## Abstract

In this paper, we present an active controllable terahertz absorber with dual broadband characteristics, comprised by two diagonal identical patterns of vanadium dioxide in the top layer of the classical three-layer structure of metamaterial perfect absorbers. Simulation results show that two bandwidths of 80% absorption are 0.88 THz and 0.77 THz from 0.56 to 1.44 THz and 2.88 to 3.65 THz, respectively. By using thermal control to change the conductivity of the vanadium dioxide, absorptance can be continuously adjusted from 20% to 90%. The impedance matching theory is introduced to analyze and elucidate the physical mechanism of the perfect absorption. Field analyses are further investigated to get more insight into the physical origin of the dual broadband absorption. In addition, incident polarization insensitivity and wide-angle absorption are also demonstrated. The proposed absorber promises diverse applications in terahertz regime, such as imaging, modulating, sensing and cloaking.

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

## 1. Introduction

Metamaterial perfect absorbers (MPAs) have always been one of the hottest research branches of terahertz (THz) devices due to its extensive applications, such as photovoltaic cells [1,2], thermal emitters [3,4] and stealth technology [5,6]. MPAs are generally designed as three-layer structures with the top metal patterns and a bottom metal ground plane separated by a middle dielectric layer [7,8]. By designing different metal patterns and optimizing the thickness of the dielectric layer, the real and the imaginary parts of the effective permittivity $\varepsilon (\omega )$ and permeability $\mu (\omega )$ can be tailored to adjust the effective impedance of MPAs [9]. When the effective impedance, defined as $Z = \sqrt {{{\mu (\omega )} \mathord{\left/ {\vphantom {{\mu (\omega )} {\varepsilon (\omega )}}} \right.} {\varepsilon (\omega )}}}$, matches to the impedance ${Z_0}$ of the free space, the reflection of MPAs reaches minimum value as 0. At the same time, the bottom metal ground plane will block the propagation of the electromagnetic wave with the thickness more than the skin depth, resulting in zero transmission. According to $\textrm{A = 1 - R - T}$, these make the perfect absorption [10,11].

As is well known, two drawbacks of THz MPAs greatly hamper practical applications, *i.e.*, the fixed operating frequency range and the narrow working bandwidth [12–14]. In the past few years, a large number of researchers have been dedicated to realizing THz MPAs with the reconfigurable characteristics or the broadband absorption. On one hand, in order to realize the reconfigurable characteristics, many tunable hybrid MPAs with graphene, semiconductors, liquid crystal, and vanadium dioxide (VO_{2}) have been reported [15–21]. Among these materials, VO_{2}, as a phase transition material, has advantages of the fast response [22], large modulation depth [23], and multiple modulation methods, such as optical pumping [24], thermal control [25,26] and extra electric fields [27,28]. Therefore, it is widely used in THz active controllable devices. On the other hand, in order to obtain the broadband or multiband absorption, two common methods are developed. One method involves combining similar resonators with different size in one unit cell [29–32], and the other one is stacking multiple layers of the resonators separated by dielectric spaces with different thicknesses [33–35]. However, the designed multi-band and broadband absorbers based on these methods are complicated for fabrication and difficult to evolve into active controllable devices. Recently, several MPAs with both dual band and broadband characteristics have also been reported. For example, in 2013, Liu *et al.* proposed a dual broadband perfect absorber based on a hybrid plasmonic-photonic microstructure in near-infrared band, the corresponding relative bandwidths of above 90% absorption were 13% and 16% [36]. In 2015, Kim *et al*. reported a THz absorber utilizing metal-dielectric-multilayer truncated cones, the relative bandwidths of over 90% absorption were 21% and 22%, respectively [37]. In 2018, Hu *et al.* presented a dual broadband absorber with six-layer structure, the bandwidths with the absorption above 95% were 0.5 THz and 0.6 THz in the frequency ranges of 1.4-1.9 THz and 4.5-5.1 THz. And the corresponding relative bandwidths were 30% and 12.5%, respectively [38]. Although there are many creative designs and great progress in the perfect absorbers, the properties of the broad bandwidth and actively control unfortunately still have a distance to reach the expectations for practical applications.

