We demonstrated a dynamically controlled broadband terahertz (THz) metamaterials absorber, which composed of continuous vanadium dioxide (VO2) film, a silicon dioxide (SiO2) layer, and a structured borophene layer. When VO2 is in its metallic state and the armchair direction of borophene along x axis, the proposed absorber realizes an absorptivity peak value of 100% at 7.2 THz for y polarized normal incidence, and an absorptivity peak value of 79% at 8.9 THz for x polarized normal incidence. It is the anisotropic property of borophene that results in the absorptivity difference for x and y polarization in the whole frequency range. Simulated electric field distribution and surface current oscillation has been extracted to explain the physical mechanism of THz wave absorption. Through modifying the geometric parameters of metamaterials microstructure, the broadband absorption performance can be tailored passively. Additionally, the proposed metamaterials absorber has been actively controlled by manipulating the carrier density of borophene and the conductivity of VO2, respectively. The absorptivity can be switched from 45% to 100% at 7.2 THz by changing the carrier density of borophene, and from 22% to 100% at 7.2 THz by changing the conductivity of VO2. Moreover, the proposed absorber exhibits an excellent operation tolerance for oblique TE and TE polarized incidence from 0° to 60°. This work provides a novel approach to design dynamically controlled broadband THz absorbers, which reveals promising applications in the devices of optoelectronic switches, cloakings, filters, and sensors, etc.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Terahertz (THz) waves are located between microwave and infrared in the electromagnetic spectrum , which belong to the transition area of electronics and photonics. This unique spectral location endows THz waves many advantage properties, such as coherence, transient, broadband, and low photon energy. Benefiting from these properties, THz science and technology exhibit promising applications in the field of sensing , imaging , communications , biomedical science , etc. Due to the dimensional mismatch between molecular diameter and THz wavelength, traditional THz modulators are thick and heavy, which limits the integration of optical systems. On the other hand, metamaterials  provide an alternative approach to ease the above burden. Metamaterials, composed of an array of artificially designed subwavelength microstructures (metallic or dielectric resonators), can manipulate electromagnetic waves at will by reasonable structure design and chemical element selection. Metamaterials has been realized many novel effects which cannot be achieved from traditional materials, such as negative refractive index , invisibility cloaks , and super lenses . The most pivotal example is metamaterials absorber, which exhibits promising applications in the area of imaging , modulation  and detection . Thus, a number of different approaches have been utilized to realize metamaterials absorber, Tao et al. proposed and fabricated a single-band THz metamaterial absorber in 2008 . Subsequently, a variety of terahertz absorbers, including dual-band, multi-band, and broadband absorbers have been [14–16]. The design and fabrication of single-band metamaterials absorber is simple and robust, however, they exhibit drawbacks of frequency-agile and single-functional performance. Dual-band and multi-band metamaterial absorbers exhibit more integrated function, whereas, its design and fabrication are complicated. The broadband metamaterials is robust for the fabrication, nevertheless, its broadband and efficient spectra performance are insensitive to the change of surrounding environment. Most important of all, these absorbers operate in a fixed or limited frequency range. Although the resonant frequency can be tuned by tailoring the geometric parameters of metamaterials resonators passively, it is impossible to modify the resonator structure in real time once it has been fabricated . Recently, two-dimensional materials graphene and black phosphorus (BP) have been considered as a promising candidate to realize active control of metamaterial absorbers [18–23], since they exhibit adjustable optical and electrical property by external stimuli [24–26]. This brings opportunity for the development of dynamically controlled THz metamaterial absorbers. Therefore, dynamically tuned metamaterials absorbers have been realized by exerting adjustable external voltage to modify the conductivity of BP and graphene .
