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Abstract
We demonstrate the perfect trapping of electromagnetic fields over multi-band frequencies through all-dielectric terahertz absorbers using water graphene cascade metamaterials. More specifically, the coating water layer greatly enhances the higher-order Fabry-Pérot resonant absorbing modes and can achieve more than 8 absorbing peaks with the absorptions exceeding 99% in the spectrum below 3 THz. Especially such multiple perfect absorbing bands can readily be reset when the proposed water-graphene metamaterial absorbers integrate with thermal controlled vanadium dioxide. Such a perfect absorbing capacity would also be valid for the wide angular illuminations with different polarizations, and the reconfigurable characteristics of graphene can also enable the dynamically tuning of the absorbing frequencies, offering great freedom of extensive applications in energy harvesting and wave manipulation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Graphene metamaterial absorbers as promising candidates to trap electromagnetic fields have been widely adopted in various applications of energy harvesting [1–3]. Especially, multi-band metamaterials with specific graphene patterns have shown to be capable of achieving super-absorptions efficiently. For example, M.S. Islam et al. demonstrated the multiband super-absorptions utilizing a localized surface plasmon graphene metasurface [4]. Bao et al. reported a tunable multi-band absorber design using multi-layer film with graphene [5]. These schemes demonstrating more than 95% absorption at a single or a few specific frequency points have proved the great absorbing capacities of the graphene metamaterial absorbers. However, the present multi-band absorbers are normally limited to less than four perfect operating bands, and these designs can hardly trap electromagnetic fields with above 99% absorption for all the absorbing peaks [6–9].
On the other hand, pure water as a ubiquitous broadband absorbing material possessing the merit of good dielectric loss should offer the opportunities to enhance the multi-band absorbing functionalities [10–13]. It has demonstrated unique potential for improving wide-band impedance match in the absorbers [14–18], while yielding promising characteristics of the optical transparency and thermal stability [19]. Based on these considerations, we demonstrate the perfect trapping of electromagnetic fields over multi-band frequencies through all-dielectric terahertz absorbers using water-graphene cascade metamaterials. More specifically, the coating water layer greatly enhances the higher-order Fabry-Pérot resonant absorbing modes and can achieve more than 8 absorbing peaks with the absorptions exceeding 99% in the spectrum below 3 THz. In addition, thermal controlled vanadium dioxide (${\rm {V}}{{\rm {O}}_{\rm {2}}}$) as a phase change material can realize the reversible phase transition from insulator to metal and lead to dramatic change in dielectric function and optical properties [20–25]. On this basis, we show that the multiple perfect absorbing bands can be readily reset when the proposed water-graphene metamaterial absorbers integrated with thermal controlled vanadium dioxide. We will show that such a perfect absorbing capacity will also be valid for the wide angular illuminations with different polarizations, and the reconfigurable characteristics of graphene enable the dynamically tuning of the absorbing frequencies, offering great freedom of extensive applications in energy harvesting and wave manipulation.
2. Modeling and absorption characteristics
Figure 1 schematically demonstrates the proposed water-graphene cascade metamaterial perfect absorber under the illumination of electromagnetic fields, consisting of a pure water layer, a graphene sheet, silicon-dielectric layer, vanadium dioxide and a ground plane. The structural parameters are $h_{\text {gold }}=2~ \mu \mathrm {m}$, $h_{\text {silicon1 }}=55~ \mu \mathrm {m}$, $h_{\mathrm {vo}_{2}}=3~ \mu \mathrm {m}$, $h_{\text {silicon2 }}=55~ \mu \mathrm {m}$, $h_{\text {graphene }}=0.1~ \mu \mathrm {m}$ and $h_{\text {water }}=7~ \mu \mathrm {m}$.
Fig. 1. The schematic demonstration of reconfigurable multi-band water-graphene cascade metamaterial perfect absorbers loaded with vanadium dioxide.