In this paper, we propose a dual broadband THz metamaterial absorber with continuous tunability, which constituted by two identical VO_{2} patterns arranged diagonally in the top layer of classical metal-dielectric-metal structure of MPAs. By inducing the insulator-to-metal transition (IMT) of VO_{2} under thermal control, the absorptances of both bands can be continuously adjusted. The physical mechanism of the perfect absorption is investigated by the impedance matching theory. And the field analyses are further discussed to get more insight into the physical origin of the dual broadband absorption. In addition, the absorption performances with different incident angles and polarization angles are also investigated. This dual broadband MPA promises great application prospects in THz field.

## 2. Structure design and simulation methods

The unit cell of the proposed THz absorber consists of three layers and is presented in Fig. 1. The top layer is two identical 0.1-µm-thick VO_{2} patterns with an interval of 5 µm. The middle layer is 35-µm-thick silicon dioxide (SiO_{2}) with the relative permittivity ${{\varepsilon}_\textrm{d}} = \textrm{3}\textrm{.9 + 0}\textrm{.03}i$. The bottom is an aluminum ground plane with the thickness of 0.2 µm, which is larger than skin depth to insure no transmission. The period of the unit cell is $\textrm{P} = 180$ µm. And the structure dimensions of a single VO_{2} pattern are listed as follows: ${\textrm{P}_\textrm{1}} = 80$ µm, $\textrm{w = 20}$ µm, $\textrm{h = 10}$ µm.

In order to effectively investigate the electromagnetic responses of the absorber, the simulations are performed by CST Microwave Studio 2015. The open boundary condition is applied in the z direction and the unit cell boundary conditions are applied in the x and y directions. Adaptive tetrahedral mesh refinement is used to improve the simulation precision. The optical properties of VO_{2} in THz range is described by the Drude model [39,40], which is expressed by $\varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{({\omega ^2} + i\gamma \omega )}}$, where is the permittivity at high frequency and $\gamma = 5.75 \times {10^{13}}\;\textrm{rad/s}$ is the collision frequency. The plasma frequency ${\omega _\rho }$ can be approximately described as ${\omega _p}^2(\sigma ) = \frac{\sigma }{{{\sigma _0}}}{\omega _p}^2({\sigma _0})$ with ${\sigma _0} = 3 \times {10^5}\;\textrm{S/m}$ and ${\omega _p}({\sigma _0}) = 1.4 \times {10^{15}}\;\textrm{rad/s}$. In this paper, ${\varepsilon _\infty }\textrm{ = 12}$ VO_{2} is modeled as a material with the permittivity of 9 in the insulator phase, and that with a conductivity of $\textrm{2} \times \textrm{1}{\textrm{0}^\textrm{5}}\;\textrm{S/m}$ in the metal phase []. The absorptance can be obtained by $A(\omega ) = 1 - R(\omega ) - T(\omega ) = 1 - |{S_{11}}(\omega ){|^2} - |{S_{21}}(\omega ){|^2}$, where $A(\omega )$, $T(\omega )$, and $R(\omega )$ are absorptance, transmittance, and reflectance, respectively. ${S_{11}}(\omega )$ and ${S_{21}}(\omega )$ are the scattering parameters of the reflection and transmission retrieved from the simulation. Due to the existence of the bottom metal ground plane, the transmittance $T(\omega )$ is 0. Therefore, the absorptance is simplified as $A(\omega ) = 1 - |{S_{11}}(\omega ){|^2}$.

## 3. Results and discussions

The absorption spectrums for both the transverse-electric (TE) polarization (the electric field is parallel to x-axis) and transverse-magnetic (TM) polarization (the electric field is parallel to the y-axis) under the normal incidence are displayed in Fig. 2(a), when VO_{2} patterns are in the metal phase. The results show that the absorption spectrums for TE and TM polarizations are coincident. There are two broad absorption bands, and the bandwidths with absorption over 80% are as wide as 0.88 THz and 0.77 THz in the frequency range of 0.56-1.44 THz and 2.88-3.65 THz. And there are also four near-perfect absorption peaks located at ${f_1} = 0.704\;\textrm{THz}$, ${f_2} = 1.332\;\textrm{THz}$, ${f_3} = 2.936\;\textrm{THz}$, and ${f_4} = 3.508\;\textrm{THz}$, respectively. Due to the continuous metal ground plane at the bottom, the transmission is zero. Figure 2(b) is the color map of the absorption spectra with different polarization angles. It is obvious that the designed absorber has an excellent polarization-insensitive characteristic, which is attributed to the C4 rotational symmetry of the structure [41].