Vanadium dioxide (VO2) experience a reversible phase transition from insulator to metal across the critical temperature near 65-68 ℃ [28–30]. Furthermore, it can also be trigged electrically or optically with fast switching speeds. Structural transition from monoclinic phase to tetragonal phase accompanied not only by drastic conductivity change exceeding four orders of magnitude, but also by remarkable modification of electrical and optical properties at all wavelengths. Thus, VO2-based optoelectronic functional device has been intensively studied to realize active control of electromagnetic wave [31–33]. M. Zhang et al. proposed a terahertz bifunctional absorber based on a graphene-spacer-VO2-spacer-metal metamaterials, its working bandwidth and intensity of narrowband absorption and broadband absorption can be dynamically tuned by tailoring the Fermi energy of graphene and conductivity of VO2 . J. Zhang et al. realized a dynamically controlled THz absorber based on graphene-VO2-metal metamaterials, which can be switched between narrowband and dual-band absorption by changing the conductivity of VO2 . L. Liu et al proposed an electrically actuated metadevice with VO2 film, to realize a switchable reflection at infrared frequency . S. Wang et al. realized an actively controlled broadband THz absorber with VO2 metamaterials . Z. Song et al. proposed a reflective metadevice based on VO2 metamaterials, to realize a switching between broadband and narrowband absorption . And also, J. Liang et al. realized a bandwidth-tunable THz absorber based on diagonally distributed double-sized VO2 disks . Our research group has also carried out research on active metamateials absorber by using VO2, BP, and graphene materials, including dual-controlled switchable broadband terahertz absorber [40,41].
Furthermore, H. Li and J. Yu et al. proposed a series of switchable and tunable THz absorbers based on hybrid VO2/graphene metamaterials. These multifunctional devices can be dynamically switched between tunable dual-band absorber and broadband absorber , as well as switched between tunable broadband/dual-band absorber and broadband electromagnetically induced transparency device . Their research provides a novel strategy to realize multifunctional devices and gains comprehensive attention.
However, graphene exhibits zero or near-zero band gap, which limits its application in the area of high on/off ratios and strong light-matter interaction. Furthermore, there are also limitations to the practical application of BP, because it can be inevitably oxidized in the air . Recently, a novel two-dimensional materials borophene attracts increasing attention [44,45], because it exhibits excellent property of high carrier density, superior anisotropy and metallicity. Compared with BP, the carrier density of borophene (4.3 × 1015 cm-2) is higher than that of BP (theoretical maximum value is 2.6 × 1014 cm-2) . In addition, borophene is almost non-oxidized in the air, which surmounts the shortcoming of BP and expands the application area of two-dimensional materials. Additionally, borophene exhibits anisotropic property between the armchair and zigzag direction. The carrier density of borophene can be modified by applying voltage or chemical doping, realizing a dynamically modification for the conductivity of borophene [47,48]. Liu et al. realized anisotropic localized surface plasmons in borophene absorber, the absorption of this metamaterials reach 50% without using metal mirror. Furthermore, the above absorption can be enhanced to 100% by adding a metal layer . Thus, metal plate were always applied in the conventional borophene metamaterials absorbers to eliminate transmission, however, the metal plate limits the dynamic tuning range of resonance frequency. The hybrid metamaterials absorber composed of borophene and VO2 structure can improve the modulation depth and tuned frequency range.
In this paper, we proposed a tunable broadband THz absorber based on borophene metamaterials and continuous VO2 film in the THz band, to develop an actively dual-controlled absorber. The absorption of broadband absorber can be dynamically tuned by changing the carrier density of borophene and conductivity of VO2. The absorption physical mechanism has been analyzed based on the electric field distribution and the surface current oscillation at the absorption frequencies. Moreover, the proposed absorber exhibits a robust absorption performance for a broad incident angle (0°-60°). The proposed broadband absorber is simple in design, easy to process, and exhibits promising application prospects.
2. Structure design and method
Figure 1 shows the schematic of proposed THz metamaterials absorber, panel (a) is the perspective view of the unit cell configuration, from bottom to top are continuous VO2 layer, SiO2 spacer, borophene ring layer, and ion-gel layer, respectively. The thickness of each layer is h1 = 0.1 μm, h3 = 6 μm, h4 = 0.5 μm, respectively. Borophene ring unit cells are arranged in square array with lattice period P = 2 μm as shown in panel (b), the radius of outer and inner circle of borophene ring are r1 = 0.9 μm and r2 = 0.6 μm. The thickness of borophene ring layer is h2 = 0.0003 μm, with armchair direction along x axis as shown in panel (c). We employed an ion-gel gating technique to modulate the carrier density and Femi energy of borophene ring by manipulating the external voltage VB and VT [49,50]. On the other hand, the conductivity of VO2 can be independently modulated by using the bottom external circuit . Through applying an external current IVO2, the bottom metal wires generate an effect of localized Joule heat, which leads to the phase transition of VO2 film and avoids the property disturbance of other materials. The proposed sample can be fabricated by lithography and deep reactive ion etching technology.
