig. 8(b), the absorptance of the monolayer graphene to electromagnetic waves can only reach up to 50% in the free space, and the absorptance will gradually decrease as the frequency increases [41]. Hence, adhering to the principle of improving the absorptance, a monolayer graphene sheet without a pattern is placed on the top to achieve a sandwich metamaterial perfect absorber. From Fig. 8(d), we can clearly see that the absorptance has been enhanced. Compared with the previous structure, the absorption bandwidth and amplitude have been significantly improved since the impedance between the absorber and the free space has matched. However, that VO2 is served as a dielectric and the upper ToPaS spacer exists leads to the different absorption and operating bandwidth according to the relative impedance theory. The calculation result obtained by the three-layer structure is only slightly different from the simulation result of the proposed device. Therefore, a dual-band perfect absorber is achieved.

 figure: Fig. 8.

Fig. 8. (a) The reflection and transmission spectra of the dielectric layer. (b) The absorption, transmission and reflection spectra of monolayer graphene sheet in the free space. (c) The absorption spectrum of dielectric-gold structure. (d) The absorption spectrum of the graphene sheet-dielectric-gold structure. When VO2 is in the insulator-phase.

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As the polarization independence and wide-angle tolerance of the proposed absorber plays an important role in practical applications so that it is necessary to investigated the oblique angle insensitive of the device. As shown in Fig. 9(a) and Fig. 10(a), for both broadband absorption and dual-band absorption, it is obvious that the absorption curves under different polarization angles have completely coincided under normal incidence, which indicates that the proposed absorber could work well in different polarization modes. In fact, the symmetric unit cell is the inherent reason for the perfect polarization independence.

 figure: Fig. 9.

Fig. 9. Absorption spectrum of the proposed absorber under different (a) polarization angle and incident angles of (b) TE polarization, (c) TM polarization when VO2 is in the metal-phase.

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 figure: Fig. 10.

Fig. 10. Absorption spectrum of the proposed absorber under different (a) polarization angle and incident angles of (b) TE polarization, (c) TM polarization when VO2 is in the insulator-phase.

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Next, we studied the effects of obliquely incident THz waves on the absorption spectrum in transverse electric (TE) and transverse magnetic (TM) polarization modes, respectively. For TE polarization, as can be seen from Fig. 9(b), the broad absorption band has excellent absorption performance in the range of incident angles of 0° to 85°. The absorption bandwidth remains almost unchanged until the incident angle exceeds 45°. For TM polarization, as shown in Fig. 9(c), the result is similar to TE polarization that the absorption peak splits into six for large incident angles. Additionally, when the incident angle continuous increases, both of the two broadbands decrease significantly and finally disappear. On the other hand, according to the transmission line theory [31,42], the propagation constant ${k_z}$ along z-direction is molded by ${k_z} = {k_p}({1 - si{n^2}\xi } )$, where ${k_p}$ is the wave number in dielectric layer. We can find that the phase-matching condition is not satisfied (${k_z} \ne {k_p}$) on the hybrid metasurface since ${k_z}$ increases with the increasing incident angel $\theta $. The excellent impedance matching between the absorber and the free space will be destroyed, which will weaken the absorptance. When the VO2 of the structure changes from metal to insulator phase, for TE polarization, as shown in Fig. 10(b), the two absorption bands remain perfect performance until the incident angle raises up to 65° for the first band and to 85° for the second band. Meanwhile, the second band has a blue-shift and the bandwidth turns narrower gradually with the incident angle increases. For TM polarization, we can see from Fig. 10(c) that the first absorption band becomes wider for large incidence angle and there is a slight blue-shift for the second absorption spectrum. And the absorption performance for both bands remain stable until the incident angle raises up to over 85°. So, the function of the absorber is almost insensitive to incidence angle.

4. Conclusion

In conclusion, we proposed and demonstrated a terahertz absorber with broadband absorption and dual-band absorption properties on a simple structure. Switchable functionalities properties are achieved based on the phase transition of VO2. When VO2 is in the metallic state, it is an ultra-broadband absorber. Numerical simulation results indicate that the magnitude of the spectrum can be dynamically adjusted when the Fermi energy of graphene is fixed at 0.01 eV. Polarization-insensitive properties are achieved and the device maintains excellent absorption performance over a wide range of incident angles up to 50°. In contrast, when the VO2 changes from metal to insulator phase, the designed device can be regarded as a tunable dual-band perfect absorber at the resonance frequency of 0.81 THz and 3.17 THz. As the Fermi energy of graphene increases from 0.01 eV to 0.8 eV, the amplitude of the two absorptance peaks can be continually adjusted. And this system also shows the properties of ultra-wide incident angle and polarization independence. The Fabry-Perot resonance model can explain the inherent mechanism reasonably. In a word, we present a new method for designing high-performance terahertz devices, such as modulator, thermal emitter, and photovoltaics device.

