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Abstract
A bi-tunable triple-band metamaterial absorber based on Dirac semimetal films (DSFs) and vanadium dioxide (VO2) is presented. When VO2 is in the fully metallic state, the proposed absorber presents three distinctive absorption peaks in the terahertz range with absorptance 97%. Because the conductivity of VO2 changes from 100000 to 10 S/m, the reflectance and absorptance intensities achieve dynamic tunability at the three absorption peaks, and the proposed triple-band absorber exhibits a switchable function by the insulation-to-metal transition of VO2. Moreover, the frequencies of the three absorption peaks can also be tuned by varying the Fermi energies of the DSFs.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificially fabricated materials with extraordinary properties, such as negative refraction [1], photodetection [2], and superlens properties [3], which are not achievable in natural materials. In the last decade, numerous approaches have been extensively explored to develop metamaterial absorbers because of their promising applications in sensors, switches, modulators, and spectroscopy [4–7]. Since the first experimental demonstration of metamaterial absorber by Landy et al., [8], various types have been demonstrated to realize single-, dual-, multi-, and broadband absorptions at different frequencies, including microwave, terahertz (THz), infrared, and optical [9–13]. However, these absorbers are formed of metals and suffer from fixed functionality and non-adjustability after fabrication. To achieve absorption control [14–16], two-dimensional materials, such as graphene, black phosphorus, germanium telluride, and vanadium dioxide (VO2), have been adopted in the design of dynamically tunable metamaterial absorbers [17–20]. Among them, VO2 is a common type of phase-change material that undergoes an insulator-to-metal phase transition under electrical, thermal, or optical stimuli [21–23]. Taking advantage of its conductivity increase of approximately 4–5 orders of magnitude during the transition [23], a tunable response property can be realized by combining VO2 with a metamaterial absorber. Huang et al., demonstrated a controllable dual broadband absorber based on the hybridization of a metamaterial with VO2; it presented two adjustable absorption bandwidths in the THz range [24]. Kocer et al., proposed a broadband metamaterial–VO2 absorber, whose absorption range can be tuned from 90% to 30% over the mid-wavelength infrared region [25]. Song et al., investigated a composite VO2 meta-surface with a sandwich microstructure as a tunable broadband THz absorber [26].
Recently, metamaterial absorbers based on Dirac semimetal films (DSFs) have also been extensively studied owing to their dynamically tunable properties. Three-dimensional (3D) DSFs are 3D analogs of graphene, which not only possess all the advantages of graphene as a photosensitive material [27,28] but also present a relative stability to the environment and a higher carrier mobility than graphene [29,30]. Moreover, a DSF has an adjustable permittivity, which can be tuned by changing the Fermi energy by the in situ electron doping method [29]. Luo et al., demonstrated a tunable multiband THz absorber based on a bulk Dirac semimetal, which can be implemented as a sensor owing to its outstanding sensing performance with a figure of merit of 813 [31]. Fang et al., proposed a tunable bulk Dirac semimetal-based absorber that can convert a dual-band absorption into a narrowband absorption in the THz range by changing the radius of the structure [32]. However, these studies have only one available pathway to control the response of the absorber. Although bi-tunable single-band [33] and broadband [34] absorbers have been investigated, a combination of metamaterials with both DSFs and VO2 to produce bi-tunable multiband absorbers is yet to be reported.
In this study, we propose a theoretical bi-tunable triple-band metamaterial absorber based on VO2 and DSFs in the THz range. The proposed triple-band absorber can realize bi-tunable characteristics by adjusting both the conductivity of VO2 and the Fermi energy of the DSFs, which is extremely beneficial for practical applications. The reflectance and absorptance intensities can be flexibly controlled by adjusting the conductivity of VO2, and the proposed triple-band absorber presents a switchable function by transforming VO2 from an insulator to a metallic state. Concurrently, utilizing the adjustable permittivity function of DSFs, three absorption peaks are blueshifted as the Fermi energy increases. In addition, our proposed triple-band absorber maintains high absorptance over a wide range of incident angles. This study assists in motivating the design of a bi-tunable dual- or multiband absorber.