In this work, α structured borophene was applied to construct metamaterials absorber, its conductivity can be described by Drude model :
The relative permittivity of VO2 in the THz range was described by Drude model :
Commercially available software CST Microwave Studio was applied to design the proposed metamaterials absorber and optimize its spectra performance. Permittivity spectrum of borophene can be calculated from Eqs. (1), (2), and (3) with carrier density range from 1.0×1019 m-2 to 10×1019 m-2. And then, the permittivity spectra were imported into CST software to construct a borophene material. Finally, we construct the metamaterials absorber with borophene ring to carry out electromagnetic simulation. On the other hand, the similar operation has been performed for the VO2 film. Its permittivity spectrum can be calculated from formula (4) with conductivity range from 10 S/m to 2×105 S/m. And then, they were imported into CST software to construct a VO2 material and VO2 microstructure to carry out electromagnetic simulation. In the simulation, periodic boundary conditions were adopted in the lateral directions of metamaterials unit cell, and it was illuminated by the normal incidence of THz plane wave. Furthermore, open boundary conditions were applied in the propagating direction. The absorptivity of metamaterials absorber has been calculated from this formula A = 1 - |S11|2 - |S21|2, where S11 and S21 represents the reflection and transmission coefficient, respectively.
3. Results and discussion
First of all, we investigate the influence of carrier density on the permittivity of borophene along the x and y direction, respectively. Figure 2 shows the frequency dependence of real and imaginary parts of borophene permittivity with different carrier density. For a specific carrier density as shown in panels (a) and (b), the real and imaginary part of permittivity is increasing and decreasing accordingly with the frequency ranging from 2 THz to 10 THz. Furthermore, the line shape of real and imaginary spectra in the whole frequency is decreasing and increasing respectively as the carrier density changing from 1 × 1019 m-2 to 10 × 1019 m-2. In addition, the maximum and minimum values of real and imaginary parts of borophene permittivity along x and y directions are different. Thus, it can be predicted from the Eqs. (1) and (2) that the surface conductivity and permittivity of borophene can be dynamically tuned via manipulating its carrier densities. Compared with traditional metal materials, borophene exhibits significant advantage in designing active THz metamaterials devices through electric excitation.
Next, we investigate the absorption performance of metamaterials absorber for y and x polarized normal incidence. Figure 3 reveals the spectral response of the proposed metamaterials with carrier density set to be ns = 4.3 × 1019 m-2. The blue and red curve denote that the armchair and zigzag direction of borophene along x axis, respectively. In this case, VO2 is in its metallic state with conductivity set to be σvo2 = 2 × 105 S/m, it can be considered as a total reflection layer with zero transmission. Figure 3(a) reveals the absorptivity spectra for y polarized incidence with the armchair and zigzag direction of borophene along x axis. It can be observed that, the absorptivity peak value and full width at half maximum (FWHM) reach 100% and 5.2 THz respectively for the armchair direction of borophene along x axis. However, for the armchair direction of borophene along x axis, its absorptivity peak value and FWHM are 79% and 5.4 THz respectively. It should be noted that the absorptivity spectra with the armchair direction along x axis is higher than that with the zigzag direction along x axis. Similarly, it can be observed from Fig. 3(b) that the absorptivity spectra obtained with zigzag direction along x axis is higher than that with armchair direction along x axis for x polarized normal incidence. At the same time, we observed that the absorptivity curves in Fig. 3(a) and 3(b) are interchanged, which results from the fourfold rotational symmetry of the borophene ring structure we designed. Therefore, in the following analysis we will only study the absorptivity spectra of armchair direction for y polarized normal incidence for simplicity. The proposed metamaterial absorber will contribute to the design of sensors and detectors. However, it also exhibits a disadvantage that perfect absorption at the same frequencies for two orthogonal polarizations is almost impossible.