Funding

National Natural Science Foundation of China (61162004).

Disclosures

The authors declare no conflicts of interest.

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12. Y. Zhang, Y. Li, Y. Cao, Y. Liu, and H. Zhang, “Graphene induced tunable and polarization-insensitive broadband metamaterial absorber,” Opt. Commun. 382, 281–287 (2017). [CrossRef]  

13. L. Qi and C. Liu, “Broadband multilayer graphene metamaterial absorbers,” Opt. Mater. Express 9(3), 1298 (2019). [CrossRef]  

14. Z. Xu, R. Gao, C. Ding, L. Wu, Y. Zhang, D. Xu, and J. Yao, “Photoexited switchable metamaterial absorber at terahertz frequencies,” Opt. Commun. 344, 125–128 (2015). [CrossRef]  

15. X. Li, S. Tang, F. Ding, S. Zhong, Y. Yang, T. Jiang, and J. Zhou, “Switchable multifunctional terahertz metasurfaces employing vanadium dioxide,” Sci. Rep. 9(1), 5454 (2019). [CrossRef]  

16. H. Liu, Z. H. Wang, L. Li, Y. X. Fan, and Z. Y. Tao, “Vanadium dioxide-assisted broadband tunable terahertz metamaterial absorber,” Sci. Rep. 9(1), 5751 (2019). [CrossRef]  

17. Z. Song, A. Chen, and J. Zhang, “Terahertz switching between broadband absorption and narrowband absorption,” Opt. Express 28(2), 2037 (2020). [CrossRef]  

18. L. Chen and Z. Song, “Simultaneous realizations of absorber and transparent conducting metal in a single metamaterial,” Opt. Express 28(5), 6565 (2020). [CrossRef]  

19. Z. Song, K. Wang, J. Li, and Q. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018). [CrossRef]  

20. Z. Song, Y. Deng, Y. Zhou, and Z. Liu, “Terahertz toroidal metamaterial with tunable properties,” Opt. Express 27(4), 5792–5797 (2019). [CrossRef]  

21. Z. Song, A. Cheng, J. Zhang, and J. Wang, “Integrated metamaterial with functionalities of absorption and electromagnetically induced transparency,” Opt. Express 27(18), 25196–25204 (2019). [CrossRef]  

22. Z. Song and J. Zhang, “Achieving broadband absorption and polarization conversion with a vanadium dioxide metasurface in the same terahertz frequencies,” Opt. Express 28(8), 12487–12497 (2020). [CrossRef]  

23. M. Zhang and Z. Song, “Terahertz bifunctional absorber based on a graphene-spacer-vanadium dioxide-spacer-metal configuration,” Opt. Express 28(8), 11780–11788 (2020). [CrossRef]  

24. T. Wang, Y. Zhang, H. Zhang, and M. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369 (2020). [CrossRef]  

25. Y. T. Zhao, B. Wu, B. J. Huang, and Q. Cheng, “Switchable broadband terahertz absorber/reflector enabled by hybrid graphene-gold metasurface,” Opt. Express 25(7), 7161 (2017). [CrossRef]  

26. N. Mou, S. Sun, H. Dong, S. Dong, Q. He, L. Zhou, and L. Zhang, “Hybridization-induced broadband terahertz wave absorption with graphene metasurfaces,” Opt. Express 26(9), 11728 (2018). [CrossRef]  

27. E. Radue, E. Crisman, L. Wang, S. Kittiwatanakul, J. Lu, S. A. Wolf, R. Wincheski, R. A. Lukaszew, and I. Novikova, “Effect of a substrate-induced microstructure on the optical properties of the insulator-metal transition temperature in VO2 thin films,” J. Appl. Phys. 113(23), 233104 (2013). [CrossRef]  

28. F. Fan, Y. Hou, Z. W. Jiang, X. H. Wang, and S. J. Chang, “Terahertz modulator based on insulator-metal transition in photonic crystal waveguide,” Appl. Opt. 51(20), 4589–4596 (2012). [CrossRef]  

29. C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010). [CrossRef]  

30. X. Huang, W. He, F. Yang, J. Ran, B. Gao, and W.-L. Zhang, “Polarization-independent and angle-insensitive broadband absorber with a target-patterned graphene layer in the terahertz regime,” Opt. Express 26(20), 25558 (2018). [CrossRef]  

31. N. Hu, F. Wu, L. A. Bian, H. Liu, and P. Liu, “Dual broadband absorber based on graphene metamaterial in the terahertz range,” Opt. Mater. Express 8(12), 3899–3909 (2018). [CrossRef]  