By using thermal control to induce the IMT of VO_{2}, absorptances of both broad bands can be continuously adjusted. Figures 3(a) and 3(b) present the reflection and absorption spectrums with different conductivities of VO_{2} under normal incidence. The results show that the corresponding absorptances increase from 20% to 90% for the first broadband and from 43% to 85% for the second broadband, when the conductivity changes from $2 \times \textrm{1}{\textrm{0}^2}\;\textrm{S/m}$ to $2 \times \textrm{1}{\textrm{0}^5}\;\textrm{S/m}$. The physical mechanism of the continuous modulation is mainly caused by the variation of permittivity of VO_{2}. Figures 3(c) and 3(d) display the real and imaginary parts of the permittivity of VO_{2} as a function of different conductivities. It is obvious that the real parts under different conductivities are much smaller than that of the imaginary parts. The real parts of the permittivity mainly affect the resonance frequency, and the imaginary parts mainly affect the loss. Thus, the positions of two broad bands keep almost unchanged, while the intensity of the absorption spectra changes significantly.

The impedance matching theory is introduced to elucidate the physical mechanism of the perfect absorption [42,43]. When the THz wave is under normal incidence, the absorptance and the relative impedance can be described as

*Z*and ${Z_0}$ are the effective impedances of the absorber and the free space, respectively. And ${Z_r} = {Z \mathord{\left/ {\vphantom {Z {{Z_0}}}} \right.} {{Z_0}}}$ is the relative impedance between the absorber and the free space. According to Eq. (1), when the impedance of the absorber matches to that of the free space,

*i.e.*, ${Z_r} = {Z \mathord{\left/ {\vphantom {Z {{Z_0}}}} \right.} {{Z_0}}} = 1$, the absorptance reaches the maximum. Figure 4 shows the real and imaginary parts of the relative impedance ${Z_r}$ with different conductivities of VO

_{2}. It is obvious that the real parts gradually approach to 1 and the imaginary parts gradually approach to 0 in the frequency range of 0.56-1.44 THz and 2.88-3.65 THz with the increasing of the conductivity, which means the impedance between the absorber and the free space gradually matched. Finally, when the VO

_{2}patterns are in the metal phase ($\sigma = 2 \times \textrm{1}{\textrm{0}^5}\;\textrm{S/m}$), the highest absorption and widest working bandwidth are obtained.

The roles of the dielectric layer and VO_{2} patterns on the absorption performance are also investigated, respectively. Figure 5(a) shows the reflection, transmission and absorption spectrums of the dielectric layer. The result shows that the absorption of the dielectric is lower than 20%. And there are two reflection peaks located at $1.08\;\textrm{THz}$ and $3.25\;\textrm{THz}$, respectively. The frequency interval of them is $\Delta f = 2.17\;\textrm{THz}$. Figure 5(b) shows that when a metal ground plane is added to the bottom, a dual-band absorption is obtained with the frequencies located at $1.21\;\textrm{THz}$ and $3.3\;\textrm{THz}$, respectively. Compared with Fig. 5(a), the absorption is enhanced. The reason for this phenomenon is the Fabry-Perot resonance in the dielectric layer, and the frequency interval between adjacent peaks can be written as [44]

*n*and

*d*are the refractive index and the thickness of the dielectric layer, respectively. According to Eq. (3), $n = \sqrt {{\varepsilon _d}}$, $d = 35$ µm, the calculated frequency interval is $\Delta f = 2.17\;\textrm{THz}$, which is consistent with the simulation results. In order to further enhance the absorption, a single VO

_{2}pattern in the metal phase is placed on the top to compose a classic MPAs unit cell structure, as shown in Fig. 5(c). It is obvious that the absorption has been further enhanced, because the impedance further matched with that of the free space. When two identical VO

_{2}patterns in the metal phase are placed on the top together, the higher absorption and the wider bandwidth are obtained, as displayed in Fig. 5(d). According to the relative impedance presented in Fig. 4, the impedance between the absorber and the free space has matched, which leads to the high absorption and the wide working bandwidth. It should be noted that the relatively large periodicity of the unit cell and the broad frequency range will lead to higher-order diffraction modes. However, there are two reasons why the higher-order modes are not considered in our calculations. First, they carry rather limited power, and the second is that they usually occur at a higher frequency, while both two reflection peaks are located in the lower frequency range. Therefore, they have little influences on the calculation results.