In order to illustrate the physical mechanism of resonant absorption of this broadband absorber for y polarized normal incidence, Fig. 4 provides the electric field distribution (Ey) and magnetic field distribution (Hz) at 5.3 THz, 7.2 THz and 10 THz, respectively. The instantaneous directions of currents are marked by white lines with arrows as shown in panels (d-f). It can be seen from Fig. 4(a) and 4(b) that, the electric field is mainly distributed on the upper and lower sides of the ring due to the localized surface plasmon resonance of borophene, which forms the electric dipole resonance along y direction. At the same time, Figs. 4(d) and 4(e) reveals that the magnetic field and surface currents are symmetrically resonant along y direction with the maximum amplitude at the middle of each branch. In this situation, the localized energy was dissipated by borophene ring and VO2 film, leading to the perfect absorption as shown in Fig. 3(a). In addition, the absorptivity of proposed metamaterials absorber is only about 24% at 10 THz as shown in Fig. 3. As a result, Figs. 4(c) and 4(f) reveal that the electric field intensity and surface current oscillation are weak at the absorption frequency of 10 THz. Thus, microstructural resonance plays a critical role in the absorption performance of proposed metamaterials absorber.
It can be conclude that, the combination of sandwich structure (including metal plate, dielectric spacer, and metamaterials structure) and isotropic metamaterials can realize an absorber with broadband, high-efficiency, and polarization-independent property. Most important of all, anisotropic materials can be used to construct a metamaterials absorber with an absorption difference in the two orthogonal directions, though the metamaterials unit cell and its configuration are isotropic.
Absorption performance of proposed broadband absorber can be passively modulated by tailoring the geometric parameters of metamaterials microstructures. Absorptivity spectra with different inner radius r2 have been provided in Fig. 5(a). When the inner radius r2 set to be 0.1 μm, the absorptivity spectra exhibit a broadband performance, with the peak value reaches 62%. Then, as r2 increases from 0.2 μm to 0.5 μm, the FWHM and peak value of absorptivity spectra is decreasing and increasing respectively. Finally, the FWHM and peak value reach 5.2 THz and 100% with r2 set to be 0.6 μm. At the same time, the resonance frequency of absorption peak reveals a slight red shift. In addition, the influence of dielectric layer thickness h3 on the absorption performance was also studied. As shown in Fig. 5(b), the absorptivity curve is gradually enhanced with h3 increases from 1 μm to 6 μm. The FWHM and peak value reach 5.2 THz and 100% eventually with h3 set to be 6 μm. Thus, the absorption performance of proposed metamaterials absorber can be passively tailored by modifying the parameter of r2 and h3.
When the VO2 in its metallic state with conductivity value σvo2 set to be 2 × 105 S/m, Fig. 6 reveals the absorptivity and reflectivity spectra for y polarized normal incidence with carrier density ns as a parameter. The carrier density ns determines the permittivity of borophene, as well as the interaction between THz wave and borophene. When the carrier density increases from ns = 1 × 1019 m-2 to ns = 10 × 1019 m-2, the absorption frequency of the absorptivity spectra are blue shifts as shown in panel (a). At the same time, absorption performance of proposed broadband absorber was increased firstly and then decreased. When ns = 4.3 × 1019 m-2, the peak value of absorptivity reach the maximum absorption from 5.3 THz to 7.2 THz, in this situation perfect absorption has been achieved at 7.2 THz. Therefore, active control of absorption performance for the broadband absorber can be realized by changing the carrier density ns of borophene. In addition, for ns = 1.0 × 1019 m-2, it can be observed that the smallest reflectivity corresponding to the largest absorptivity as shown in panel (b), in this situation the absorber can be considered in the “off” state. As ns = 4.3 × 1019 m-2, the absorptivity of the proposed absorber approaching 100%, in this case it can be regarded as in the “on” state.
Benefitting from the insulator-to-metal phase transition effect excited by the external stimuli, VO2 film experiences drastic conductivity change exceeding four orders of magnitude. Figure 7 reveals simulated absorptivity, reflectivity and transmissivity spectra of proposed absorber for y polarized normal incidence with VO2 conductivity σvo2 as a parameter. When σvo2 set to be 10 S/m, VO2 is in its insulating state, the proposed absorber exhibits a low absorptivity below 22% in the whole frequency range as shown in panel (a). Whereas, it exhibits high reflectivity and transmissivity in the concerned frequency range from 5.3 THz to 7.2 THz as shown in panels (b) and (c), respectively. With the σvo2 increases from 2 × 103 S/m to 7 × 104 S/m, the reflectivity and transmissivity decrease gradually, whereas the peak value and FWHM of absorptivity spectra are increasing and decrease accordingly. Further increase σvo2 to 2 × 105 S/m, VO2 is in its metallic state, the reflectivity and transmissivity of metamaterials absorber were attenuated to zero in the concerned frequency range. Most important of all, the peak value and FWHM of the absorptivity spectra reach 100% and 5.2 THz respectively, which approaching perfect absorption. These results demonstrate that the absorptivity, reflectivity and transmissivity of proposed metamaterials absorber can be dynamically tuned by changing the conductivity of VO2.