32. J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide,” Opt. Express 28(5), 7018–7027 (2020). [CrossRef]  

33. F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016). [CrossRef]  

34. H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165 (2012). [CrossRef]  

35. S. Wu and J. Li, “Hollow-petal graphene metasurface for broadband tunable THz absorption,” Appl. Opt. 58(11), 3023 (2019). [CrossRef]  

36. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef]  

37. C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011). [CrossRef]  

38. Z. Y. Zhao, H. W. Zhao, W. Peng, and W. Z. Shi, “Polarization Dependence of Terahertz Fabry–Pérot Resonance in Flexible Complementary Metamaterials,” Plasmonics 10(6), 1587–1592 (2015). [CrossRef]  

39. K. Vadim, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry–Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011). [CrossRef]  

40. X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007). [CrossRef]  

41. L. Botten, R. McPhedran, N. Nicorovici, and G. Derrick, “Periodic models for thin optimal absorbers of electromagnetic radiation,” Phys. Rev. B 55(24), R16072 (1997). [CrossRef]  

42. J. Kong, An electromagnetic scattering model for soybean canopy, in Electromagnetic Wave Theory (EMW Publishing, 2008).

References

  • View by:

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    [Crossref]
  4. J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale 11(12), 5746–5753 (2019).
    [Crossref]
  5. F. Ding, S. Zhong, and S. I. Bozhevolnyi, “Vanadium Dioxide Integrated Metasurfaces with Switchable Functionalities at Terahertz Frequencies,” Adv. Opt. Mater. 6(9), 1701204 (2018).
    [Crossref]
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  13. L. Qi and C. Liu, “Broadband multilayer graphene metamaterial absorbers,” Opt. Mater. Express 9(3), 1298 (2019).
    [Crossref]
  14. Z. Xu, R. Gao, C. Ding, L. Wu, Y. Zhang, D. Xu, and J. Yao, “Photoexited switchable metamaterial absorber at terahertz frequencies,” Opt. Commun. 344, 125–128 (2015).
    [Crossref]
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    [Crossref]
  16. H. Liu, Z. H. Wang, L. Li, Y. X. Fan, and Z. Y. Tao, “Vanadium dioxide-assisted broadband tunable terahertz metamaterial absorber,” Sci. Rep. 9(1), 5751 (2019).
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  17. Z. Song, A. Chen, and J. Zhang, “Terahertz switching between broadband absorption and narrowband absorption,” Opt. Express 28(2), 2037 (2020).
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    [Crossref]
  19. Z. Song, K. Wang, J. Li, and Q. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
    [Crossref]
  20. Z. Song, Y. Deng, Y. Zhou, and Z. Liu, “Terahertz toroidal metamaterial with tunable properties,” Opt. Express 27(4), 5792–5797 (2019).
    [Crossref]
  21. Z. Song, A. Cheng, J. Zhang, and J. Wang, “Integrated metamaterial with functionalities of absorption and electromagnetically induced transparency,” Opt. Express 27(18), 25196–25204 (2019).
    [Crossref]
  22. Z. Song and J. Zhang, “Achieving broadband absorption and polarization conversion with a vanadium dioxide metasurface in the same terahertz frequencies,” Opt. Express 28(8), 12487–12497 (2020).
    [Crossref]
  23. M. Zhang and Z. Song, “Terahertz bifunctional absorber based on a graphene-spacer-vanadium dioxide-spacer-metal configuration,” Opt. Express 28(8), 11780–11788 (2020).
    [Crossref]
  24. T. Wang, Y. Zhang, H. Zhang, and M. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369 (2020).
    [Crossref]
  25. Y. T. Zhao, B. Wu, B. J. Huang, and Q. Cheng, “Switchable broadband terahertz absorber/reflector enabled by hybrid graphene-gold metasurface,” Opt. Express 25(7), 7161 (2017).
    [Crossref]
  26. N. Mou, S. Sun, H. Dong, S. Dong, Q. He, L. Zhou, and L. Zhang, “Hybridization-induced broadband terahertz wave absorption with graphene metasurfaces,” Opt. Express 26(9), 11728 (2018).
    [Crossref]
  27. E. Radue, E. Crisman, L. Wang, S. Kittiwatanakul, J. Lu, S. A. Wolf, R. Wincheski, R. A. Lukaszew, and I. Novikova, “Effect of a substrate-induced microstructure on the optical properties of the insulator-metal transition temperature in VO2 thin films,” J. Appl. Phys. 113(23), 233104 (2013).
    [Crossref]
  28. F. Fan, Y. Hou, Z. W. Jiang, X. H. Wang, and S. J. Chang, “Terahertz modulator based on insulator-metal transition in photonic crystal waveguide,” Appl. Opt. 51(20), 4589–4596 (2012).
    [Crossref]
  29. C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010).
    [Crossref]
  30. X. Huang, W. He, F. Yang, J. Ran, B. Gao, and W.-L. Zhang, “Polarization-independent and angle-insensitive broadband absorber with a target-patterned graphene layer in the terahertz regime,” Opt. Express 26(20), 25558 (2018).
    [Crossref]
  31. N. Hu, F. Wu, L. A. Bian, H. Liu, and P. Liu, “Dual broadband absorber based on graphene metamaterial in the terahertz range,” Opt. Mater. Express 8(12), 3899–3909 (2018).
    [Crossref]
  32. J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide,” Opt. Express 28(5), 7018–7027 (2020).
    [Crossref]
  33. F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
    [Crossref]
  34. H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165 (2012).
    [Crossref]
  35. S. Wu and J. Li, “Hollow-petal graphene metasurface for broadband tunable THz absorption,” Appl. Opt. 58(11), 3023 (2019).
    [Crossref]
  36. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
    [Crossref]
  37. C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
    [Crossref]
  38. Z. Y. Zhao, H. W. Zhao, W. Peng, and W. Z. Shi, “Polarization Dependence of Terahertz Fabry–Pérot Resonance in Flexible Complementary Metamaterials,” Plasmonics 10(6), 1587–1592 (2015).
    [Crossref]
  39. K. Vadim, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry–Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
    [Crossref]
  40. X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
    [Crossref]
  41. L. Botten, R. McPhedran, N. Nicorovici, and G. Derrick, “Periodic models for thin optimal absorbers of electromagnetic radiation,” Phys. Rev. B 55(24), R16072 (1997).
    [Crossref]
  42. J. Kong, An electromagnetic scattering model for soybean canopy, in Electromagnetic Wave Theory (EMW Publishing, 2008).