The relative permittivity of gold, silicon, ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ are described by Drude model with
On the other hand, graphene is modeled as a conductive surface with conductivity calculated from Kubo formula
Full wave simulations (CST Microwave Studio) are carried out to verify our design in Fig. 2. We mimic the interactions between the electromagnetic fields and the proposed metamaterial absorber using the Floquet mode analysis with boundary conditions virtually repeating the modeled structure periodically in $x$ and $y$ directions as shown in Fig. 2(a). The absorbance $A(\omega )$ can be obtained by $A(\omega ) = 1 - R(\omega ) - T(\omega )$, where $R(\omega ) = {\left | {S_{11}} \right |^2}$ and $T(\omega ) = {\left | {S_{21}} \right |^2}$ are defined as reflectance and transmittance, respectively. Figure 2(b) demonstrates the proposed metamaterial absorber possesses eight absorbing peaks at the frequencies of 0.19 THz, 0.57 THz, 0.96 THz, 1.34 THz, 1.72 THz, 2.1 THz, 2.48 THz and 2.86 THz respectively when $\mu _{\mathrm {c}}=0.2 \mathrm {~eV}$ and ${\mathop {\rm T}\nolimits } = 323.15{\mathop {\rm ~K}\nolimits }$ with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, and the absorptions all exceed 99%. Such Fabry–Pérot resonant absorptions can be estimated by
where c is the velocity of light, $\xi$ is the incident angle of the THz wave and $d$ is the thickness of dielectric absorber [24]. n refers to the equivalent refractive index of dielectrics, where we can roughly use $n = 3.45$ of silicon for the approximation as water, graphene and ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ are very thin layers compared with silicon. In this way with $d=120~ \mu \mathrm {m}$, we can have $\Delta f=0.362 \mathrm {~THz}$, and this is very closed to $\Delta f_{1}=0.567 \mathrm {~THz}-0.19 \mathrm {~THz}=0.357 \mathrm {~THz}$ in the full wave simulations. On the other hand, the proposed metamaterial absorber will trap the electromagnetic fields at 0.385 THz, 1.157 THz, 1.918 THz, and 2.676 THz when $\mu _{\mathrm {c}}=0.1 \mathrm {~eV}$ and $\mathrm {T}=343.15 \mathrm {~K}$ with conducting state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$. We can also observe that the absorber achieves strong fields confinement due to the water-graphene in the top that restrain the propagation of the electromagnetic wave in Fig. 2(c). The metal film that is larger than the typical skinning depth at THz frequencies thereby impeding wave transmission, and the intermediate silicon that forms a Fabry–Pérot cavity between the top water-graphene layer and the bottom metal with highly efficient terahertz field resonant absorptions [24]. Similarly, when ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in the conducting-state, and the top water-graphene layer and the ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ will thus create the resonant absorptions [28]. In this way, the multiple perfect absorbing bands will readily be reset as the conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ actually shorten the length of proposed metamaterial absorber, and this can be also observed from the E-filed distributions in Fig. 2(d).Fig. 2. Multi-band absorptions from the proposed water-graphene cascade metamaterial perfect absorbers loaded with vanadium dioxide. (a) Floquet mode analysis. (b) Absorbing characteristics for both TE and TM polarized normal terahertz incidence with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ at $\mathrm {T}=323.15 \mathrm {~K}$ and $\mu _{\mathrm {c}}=0.2 \mathrm {~eV}$ and conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ at $\mathrm {T}=343.15 \mathrm {~K}$ and $\mu _{\mathrm {c}}=0.1 \mathrm {~eV}$. (c) The corresponding E-field distributions at the eight resonant absorbing peaks with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$. (d) The corresponding E-field distributions at the four resonant absorbing peaks with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$.
3. Key factors on the absorption characteristics
We continue to demonstrate the material superiority of the proposed metamaterial absorber in Fig. 3, where the original proposal is investigated in the case without water-graphene, and the one just without water. As shown in Fig. 3(a), with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, we can observe that the proposed design will lose the most of the absorbing capacity when only silicon layer is loaded. When solely remove the water, the metamaterial absorber with silicon and graphene can also produce eight absorbing peaks, but only the absorption rates of the first four peaks are greater than 90%, while the absorption rates of the last four absorbing peaks are ranging from 58% to 82%. On the other hand, when silicon, graphene and water layers are simultaneously loaded as the original proposal, absorption rates will exceed 99% for all the eight absorbing peaks. Similarly, we can also observe in Fig. 3(b) that the proposed design with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ will lose most of the absorption abilities by only having silicon layer with less than 65% absorption rates of all the four absorbing peaks in 0-3 THz. When only remove the water, the first absorbing peak of the four will exceed 90%, but the absorption rates of the last three absorbing peaks will be ranging from 78% to 86%. On the other hand, when silicon, graphene and water layers are all loaded simultaneously, as the original proposal, all four absorbing peaks will be significantly increased with more than 99% absorption rates.