Furthermore, the dependence of absorptivity spectra on the thicknesses of metallic-state VO2 has also been studied. When VO2 in its metallic state with σvo2 set to be 2 × 105 S/m, Fig. 7(d) shows the absorptivity spectra of the proposed metamaterials absorber with VO2 thicknesses h4 as a parameter. Simulated results indicate that the resonance frequency of broadband absorption lies between 5.3 THz and 7.2 THz. While the absorption intensity is increasing greatly in this concerned frequency range. In this situation, the strong absorption effect mainly from the suppressed transmission by the increasing thickness of VO2 film.
Finally, we also studied the absorption performance of proposed absorber under oblique incidence for both TE and TM polarized incidence. Figure 8(a) reveals the simulated absorptivity spectra with incident angle range from 0° to 80° for TE polarized oblique incidence. It can be observed that the absorption spectra stay nearly the same for an incidence angle from 0° to 60°, since the resonant absorption wavelength were only determined by the radius and the Fermi energy of the borophene ring. Considering the high symmetry of our proposed borophene ring structure, the influence of incidence angle was expected to be weak. However, at a large angle of incidence from 60° to 80°, the absorption spectra were split from broadband line into dual-band curve, because the equivalent period of metamaterials unit cell along the propagation direction is stretched in this situation. On the other hands, Fig. 8(b) provides the absorptivity spectra with incident angle range from 0° to 80° for TM polarized oblique incidence. In this case, the absorption spectra also remain nearly the same for an incidence angle from 0° to 60°. Whereas, the broadband absorption turn to narrow and weak with the incident angle increase from 60° to 80°, due to the change of equivalent period of metamaterials unit cell along propagation direction. Therefore, the proposed absorber exhibits an excellent operation tolerance for oblique TM and TE polarized incidence.
In conclusion, we have realized an actively controlled tunable broadband terahertz metamaterials absorber based on continuous VO2 and SiO2 layer, as well as structured borophene layer. Simulated electric field distribution and surface current oscillation has been extracted to elucidate the physical mechanism for THz wave absorption. The broadband absorption performance can be tailored passively through modifying the geometric parameters of metamaterials microstructure. And also, the proposed metamaterials absorber can be dynamically manipulated by manipulating the carrier density of borophene and conductivity of VO2, respectively. The absorptivity can be switched from 45% to 100% at 7.2 THz via changing the carrier density of borophene, and from 22% to 100% at 7.2 THz by changing the conductivity of VO2. Moreover, the proposed absorber exhibits a robust absorption performance for a broad incident angle range (0°-60°). This work provides a novel approach to design dynamically controlled broadband THz absorber, which reveals promising applications in the devices of optoelectronic switch, cloaking, filter, and sensor, etc.
National Natural Science Foundation of China (61775123, 61875106); Key Research and Development Program of Shandong Province (2019GGX104039, 2019GGX104053); National Key Research and Development Program of China (2017YFA0701000).