2020 (8)

X. Chen, Z. Tian, Y. Lu, Y. Xu, X. Zhang, C. Ouyang, J. Gu, J. Han, and W. Zhang, “Electrically Tunable Perfect Terahertz Absorber Based on a Graphene Salisbury Screen Hybrid Metasurface,” Adv. Opt. Mater. 8(3), 1900660 (2020).
[Crossref]

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

Z. Song, A. Chen, and J. Zhang, “Terahertz switching between broadband absorption and narrowband absorption,” Opt. Express 28(2), 2037 (2020).
[Crossref]

L. Chen and Z. Song, “Simultaneous realizations of absorber and transparent conducting metal in a single metamaterial,” Opt. Express 28(5), 6565 (2020).
[Crossref]

Z. Song and J. Zhang, “Achieving broadband absorption and polarization conversion with a vanadium dioxide metasurface in the same terahertz frequencies,” Opt. Express 28(8), 12487–12497 (2020).
[Crossref]

M. Zhang and Z. Song, “Terahertz bifunctional absorber based on a graphene-spacer-vanadium dioxide-spacer-metal configuration,” Opt. Express 28(8), 11780–11788 (2020).
[Crossref]

T. Wang, Y. Zhang, H. Zhang, and M. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369 (2020).
[Crossref]

J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide,” Opt. Express 28(5), 7018–7027 (2020).
[Crossref]

2019 (7)

S. Wu and J. Li, “Hollow-petal graphene metasurface for broadband tunable THz absorption,” Appl. Opt. 58(11), 3023 (2019).
[Crossref]

Z. Song, Y. Deng, Y. Zhou, and Z. Liu, “Terahertz toroidal metamaterial with tunable properties,” Opt. Express 27(4), 5792–5797 (2019).
[Crossref]

Z. Song, A. Cheng, J. Zhang, and J. Wang, “Integrated metamaterial with functionalities of absorption and electromagnetically induced transparency,” Opt. Express 27(18), 25196–25204 (2019).
[Crossref]

X. Li, S. Tang, F. Ding, S. Zhong, Y. Yang, T. Jiang, and J. Zhou, “Switchable multifunctional terahertz metasurfaces employing vanadium dioxide,” Sci. Rep. 9(1), 5454 (2019).
[Crossref]

H. Liu, Z. H. Wang, L. Li, Y. X. Fan, and Z. Y. Tao, “Vanadium dioxide-assisted broadband tunable terahertz metamaterial absorber,” Sci. Rep. 9(1), 5751 (2019).
[Crossref]

L. Qi and C. Liu, “Broadband multilayer graphene metamaterial absorbers,” Opt. Mater. Express 9(3), 1298 (2019).
[Crossref]