Fig. 3. The material superiority of the proposed metamaterial absorber for achieving the perfect absorption. (a) With insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, (b) With conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$.
Figure 4 demonstrates the absorption spectra with different structural parameters under normal TE-polarized incident wave. Figures 4(a) and 4(b) demonstrate the effects of different water thickness on the absorber absorptivity with different ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ states, respectively. As shown in Fig. 4(a), with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, we can observe that the absorption rates of the last four absorbing peaks vary from 91% to 100% when the thickness of the water layer increases from $3~ \mu \mathrm {m}$ to $7~ \mu \mathrm {m}$. The absorption will remain basically the same when the water layer is thicker than $7~ \mu \mathrm {m}$. As shown in Fig. 4(b) with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, we can observe that the absorption intensities of the last three absorbing peaks vary from 97% to 100% when the thickness of the water layer increases from $3~ \mu \mathrm {m}$ to $5~ \mu \mathrm {m}$. The absorption will remain basically the same when the water layer is thicker than $5~ \mu \mathrm {m}$. In both cases, the absorption frequencies will be redshifted with the increase of the water layer thickness, and this is because the metamaterial absorber is based on the resonant property of Fabry–Pérot cavity, where the absorption frequencies will vary accordingly with the height of the media. Similarly, we analyze the effect of silicon thickness on the absorption rate of the absorber as shown in Figs. 4(c) and 4(d), where the ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is always inserted in the middle of the silicon. We can observe that the number of absorbing peaks increases in 0-3 THz range as the thickness of the medium increases from $110~ \mu \mathrm {m}$ to $210~ \mu \mathrm {m}$, and all absorbing peaks can be always perfect even with 15 absorbing peaks.
Fig. 4. Absorption spectra with different structural parameters under normal TE-polarized incident wave. (a) Different $h_{\text {water }}$ with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, (b) Different $h_{\text {water }}$ with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, (c) Different $h_{\text {silicon }}=h_{\text {silicon1 }}+h_{\text {silicon2 }}$ with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, (d) Different $h_{\text {silicon }}$ with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$.
Figure 5 demonstrates the thermal controlled absorptions of the proposed water-graphene cascade metamaterial absorbers, where the characteristics of water-graphene, and ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ in the structure will be set with the same temperature. We can find that the absorption will increase for all the absorbing peaks when the system temperature gradually increases in the range of $273.15 \mathrm {~K}-343.15 \mathrm {~K}$ with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$. The absorption will be perfect when the temperature is beyond $323.15 \mathrm {~K}$. On the other hand, we can also observe that the temperature can scarcely influence the absorption performance of the proposed absorber when ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in the conducting-state, and either the absorption intensities or the frequencies of the four absorbing peaks remain the same and all the absorptions can maintain absolutely perfect in the range of $343.15 \mathrm {~K}-363.15 \mathrm {~K}$.
Fig. 5. Absorption spectra with different temperatures. (a) Thermal controlled absorption in the range of $273.15 \mathrm {~K}-338.15 \mathrm {~K}$ when ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in the insulating-state; (b) Thermal controlled absorption in the range of $343.15 \mathrm {~K}-363.15 \mathrm {~K}$ when ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in the conducting-state.
Figure 6 demonstrates the graphene Fermi energy-controlled absorption of the proposed water-graphene cascade metamaterial absorber. We can observe that the absorbing peaks move to high frequencies slightly with blue-shifts when the Fermi energies imposed over the graphene grow bigger. In addition, we can also observe that the overall absorption rate of metamaterial absorber can be dynamically adjusted by the Fermi energies of the graphene. Especially, perfect absorptions for all the eight absorbing bands will be achieved when we have 0.2 eV Fermi energy imposed over the graphene for the proposed metamaterial absorber with the insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$. In the meanwhile, we can have four perfect absorptions by imposing 0.1 eV Fermi energy over the graphene for the proposed metamaterial absorber with the conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$.
Fig. 6. Absorption spectra with different Fermi energies imposed over the graphene. (a) Fermi energy-controlled absorption with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, (b) Fermi energy-controlled absorption with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$.