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
1. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50(3), 910–928 (2002). [CrossRef]
2. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef]
3. C. M. Watts, D. Shrekenhamer, and J. Montoya, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014). [CrossRef]
4. A. J. Fitzgerald, E. Berry, and N. N. Zinov’Ev, “Catalogue of human tissue optical properties at terahertz frequencies,” J. Biol. Phys. 29(2/3), 123–128 (2003). [CrossRef]
5. M. Naftaly, N. Vieweg, and A. Deninger, “Industrial applications of terahertz sensing: state of play,” Sensors 19(19), 4203 (2019). [CrossRef]
6. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef]
7. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]
8. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef]
9. X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008). [CrossRef]
10. N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009). [CrossRef]
11. F. Hu, Q. Rong, Y. Zhou, T. Li, W. Zhang, S. Yin, Y. Chen, J. Han, G. Jiang, P. Zhu, and Y. Chen, “Terahertz intensity modulator based on low current controlled vanadium dioxide composite metamaterial,” Opt. Commun. 440(1), 184–189 (2019). [CrossRef]
12. Q. Y. Wen, Y. S. Xie, H. W. Zhang, Q. H. Yang, Y. X. Li, and Y. L. Liu, “Transmission line model and fields analysis of metamaterial absorber in the terahertz band,” Opt. Express 17(22), 20256–20265 (2009). [CrossRef]
13. 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), 7181–7188 (2008). [CrossRef]
14. Y. Q. Ye, Y. Jin, and S. L. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010). [CrossRef]
15. L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S. N. Luo, A. J. Taylor, and H. T. Chen, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Opt. Lett. 37(2), 154–156 (2012). [CrossRef]
16. L. Cong, S. Tan, and R. Yahiaoui, “Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: A comparison with the metasurfaces,” Appl. Phys. Lett. 106(3), 031107 (2015). [CrossRef]
17. B. X. Wang, X. Zhai, and G. Z. Wang, “A novel dual-band terahertz metamaterial absorber for a sensor application,” J. Appl. Phys. 117(1), 2075 (2015). [CrossRef]
18. M. Amin, M. Farhat, and H. Bağcı, “An ultra-broadband multilayered graphene absorber,” Opt. Express 21(24), 29938–29948 (2013). [CrossRef]
19. A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013). [CrossRef]
20. Y. M. Qing, H. F. Ma, and T. J. Cui, “Tailoring anisotropic perfect absorption in monolayer black phosphorus by critical coupling at terahertz frequencies,” Opt. Express 26(25), 32442–32450 (2018). [CrossRef]
21. G. Yao, F. R. Ling, J. Yue, C. Y. Luo, J. Ji, and J. Q. Yao, “Dual-band tunable perfect metamaterial absorber in the THz range,” Opt. Express 24(2), 1518–1527 (2016). [CrossRef]
22. L. Qi, C. Liu, and S. Shah, “A broad dual-band switchable graphene-based terahertz metamaterial absorber,” Carbon 153, 179–188 (2019). [CrossRef]
23. M. Faraji, M. K. Moravvej-Farshi, and L. Yousefi, “Tunable THz perfect absorber using graphene-based metamaterials,” Opt. Commun. 355(15), 352–355 (2015). [CrossRef]
24. F. Bonaccorso, Z. Sun, and T. Hasan, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]
25. A. K. Geim and K. S. Novoselov, “The electronic properties of graphene,” Rev. Mod. Phys. 244(11), 4106–4111 (2010). [CrossRef]
26. A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
27. S. Q. Wang, S. L. Li, Y. G. Zhou, J. P. Huang, Q. Ren, J. M. Zhuo, and Y. J. Cai, “Enhanced terahertz modulation using a plasmonic perfect absorber based on black phosphorus,” Appl. Opt. 59(29), 9279–9283 (2020). [CrossRef]
28. Q. Y. Wen, H. W. Zhang, Q. H. Yang, Y. S. Xie, K. Chen, and Y. L. Liu, “Terahertz metamaterials with VO2 cut-wires for thermal tunability,” Appl. Phys. Lett. 97(2), 597 (2010). [CrossRef]
29. Y. Guo, Y. Zhang, and X. Chai, “Tunable broadband, wide angle and lithography-free absorber in the near-infrared using an ultrathin VO2 film,” Appl. Phys. Express 12(7), 071005 (2019). [CrossRef]