J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale 11(12), 5746–5753 (2019).
[Crossref]

2018 (6)

2017 (3)

2016 (1)

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref]

2015 (2)

Z. Xu, R. Gao, C. Ding, L. Wu, Y. Zhang, D. Xu, and J. Yao, “Photoexited switchable metamaterial absorber at terahertz frequencies,” Opt. Commun. 344, 125–128 (2015).
[Crossref]

Z. Y. Zhao, H. W. Zhao, W. Peng, and W. Z. Shi, “Polarization Dependence of Terahertz Fabry–Pérot Resonance in Flexible Complementary Metamaterials,” Plasmonics 10(6), 1587–1592 (2015).
[Crossref]

2013 (1)

E. Radue, E. Crisman, L. Wang, S. Kittiwatanakul, J. Lu, S. A. Wolf, R. Wincheski, R. A. Lukaszew, and I. Novikova, “Effect of a substrate-induced microstructure on the optical properties of the insulator-metal transition temperature in VO2 thin films,” J. Appl. Phys. 113(23), 233104 (2013).
[Crossref]

2012 (2)

2011 (3)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

K. Vadim, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry–Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
[Crossref]

2010 (1)

C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010).
[Crossref]

2009 (1)

Q. Y. Wen, H. W. Zhang, Y. S. Xie, Q. H. Yang, and Y. L. Liu, “Dual band terahertz metamaterial absorber: Design, fabrication, and characterization,” Appl. Phys. Lett. 95(24), 241111 (2009).
[Crossref]

2008 (2)

2007 (1)

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75(4), 045103 (2007).
[Crossref]

2005 (1)

S. Anantha Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref]

1997 (1)

L. Botten, R. McPhedran, N. Nicorovici, and G. Derrick, “Periodic models for thin optimal absorbers of electromagnetic radiation,” Phys. Rev. B 55(24), R16072 (1997).
[Crossref]

Anantha Ramakrishna, S.

S. Anantha Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
[Crossref]

Averitt, R. D.

Bernussi, A.

C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010).
[Crossref]

Bian, L. A.

Bingham, C. M.

Botten, L.

L. Botten, R. McPhedran, N. Nicorovici, and G. Derrick, “Periodic models for thin optimal absorbers of electromagnetic radiation,” Phys. Rev. B 55(24), R16072 (1997).
[Crossref]

Boudouris, B. W.

C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

Bozhevolnyi, S. I.

F. Ding, S. Zhong, and S. I. Bozhevolnyi, “Vanadium Dioxide Integrated Metasurfaces with Switchable Functionalities at Terahertz Frequencies,” Adv. Opt. Mater. 6(9), 1701204 (2018).
[Crossref]

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref]

Cao, M.

Cao, Y.

Y. Zhang, Y. Li, Y. Cao, Y. Liu, and H. Zhang, “Graphene induced tunable and polarization-insensitive broadband metamaterial absorber,” Opt. Commun. 382, 281–287 (2017).
[Crossref]

Chang, S. J.

Chang-Hasnain, C. J.

Chase, C.

Chen, A.

Chen, C.

C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010).
[Crossref]

Chen, H.-T.

Chen, L.

Chen, X.

X. Chen, Z. Tian, Y. Lu, Y. Xu, X. Zhang, C. Ouyang, J. Gu, J. Han, and W. Zhang, “Electrically Tunable Perfect Terahertz Absorber Based on a Graphene Salisbury Screen Hybrid Metasurface,” Adv. Opt. Mater. 8(3), 1900660 (2020).
[Crossref]

Chen, Y.

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref]

Cheng, A.

Cheng, Q.

Crisman, E.

E. Radue, E. Crisman, L. Wang, S. Kittiwatanakul, J. Lu, S. A. Wolf, R. Wincheski, R. A. Lukaszew, and I. Novikova, “Effect of a substrate-induced microstructure on the optical properties of the insulator-metal transition temperature in VO2 thin films,” J. Appl. Phys. 113(23), 233104 (2013).
[Crossref]

Crommie, M. F.

C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

Dai, H.

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Yang, F.

Yang, M.

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

Yang, Q. H.

Q. Y. Wen, H. W. Zhang, Y. S. Xie, Q. H. Yang, and Y. L. Liu, “Dual band terahertz metamaterial absorber: Design, fabrication, and characterization,” Appl. Phys. Lett. 95(24), 241111 (2009).
[Crossref]

Yang, Y.

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide,” Opt. Express 28(5), 7018–7027 (2020).
[Crossref]

J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale 11(12), 5746–5753 (2019).
[Crossref]

X. Li, S. Tang, F. Ding, S. Zhong, Y. Yang, T. Jiang, and J. Zhou, “Switchable multifunctional terahertz metasurfaces employing vanadium dioxide,” Sci. Rep. 9(1), 5454 (2019).
[Crossref]

Yao, J.