2. Design and analysis of structure
A schematic of the DSFs- and VO2-based bi-tunable triple-band metamaterial absorber is illustrated in Fig. 1. The proposed absorber consists of a DSF top layer and a VO2 bottom layer separated by a dielectric layer of silica (SiO2). The DSF and VO2 layers have thicknesses of 0.3 µm and h=0.8 µm, respectively. The substrate is considered as the lossless SiO2 spacer [35,36] which has a relative permittivity of 3.9 and a thickness of 9 µm. The DSF layer is composed of two DSF square rings with two gaps and DSF ring resonators, whose parameters are schematically depicted in Fig. 1(a). The period of the proposed absorber is P = 30 µm. The numerical simulations were performed using CST Microwave Studio, and the frequency domain solver was selected to obtain the transmission coefficient, |S21|, and the reflection coefficient, |S11|. The electric polarization was set along the x-axis, which was vertically illuminated on the absorber. In the simulation, the unit cell boundary condition was set along both the x- and y-axes, and the open boundary condition was along the z-axes. The absorptance of the proposed absorber is determined by the equation: A = 1 − R − T = 1 − |S11|2 − |S21|2, where R and T represent the reflectance and transmittance, respectively [37]. When VO2 is in the fully metallic state, the bottom layer prevents transmission, and the transmission of the absorber is very close to zero, so that it can be considered as a conventional sandwich absorber with a metal ground plane.
Fig. 1. Schematic of DSF- and VO2-based bi-tunable triple-band metamaterial absorber: (a) top and (b) perspective views of structure with P = 30 µm, L1 = 24.5 µm, L2 = 18 µm, Rout = 7 µm, Rin = 6 µm, g = 4 µm, and w = 1.7 µm.
The dynamic conductivity of the DSFs in the long-wavelength limit can be calculated from the Kubo formalism in random-phase approximation theory [38] and can be expressed as $\sigma = {\sigma _{intra}} + {\sigma _{inter}}$, where ${\sigma _{intra}}$ and ${\sigma _{inter}}$ are the intraband and interband conductivity, respectively, defined as follows [39]:
Above, ${k_F} = {E_F}/({\hbar {v_F}} )$ is the Fermi momentum, ћ is the reduced Planck constant, EF is the Fermi energy, and ${v_F} \approx {10^6}\; \textrm{m}/\textrm{s}$ is the Fermi velocity. In addition, $\textrm{G}(E )= \textrm{n}({ - E} )-{-}\textrm{n}(E )= \frac{{\textrm{sinh}({E/T} )}}{{\cosh ({{E_F}/T} )+ \textrm{cosh}({E/T} )}}$, where $\textrm{E} = \hbar \omega /2$ and ${\Omega } = \hbar \omega /{E_F} + \textrm{i}\hbar {\mathrm{\tau }^{\textrm{ - 1}}}\textrm{/}{\textrm{E}_\textrm{F}}$, $\mathrm{\tau }\textrm{= 4}\textrm{.5} \times {10^{ - 13}}s$. Correspondingly, the permittivity of the DSFs can be obtained using a two-band model [40] as follows:
Where ɛ0 is the permittivity of vacuum and ɛb is the effective background dielectric, which is 1 for g = 40 (AlCuFe quasi-crystals [41]).The relative permittivity of VO2 in the THz range can be expressed by the Drude model [42] as follows:
Above, the permittivity at infinite frequency, ${\varepsilon _\infty } = 12$, the damping frequency, $\gamma = 5.75 \times {10^{13}}\; {\textrm{s}^{ - 1}}$, and the plasma frequency, ${\omega _p}^2({{\sigma_{v{o_2}}}} )= \frac{{{\sigma _{v{o_2}}}}}{{{\sigma _0}}}{\omega _p}^2({{\sigma_0}} )$, where ${\sigma _0} = 3 \times {10^5}\;\textrm{S}/\textrm{m}$ and ${\omega _p}({{\sigma_0}} )= 1.4 \times {10^{15}}\;\textrm{rad}/\textrm{s}$. In the simulation, we set the conductivity of VO2 to increase from 10 to 100000 S/m, to represent the insulator-to-metal transition. Specifically, we assumed that VO2 was in the fully metallic (insulator) state with a conductivity of 100000 S/m (10 S/m).