30. P. U. Jepsen, B. M. Fischer, and A. Thoman, “Metal-insulator phase transition in a VO2 thin film observed with terahertz spectroscopy,” Phys. Rev. B 74(20), 205103 (2006). [CrossRef]
31. Y. Zhao, Y. Zhang, Q. Shi, S. Liang, W. Huang, W. Kou, and Z. Yang, “Dynamic photoinduced controlling of the large phase shift of terahertz waves via vanadium dioxide coupling nanostructures,” ACS Photonics 5(8), 3040–3050 (2018). [CrossRef]
32. R. Zhou, T. Jiang, and Z. Peng, “Tunable broadband terahertz absorber based on graphene metamaterials and VO2,” Opt. Mater. 114, 110915 (2021). [CrossRef]
33. T. T. Lv, Y. X. Li, and H. F. Ma, “Hybrid metamaterial switching for manipulating chirality based on VO2 phase transition,” Sci. Rep. 6(1), 23186 (2016). [CrossRef]
34. M. Zhang and Z. Y. Song, “Terahertz bifunctional absorber based on a graphene-spacer-vanadium dioxide-spacer-metal configuration,” Opt. Express 28(8), 11780–11788 (2020). [CrossRef]
35. J. Zhang, X. Yang, and X. Huang, “Dynamically controllable terahertz absorber based on a graphene-vanadium dioxide-metal configuration,” Superlattices Microstruct. 150, 106809 (2021). [CrossRef]
36. L. Liu, L. Kang, T. S. Mayer, and D. H. Werner, “Hybrid metamaterials for electrically triggered multifunctional control,” Nat. commun. 7(1), 1–8 (2016). [CrossRef]
37. S. X. Wang, C. F. Cai, M. H. You, F. Y. Liu, M. H. Wu, S. Z. Li, H. G. Bao, L. Kang, and D. H. Werner, “Vanadium dioxide based broadband THz metamaterial absorbers with high tunability: simulation study,” Opt. Express 27(14), 19436–19447 (2019). [CrossRef]
38. Z. Y. Song, A. P. Chen, and J. H. Zhang, “Terahertz switching between broadband absorption and narrowband absorption,” Opt. Express 28(2), 2037–2044 (2020). [CrossRef]
39. J. R. Liang, K. Zhang, D. Y. Lei, L. Z. Yu, and S. L. Wang, “Bandwidth-tunable THz absorber based on diagonally distributed double-sized VO2 disks,” Appl. Opt. 60(11), 3062–3070 (2021). [CrossRef]
40. T. L. Wang, Y. P. Zhang, H. Y. Zhang, and M. Y. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369–386 (2020). [CrossRef]
41. T. L. Wang and L. Z. Qu, “Tunable broadband terahertz metamaterial absorber using multi-layer black phosphorus and vanadium dioxide,” J. Phys. D: Appl. Phys. 53(14), 145105 (2020). [CrossRef]
42. H. Li and J. Yu, “Bifunctional terahertz absorber with a tunable and switchable property between broadband and dual-band,” Opt. Express 28(17), 25225–25237 (2020). [CrossRef]
43. H. Li, W. H. Xu, Q. Cui, Y. Wang, and J. Yu, “Theoretical design of a reconfigurable broadband integrated metamaterial terahertz device,” Opt. Express 28(26), 40060–40074 (2020). [CrossRef]
44. Y. Huang, S. N. Shirodkar, and B. I. Yakobson, “Two-dimensional boron polymorphs for visible range plasmonics: a first-principles exploration,” J. Am. Chem. Soc. 139(47), 17181–17185 (2017). [CrossRef]
45. T. Liu, C. Zhou, and S. Xiao, “Tailoring anisotropic absorption in a borophene-based structure via critical coupling,” Opt. Express 29(6), 8941–8950 (2021). [CrossRef]
46. Y. J. Cai, K. D. Xu, N. X. Feng, R. R. Guo, H. J. Lin, and J. F. Zhu, “Anisotropic infrared plasmonic broadband absorber based on graphene-black phosphorus multilayers,” Opt. Express 27(3), 3101–3112 (2019). [CrossRef]
47. S. A. Dereshgi, Z. Z. Liu, and K. Aydin, “Anisotropic localized surface plasmons in borophene,” Opt. Express 28(11), 16725–16739 (2020). [CrossRef]
48. A. Onyow and W. J. Cad, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(28), 182–194 (2017). [CrossRef]
49. S. Y. Xiao, T. L. Wang, Y. B. Xu, C. H. Xu, and X. C. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016). [CrossRef]
50. Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015). [CrossRef]
51. Z. Song, Y. Deng, Y. Zhou, and Z. Liu, “Terahertz toroidal metamaterial with tunable properties,” Opt. Express 27(4), 5792–5797 (2019). [CrossRef]
52. S. X. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 1–8 (2017). [CrossRef]