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide,” Opt. Express 28(5), 7018–7027 (2020).
[Crossref]

J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale 11(12), 5746–5753 (2019).
[Crossref]

Z. Xu, R. Gao, C. Ding, L. Wu, Y. Zhang, D. Xu, and J. Yao, “Photoexited switchable metamaterial absorber at terahertz frequencies,” Opt. Commun. 344, 125–128 (2015).
[Crossref]

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Zeng, X.-P.

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Zettl, A.

C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

Zhang, H.

T. Wang, Y. Zhang, H. Zhang, and M. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369 (2020).
[Crossref]

Y. Zhang, Y. Li, Y. Cao, Y. Liu, and H. Zhang, “Graphene induced tunable and polarization-insensitive broadband metamaterial absorber,” Opt. Commun. 382, 281–287 (2017).
[Crossref]

Zhang, H. W.

Q. Y. Wen, H. W. Zhang, Y. S. Xie, Q. H. Yang, and Y. L. Liu, “Dual band terahertz metamaterial absorber: Design, fabrication, and characterization,” Appl. Phys. Lett. 95(24), 241111 (2009).
[Crossref]

Zhang, J.

Zhang, L.

Zhang, M.

Zhang, W.

X. Chen, Z. Tian, Y. Lu, Y. Xu, X. Zhang, C. Ouyang, J. Gu, J. Han, and W. Zhang, “Electrically Tunable Perfect Terahertz Absorber Based on a Graphene Salisbury Screen Hybrid Metasurface,” Adv. Opt. Mater. 8(3), 1900660 (2020).
[Crossref]

Zhang, W.-L.

Zhang, X.

X. Chen, Z. Tian, Y. Lu, Y. Xu, X. Zhang, C. Ouyang, J. Gu, J. Han, and W. Zhang, “Electrically Tunable Perfect Terahertz Absorber Based on a Graphene Salisbury Screen Hybrid Metasurface,” Adv. Opt. Mater. 8(3), 1900660 (2020).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express 16(10), 7181 (2008).
[Crossref]

Zhang, Y.

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

T. Wang, Y. Zhang, H. Zhang, and M. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369 (2020).
[Crossref]

J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide,” Opt. Express 28(5), 7018–7027 (2020).
[Crossref]

J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale 11(12), 5746–5753 (2019).
[Crossref]

Y. Zhang, Y. Li, Y. Cao, Y. Liu, and H. Zhang, “Graphene induced tunable and polarization-insensitive broadband metamaterial absorber,” Opt. Commun. 382, 281–287 (2017).
[Crossref]

Z. Xu, R. Gao, C. Ding, L. Wu, Y. Zhang, D. Xu, and J. Yao, “Photoexited switchable metamaterial absorber at terahertz frequencies,” Opt. Commun. 344, 125–128 (2015).
[Crossref]

Zhang, Z.

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale 11(12), 5746–5753 (2019).
[Crossref]

Zhao, H. W.

Z. Y. Zhao, H. W. Zhao, W. Peng, and W. Z. Shi, “Polarization Dependence of Terahertz Fabry–Pérot Resonance in Flexible Complementary Metamaterials,” Plasmonics 10(6), 1587–1592 (2015).
[Crossref]

Zhao, Y.

C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010).
[Crossref]

Zhao, Y. T.

Zhao, Z. Y.

Z. Y. Zhao, H. W. Zhao, W. Peng, and W. Z. Shi, “Polarization Dependence of Terahertz Fabry–Pérot Resonance in Flexible Complementary Metamaterials,” Plasmonics 10(6), 1587–1592 (2015).
[Crossref]

Zheng, C.

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

Zhong, S.

X. Li, S. Tang, F. Ding, S. Zhong, Y. Yang, T. Jiang, and J. Zhou, “Switchable multifunctional terahertz metasurfaces employing vanadium dioxide,” Sci. Rep. 9(1), 5454 (2019).
[Crossref]

F. Ding, S. Zhong, and S. I. Bozhevolnyi, “Vanadium Dioxide Integrated Metasurfaces with Switchable Functionalities at Terahertz Frequencies,” Adv. Opt. Mater. 6(9), 1701204 (2018).
[Crossref]

Zhou, J.

X. Li, S. Tang, F. Ding, S. Zhong, Y. Yang, T. Jiang, and J. Zhou, “Switchable multifunctional terahertz metasurfaces employing vanadium dioxide,” Sci. Rep. 9(1), 5454 (2019).
[Crossref]

Zhou, L.