3. Results and discussion
Figure 2(a) shows the reflectance, transmittance, and absorptance spectra of the proposed triple-band absorber when VO2 is in the fully metallic state with a conductivity of 100000 S/m. We set the initial Fermi energy of the DSFs as 0.13 eV. The blue dotted line denotes the transmission of the proposed triple-band absorber, which is close to zero because of the highly reflective characteristics of the VO2 layer. It can be seen from the red solid line that three absorption peaks emerge at frequencies 1.44 THz, 2.313 THz, and 3.13 THz with absorptance of 97.8%, 99.27%, and 99.54%, respectively. The three resonance absorption peaks originate from the overlapping of the three differently positioned resonance frequencies generated by the three different-sized resonators. Based on the LC circuit model, the frequency of the resonance can be expressed as [43,44] $f = 1/\left( {2\pi \sqrt {({LC/2} )} } \right) \propto W \propto 1/l$, where W represents the width of the square split-ring or ring and l represents the length or radius of the square split-ring or ring. From this equation, we can find that the frequency of absorptance is proportional and inversely proportional to the width and length respectively. Therefore, due to the frequencies of the absorption peaks are inversely proportional to the lengths of the three resonators, the outer square split-ring, middle square split-ring, and inner ring resonators, respectively, contribute to the A, B, and C absorption peaks. It is obvious from Figs. 2(b)–2(d) that the absorption peak A, B, and C show a blue shift as the width of the ring, middle square split-ring, and outer square split-ring increases, respectively. However, the frequency of the absorption peak C slightly decreases when increase the width of the middle square split-ring which because of the weak coupling between neighboring structure, as shown in Fig. 2(c).
Fig. 2. Calculated (a) reflectance, transmittance, and absorptance spectra of proposed triple-band absorber and the absorptance for different width of the (b) ring, (c) middle square split-ring, and (d) outer square split-ring when VO2 is in fully metallic state (EF = 0.13 eV).
To develop further understanding of the triple-band absorption mechanism, the surface and bottom electric field and current density distributions at the frequencies of three absorption peaks A, B, and C shown in Fig. 2 are presented in Fig. 3. For absorption peak A, positive and negative induced charges accumulate on the left and right sides of the outer square split-ring resonator, respectively, causing an electrical dipole resonance, whereas a reverse charge distribution occurs on the bottom layer (see Fig. 3(a)). Concurrently, high-intensity current densities are mainly distributed on the outer square split-ring resonator and are opposite to the bottom layer distribution, which results in a magnetic dipole resonance (see Fig. 3(d)). Therefore, the proposed triple-band absorber can be coupled to the incident electric and magnetic fields, consuming the energy of the incident electromagnetic waves via the electric and magnetic dipole resonances at the frequency of absorption peak A. Similarly, at the frequencies of absorption peaks B and C, an electric dipole resonance occurs in the middle square split-ring resonator and the inner ring resonator, respectively, and the surface electric field and current density distributions are opposite to those in the bottom layer (see Figs. 3(b)–3(f)). Thus, triple-band absorption peaks can be achieved at 1.44 THz, 2.313 THz, and 3.13 THz. As expected, these results and previous analyses are in good agreement. The lower the frequencies of the absorption peaks, the longer the lengths of the three resonators where the electric field and current density are mainly distributed.
Fig. 3. (a)–(c) Electric field and (d)–(f) current density distributions of proposed triple-band absorber at three absorption peaks (frequencies are indicated below respective distributions).
Based on the insulator-to-metal transition characteristic of VO2, the reflectance, transmittance, and absorptance of the proposed triple-band absorber can be tuned by changing the conductivity of VO2, as shown in Fig. 4. When VO2 is in the insulator state, the reflectance at the frequencies of the three absorption peaks reaches the highest values: 70.4%, 54%, and 44%, respectively. As the conductivity of VO2 increases because of the enhancement in the metallic characteristics of VO2 during this process, both the reflectance and transmittance decrease, whereas the absorptance gradually increases. When VO2 is in the fully metallic state with a conductivity of 100000 S/m, three absorption peaks with absorptance of 97.8%, 99.27%, and 99.54% can be realized at 1.44 THz, 2.313 THz, and 3.13 THz, respectively. Therefore, we can consider that the proposed triple-band absorber displays a switchable function by changing the conductivity of VO2. When VO2 is in the insulator and metallic states, the absorber is in the off and on state, respectively. For example, the state of the proposed triple-band absorber can be switched from absorption (97.8%) to reflection (70.4%) at absorption peak A. Thus, the proposed triple-band absorber presents dynamically tunable behaviors by the variation in the conductivity of VO2, which can be used as an attenuator and a modulator.