It is worthwhile to compare the different permittivity value of ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ as the dielectric permittivity will change with the different deposition processes. Figure 7 thus demonstrates such influences on the absorption performance of the proposed water-graphene cascade metamaterial absorber. Generally, we use thermal or electric stimulation to prompt the insulator-to-metal transition property of ${\rm {V}}{{\rm {O}}_{\rm {2}}}$. As a result, we can change the dielectric permittivity of ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ by adjusting its conductivity according to equation (1). ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in the insulating-state with the conductivity increasing from 40 S/m to 20000 S/m. In such cases, we can observe in Fig. 7(a)-(d) that the absorptivity of the eight absorption peaks of the proposed metamaterial absorber can maintain almost the same when the insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ possessing the conductivity less than 6000 S/m, and the absorptions will experience a significantly degradation given the conductivity of ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ of 20000 S/m. On the other hand, when ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in the conducting-state as shown in Figs. 7(e)–7(h), the proposed metamaterial absorber will have four absorbing peaks. As the conductivity of ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ increase from 40000 S/m to 200000 S/m, the absorption rates of four peaks will increase dramatically. The proposed metamaterial absorber possesses four perfect absorbing peaks when ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in the conducting state with 200000 S/m.
Fig. 7. Absorption spectra with different conductivities of ${\rm {V}}{{\rm {O}}_{\rm {2}}}$. (a)-(d) With insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ and $\mu _{\mathrm {c}}=0.2 \mathrm {~eV}$, (e)-(f) With conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ and $\mu _{\mathrm {c}}=0.1 \mathrm {~eV}$.
Figure 8 demonstrates absorption behaviors of the proposed metamaterial absorber when interacting with different polarized incidence under different incident angles. As shown in Fig. 8(a), all absorbing peaks can maintain above 90% when the incident angle $\theta$ is scanning from 0$^{\circ }$ to 50$^{\circ }$ for TE-polarized incidence. The absorption rates are still greater than 80% for the first four absorbing peaks, and more than 90% for the last four peaks when the incident angle reaches 65$^{\circ }$. As shown in Fig. 8(b), all the absorbing peaks can maintain greater than 80% under the illuminations of TM-polarized incidence with the scanning angle ranging from 0$^{\circ }$ to 70$^{\circ }$. When ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ is in conducting-state as shown in Fig. 8(c) and Fig. 8(d), all the four absorbing peaks can maintain greater than 80% for both TE and TM-polarized incidence scanning from 0$^{\circ }$ to 60$^{\circ }$. From the overall point of view, Blue-shifts of the absorbing frequencies will become slightly bigger with TM-polarized incidence than that with TE-polarized incidence when the incident angle increases, and the absorption rates look more stable for the TM-polarized incidence. With insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, the proposed metamaterial absorber will trap both polarized incidences perfectly with the incidence angle within 20$^{\circ }$, and absorb more than 90% energies of both polarized incidences with the incidence angle less than 50$^{\circ }$. On the other hand, with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, the proposed metamaterial absorber will have perfect absorptions of both polarized incidences scanning up to 30$^{\circ }$, and can also trap more than 90% energies of both polarized incidences with smaller than 55$^{\circ }$ incidence angle.
Fig. 8. Absorption spectra with different incidences. (a) TE-polarized incidence and (b) TM-polarized incidence illuminated on the metamaterial absorber with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, (c) TE-polarized incidence and (d) TM-polarized incidence illuminated on the metamaterial absorber with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$.
4. Potential realizations and comparisons of the absorption characteristics
Considering the practical implementation, buffer layers of $\mathrm {SiO}_{2}$ are employed to grow ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ on silicon for good switching properties. Similarly, we also include the thin layer of $\mathrm {SiO}_{2}$ to synthesize graphene on silicon. In addition, polytetrafluoroethylene (PTFE) is utilized to encapsulating water layer for the proposed metamaterial absorber, as shown in Fig. 9. The specific structural parameters are $\mathrm {P}_{\mathrm {w}}=38.6 ~\mu \mathrm {m}$, $h_{\mathrm {PTFE}}=h_{\mathrm {PTFE} 1}+h_{\text {water }}+h_{\mathrm {PTFE} 2}$, $h_{\mathrm {PTFE} 1}=0.3 ~\mu \mathrm {m}$, $h_{\mathrm {PTFE} 2}=0.1 ~\mu \mathrm {m}$, $h_{\mathrm {SiO}_{2}}=0.1 ~\mu \mathrm {m}$, $h_{\text {water }}=7 ~\mu \mathrm {m}$ with the rest of the parameters remain the same. We can observe that the PTFE cover and buffer layers of $\mathrm {SiO}_{2}$ will not degrade the original perfect absorptions when $h_{\mathrm {PTFE} 1}=0.3 ~\mu \mathrm {m}$, $h_{\mathrm {SiO}_{2}}=0.1 ~\mu \mathrm {m}$ and $\mathrm {P}_{\mathrm {w}}=38.6 ~\mu \mathrm {m}$. The absorption spectra before and after the encapsulation of the water layer with PTFE as well as the inclusions of $\mathrm {SiO}_{2}$ buffer layers are almost the same for the proposed metamaterial absorbers with both conducting- and insulating- state of ${\rm {V}}{{\rm {O}}_{\rm {2}}}$.