Zhou, Y.

Zhu, J.

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref]

Zhu, Y.

C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010).
[Crossref]

Adv. Opt. Mater. (2)

X. Chen, Z. Tian, Y. Lu, Y. Xu, X. Zhang, C. Ouyang, J. Gu, J. Han, and W. Zhang, “Electrically Tunable Perfect Terahertz Absorber Based on a Graphene Salisbury Screen Hybrid Metasurface,” Adv. Opt. Mater. 8(3), 1900660 (2020).
[Crossref]

F. Ding, S. Zhong, and S. I. Bozhevolnyi, “Vanadium Dioxide Integrated Metasurfaces with Switchable Functionalities at Terahertz Frequencies,” Adv. Opt. Mater. 6(9), 1701204 (2018).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

C. Chen, Y. Zhu, Y. Zhao, J. H. Lee, H. Wang, A. Bernussi, M. Holtz, and Z. Fan, “VO2 multidomain heteroepitaxial growth and terahertz transmission modulation,” Appl. Phys. Lett. 97(21), 211905 (2010).
[Crossref]

Q. Y. Wen, H. W. Zhang, Y. S. Xie, Q. H. Yang, and Y. L. Liu, “Dual band terahertz metamaterial absorber: Design, fabrication, and characterization,” Appl. Phys. Lett. 95(24), 241111 (2009).
[Crossref]

Carbon (1)

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wavefront modulation and near field imaging,” Carbon 163(3), 34–42 (2020).
[Crossref]

J. Appl. Phys. (1)

E. Radue, E. Crisman, L. Wang, S. Kittiwatanakul, J. Lu, S. A. Wolf, R. Wincheski, R. A. Lukaszew, and I. Novikova, “Effect of a substrate-induced microstructure on the optical properties of the insulator-metal transition temperature in VO2 thin films,” J. Appl. Phys. 113(23), 233104 (2013).
[Crossref]

Nanoscale (1)

J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale 11(12), 5746–5753 (2019).
[Crossref]

Nature (2)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

C. Chen, C. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

Opt. Commun. (2)

Y. Zhang, Y. Li, Y. Cao, Y. Liu, and H. Zhang, “Graphene induced tunable and polarization-insensitive broadband metamaterial absorber,” Opt. Commun. 382, 281–287 (2017).
[Crossref]

Z. Xu, R. Gao, C. Ding, L. Wu, Y. Zhang, D. Xu, and J. Yao, “Photoexited switchable metamaterial absorber at terahertz frequencies,” Opt. Commun. 344, 125–128 (2015).
[Crossref]

Opt. Express (15)

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express 16(10), 7181 (2008).
[Crossref]

Y. T. Zhao, B. Wu, B. J. Huang, and Q. Cheng, “Switchable broadband terahertz absorber/reflector enabled by hybrid graphene-gold metasurface,” Opt. Express 25(7), 7161 (2017).
[Crossref]

N. Mou, S. Sun, H. Dong, S. Dong, Q. He, L. Zhou, and L. Zhang, “Hybridization-induced broadband terahertz wave absorption with graphene metasurfaces,” Opt. Express 26(9), 11728 (2018).
[Crossref]

X. Huang, W. He, F. Yang, J. Ran, B. Gao, and W.-L. Zhang, “Polarization-independent and angle-insensitive broadband absorber with a target-patterned graphene layer in the terahertz regime,” Opt. Express 26(20), 25558 (2018).
[Crossref]

R. Wang, L. Li, J. Liu, F. Yan, F. Tian, H. Tian, J. Zhang, and W. Sun, “Triple-band tunable perfect terahertz metamaterial absorber with liquid crystal,” Opt. Express 25(26), 32280 (2017).
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H. Xiong, Y.-B. Wu, J. Dong, M.-C. Tang, Y.-N. Jiang, and X.-P. Zeng, “Ultra-thin and broadband tunable metamaterial graphene absorber,” Opt. Express 26(2), 1681 (2018).
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Z. Song, A. Chen, and J. Zhang, “Terahertz switching between broadband absorption and narrowband absorption,” Opt. Express 28(2), 2037 (2020).
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L. Chen and Z. Song, “Simultaneous realizations of absorber and transparent conducting metal in a single metamaterial,” Opt. Express 28(5), 6565 (2020).
[Crossref]

Z. Song, K. Wang, J. Li, and Q. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
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Z. Song, Y. Deng, Y. Zhou, and Z. Liu, “Terahertz toroidal metamaterial with tunable properties,” Opt. Express 27(4), 5792–5797 (2019).
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Z. Song, A. Cheng, J. Zhang, and J. Wang, “Integrated metamaterial with functionalities of absorption and electromagnetically induced transparency,” Opt. Express 27(18), 25196–25204 (2019).
[Crossref]