Fig. 4. Calculated (a) reflectance, (b) transmittance, and (c) absorptance spectra of the proposed triple-band absorber at various VO2 conductivities (EF = 0.13 eV).
Next, the effect of the VO2 thickness on the absorptance is presented in Fig. 5. As the thickness of VO2 increases from 0.01 µm to 0.8 µm, the absorptance of the three absorption peaks increases continuously and exhibits a gradually diminishing rate, and the three absorption peaks become increasingly noticeable. With further increase in the thickness to values greater than the optimized value, 0.8 µm, the absorptance of the three absorption peaks remains basically unchanged; this is because the VO2 thickness is sufficiently thick to prevent transmission.
Fig. 5. Calculated absorptance spectra of proposed triple-band absorber at varying VO2 thicknesses when VO2 is in fully metallic state (EF = 0.13 eV).
Taking advantage of the dynamic adjustment of the permittivity of the DSFs by varying the Fermi energy, the frequency tunability of the proposed triple-band absorber is depicted in Fig. 6. The three absorption peaks exhibit a blue shift as the Fermi energy increases from 0.11 to 0.15 eV, with the higher frequency absorption peak presenting a more rapid frequency shift. The absorption peaks at high frequencies are more sensitive to the changes in the Fermi energy. Therefore, the frequency of the triple-band absorption response can be tuned by changing the Fermi energy of the DSFs, presenting another method to control the resonance of the proposed triple-band absorber.
Fig. 6. Calculated absorptance spectra of proposed triple-band absorber at various Fermi energies of DSFs when VO2 is in fully metallic state.
Figure 7(a) presents the absorptance of proposed triple-band absorber as the polarization angle θ increases from 0° to 90°. Due to the structure asymmetry in the proposed triple-band absorber, the absorptance exhibit polarization sensitive behavior and the three absorption peaks are gradually vanished by adjusting the polarization angle. Figure 7(b) presents the absorptance as a function of frequency under different incident angles, where the proposed triple-band absorber maintains high absorptance (more than 93% absorptance) at the three absorption peaks when the incident angle is varied from 0° to 60°. As the incident angle exceeds 60°, the three absorption peaks are slightly blueshifted, and the absorptance decreases slightly. Therefore, the proposed triple-band absorber can function well over a wide range of incident angles, which is beneficial in practical applications.
Fig. 7. Calculated absorptance of proposed triple-band absorber as function of frequency and (a) polarization angle and (b) incident angle when VO2 is in fully metallic state (EF = 0.13 eV).
4. Conclusions
In conclusion, a bi-tunable DSF- and VO2-based triple-band metamaterial absorber was numerically and theoretically investigated in the THz range. When VO2 was in the metallic state with a conductivity of 100000 S/m, three perfect absorption peaks were achieved at frequencies of 1.44 THz, 2.313 THz, and 3.13 THz, respectively. When the conductivity of VO2 is changed from 10 to 100000 S/m, the absorptance of the three absorption peaks can be continuously tuned from 6.5% to 97.8%, 10% to 99.27%, and 9% to 99.54%, respectively. Furthermore, the proposed triple-band absorber exhibits a switchable function taking advantage of the insulator-to-metallic transition of VO2. Concurrently, by increasing the Fermi energy of DSFs, the absorptance of the three absorption peaks is blue-shifted. Therefore, dynamically bi-tunable behaviors can be achieved by these two methods. In addition, the absorptance of the proposed triple-band absorber exhibits good performance over a wide range of incidence angles. This study may be beneficial for applications in switching, sensing, and modulation.
Funding
National Key Research and Development Program of China (2017YFA0701000); National Natural Science Foundation of China (61775123, 61875106); Key Research and Development Program of Shandong Province (2019GGX104039, 2019GGX104053).
Disclosures
The authors declare no conflicts of interest.
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