Fig. 9. Absorbing characteristics of the metamaterial absorber with PTFE and $\mathrm {SiO}_{2}$. (a) The schematic demonstration of the absorber structure. Comparisons of absorption spectra of the metamaterial absorbers with insulating-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ (b), conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ (c) for different absorber structures including the PTFE and $\mathrm {SiO}_{2}$.
The detailed comparisons with previous publications concerning the multi-band metamaterial absorbers are demonstrated in Table 1. The absorber in Ref. [4] achieves five absorbing peaks below 2.25 THz using multilayer graphene patches and the first three absorbing peaks are perfect. Ref.[5] using a multi-layer film structure obtains four frequency bands below 1 THz to trap electromagnetic fields with two perfect absorbing peaks. The graphene nano-ribbon metamaterial absorber in Ref. [6] has three absorbing peaks in the frequency range of 10-16 THz, two of which are perfect. These absorbers4-6 are based on Fabry–Pérot resonance to synthesize multi-band absorptions, but neither of them can achieve perfect absorption for all the absorbing bands. On the other hand, Refs. [7–9] are based on resonant graphene patches with different patterns to generate multi-band absorption. More specifically, the absorber in Ref. [7] produces three absorbing peaks in the frequency range of 8-22 THz through specifically prescribed double-layer graphene structure and two of them are perfect. Ref. [8] uses the periodic arrays of multi-layer graphene disks to achieve three perfect absorbing peaks in the frequency range of 2-6 THz. The graphene disks array absorber in Ref. [9] has three absorbing peaks in the frequency range of 0-6 THz, but the absorption rates are below 99%. In addition, different from the present absorbers above [4–9] controlling the absorptions by solely tuning the energy of graphene, our proposal can manipulate the absorption through either handling the Fermi energy imposed over the graphene or re-setting the status of the with thermally controlled strategy. Especially, our proposed multi-band metamaterial absorber can generate more than 8 absorbing peaks in a fixed frequency band, and all absorbing peaks are perfect with more than 99% absorption rate, offering more freedom to perfectly trap the electromagnetic fields.
Table 1. Comparisons of the multi-band absorbersa
5. Conclusions
In conclusion, we proposed a metamaterial absorber with multi-band absorptions in the terahertz regime, consisting of cascaded water layer, graphene layer, ${\rm {V}}{{\rm {O}}_{\rm {2}}}$ layer and gold layer. By changing the temperature and adjust Fermi energy of graphene, the reconfigurable multi-band perfect absorptions can be achieved. When $\mu _{\mathrm {c}}=0.2~ \mathrm {eV}$ and $\mathrm {T}=323.15 \mathrm {~K}$ with insulating state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, the proposed metamaterial absorber can achieve perfect absorptions at 8 frequency points of 0.19 THz, 0.57 THz, 0.96 THz, 1.34 THz, 1.77 THz, 2.1 THz, 2.48 THz and 2.86 THz respectively. When $\mu _{\mathrm {c}}=0.1~ \mathrm {eV}$ and $\mathrm {T}=343.15 \mathrm {~K}$ with conducting-state ${\rm {V}}{{\rm {O}}_{\rm {2}}}$, the proposed metamaterial absorber can achieve perfect absorptions at 4 frequency points of 0.385 THz, 1.157 THz, 1.918 THz and 2.676 THz respectively. Such a perfect absorbing capacity would also be valid for the wide angular illuminations with different polarizations, and we expect the proposed reconfigurable multi-band water-graphene cascade metamaterial perfect absorbers loaded with vanadium dioxide offer additional freedom of extensive applications in the energy harvesting and wave manipulation.
Funding
National Natural Science Foundation of China (61301072, 61671344).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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