Z. Song and J. Zhang, “Achieving broadband absorption and polarization conversion with a vanadium dioxide metasurface in the same terahertz frequencies,” Opt. Express 28(8), 12487–12497 (2020).
[Crossref]

M. Zhang and Z. Song, “Terahertz bifunctional absorber based on a graphene-spacer-vanadium dioxide-spacer-metal configuration,” Opt. Express 28(8), 11780–11788 (2020).
[Crossref]

J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide,” Opt. Express 28(5), 7018–7027 (2020).
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H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165 (2012).
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Opt. Lett. (1)

Opt. Mater. Express (3)

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Plasmonics (1)

Z. Y. Zhao, H. W. Zhao, W. Peng, and W. Z. Shi, “Polarization Dependence of Terahertz Fabry–Pérot Resonance in Flexible Complementary Metamaterials,” Plasmonics 10(6), 1587–1592 (2015).
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X. Li, S. Tang, F. Ding, S. Zhong, Y. Yang, T. Jiang, and J. Zhou, “Switchable multifunctional terahertz metasurfaces employing vanadium dioxide,” Sci. Rep. 9(1), 5454 (2019).
[Crossref]

H. Liu, Z. H. Wang, L. Li, Y. X. Fan, and Z. Y. Tao, “Vanadium dioxide-assisted broadband tunable terahertz metamaterial absorber,” Sci. Rep. 9(1), 5751 (2019).
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F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
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Figures (10)

Fig. 1.
Fig. 1. The schematic of the unit cell of the proposed absorber consists of perspective, top, and side view.
Fig. 2.
Fig. 2. (a) Absorption spectrum of the proposed absorber with different phase of VO2. (b) The real and imaginary parts of the relative impedance of the absorber. (c) Absorption curves of the device with different Fermi energies. When VO2 is in the metal phase.
Fig. 3.
Fig. 3. The electric field distribution of the proposed absorber at different perfect resonance frequencies (a-b) Top view; (c-d) Side view when the conductivity of VO2 is set to 200000S/m.
Fig. 4.
Fig. 4. The (a) magnitudes and (b) phases of the transmission and reflection coefficients calculated by the interference theory. (c) Schematic of the multiple reflection and interference model. (d) Comparison of the absorption spectra calculated by interference theory and the absorption spectra simulated by CST.
Fig. 5.
Fig. 5. Effects of different parameters on broadband absorption performance. (a) different arm widths of W, (b) different outside diameter of the circle R1, and (c) different gap widths of G. (d) Electric field distributions resonance frequencies of 2.45 THz when VO2 is in the metal phase.
Fig. 6.
Fig. 6. (a-h) The calculated absorption spectrum of the absorber with different conductivity of VO2.
Fig. 7.
Fig. 7. The absorption and reflection spectrum (a) and contour map (b) of the proposed absorber with different Fermi energy, and the absorption spectrum with different thickness of SiO2 spacer (c) when the conductivity of VO2 is set to 10 S/m.
Fig. 8.
Fig. 8. (a) The reflection and transmission spectra of the dielectric layer. (b) The absorption, transmission and reflection spectra of monolayer graphene sheet in the free space. (c) The absorption spectrum of dielectric-gold structure. (d) The absorption spectrum of the graphene sheet-dielectric-gold structure. When VO2 is in the insulator-phase.
Fig. 9.
Fig. 9. Absorption spectrum of the proposed absorber under different (a) polarization angle and incident angles of (b) TE polarization, (c) TM polarization when VO2 is in the metal-phase.
Fig. 10.
Fig. 10. Absorption spectrum of the proposed absorber under different (a) polarization angle and incident angles of (b) TE polarization, (c) TM polarization when VO2 is in the insulator-phase.

Tables (1)

Tables Icon

Table 1. Comparison of properties using different parameters.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ε ( ω ) = ε ω p 2 ( σ ) ω 2 + j γ ω
σ i n t r a ( ω ) = j e 2 π 2 ( ω j 2 Γ ) 0 η ( f d ( η , E f , T ) η f d ( η , E f , T ) η ) d η
A ( ω ) = 1 R ( ω ) = 1 | Z Z 0 Z + Z 0 | 2 = 1 | Z r 1 Z r + 1 | 2
Z r = ± ( 1 + S 11 ) 2 S 21 2 ( 1 S 11 ) 2 S 21 2
r ~ = r ~ 12 t ~ 12 t ~ 21 e i 2 β ~ 1 + r ~ 21 e i 2 β ~
β ~ = β r + i β i = ε ~ t k 0 t
Δ f = c 2 n t d cos ξ

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