The influences of the losses in the dielectric and the thicknesses of VO_{2} patterns on the absorption performance are also investigated. As shown in Fig. 6(a), the variation of the tangential losses of the dielectric layer has no impact on the first absorption band but a little impact on the second absorption band, which means the main reason for the broadband absorption is the well-designed structure instead of the loss of the dielectric. Figure 6(b) shows that the absorption spectrums are very sensitive to the thickness of VO_{2}. This can be explained by the impedance matching theory. The effective impedance *Z* of the absorber depends on the effective permittivity $\varepsilon (\omega )$ and permeability $\mu (\omega )$. The effective permittivity $\varepsilon (\omega )$ is determined by different VO_{2} patterns, and the effective permeability $\mu (\omega )$ is determined by the coupling effects between VO_{2} and metal ground plane. When the thickness of VO_{2} changes, different coupling effects between the top and bottom layers lead to the variation of the permeability $\mu (\omega )$. According to $Z = \sqrt {{{\mu (\omega )} \mathord{\left/ {\vphantom {{\mu (\omega )} {\varepsilon (\omega )}}} \right.} {\varepsilon (\omega )}}}$ and ${Z_r} = {Z \mathord{\left/ {\vphantom {Z {{Z_0}}}} \right.} {{Z_0}}}$, the impedance between the absorber and the free space will change, which results in different absorption spectrums.

To get more insight into the physical origin of the dual broadband absorptions, the power loss distributions on xoy and xoz planes at four near-perfect absorption peaks for TE polarization are presented in Fig. 7. For the resonant frequencies ${f_1}$ and ${f_2}$, energy is mainly concentrated at different parts on the surface of VO_{2} patterns. For frequency ${f_3}$, the energy is not only concentrated on the near space above the surface of VO_{2} patterns, but also trapped above the blank dielectric layer which is marked by red circles in Fig. 7(c). This resulted from the coupling effects between the adjacent unit cells. For frequency ${f_4}$, a higher-order mode with more discrete field distributions appeared [45]. Both frequencies near the space above VO_{2} patterns and the dielectric layer show strong power loss distributions, which means that both of them play an important role in absorption. According to power loss distributions at these four resonance frequencies, it can be concluded that the first broadband absorption is mainly caused by the localized absorption in different parts of the surface of VO_{2} patterns, and the second broadband absorption is mainly contributed by the coupling effects between the adjacent unit cells and the metal ground plane. Due to the symmetry of the structure, the situation is the same for TM polarization.

The influences of different incident angles on the absorption performance are further discussed in Fig. 8. For TE polarization incidence, as shown in Fig. 8(a), the two absorption peaks keep excellent absorption performance until the incident angle varies up to 50° for the first broadband and 20° for the second broadband. The 78% absorptivity is indicated by the white contour curves. When the incident angle continues to increase, the absorptance of the first broadband decreases sharply, while the central frequency of the second broadband has a blue shift and the bandwidth narrows gradually. For TM polarization incidence, as shown in Fig. 8(b), the absorption maintains stable until the incident angle varies up to 60° for the first broadband and to 20° for the second broadband. As the incident angle is further increased, both of the absorptances decrease significantly.

## 4. Conclusion

In conclusion, an active controllable THz metamaterial absorber with dual broadband characteristics is proposed and investigated, which is comprised by two identical VO_{2} patterns arranged diagonally in the top layer of the classical three-layer structure of MPAs. The results show that the two bandwidths of 80% absorption are as wide as 0.88 THz and 0.77 THz in the frequency range of 0.56-1.44 THz and 2.88-3.65 THz. By using thermal control to induce the IMT of VO_{2}, absorptances of both bands can be continuously adjusted from 20% to 90% for the first broadband and 43% to 85% for the second broadband. Following the Fabry-Perot resonance and the impedance matching theory, the dual bands, high absorption and broad bandwidth are elucidated. By analyzing the power loss distributions, it demonstrated that the first broadband absorption is mainly caused by the localized absorption in different parts of the surface of VO_{2} patterns. The second broadband absorption is mainly contributed by the coupling effects between the adjacent unit cells and the metal ground plane. In addition, the excellent absorption performance of the first broadband remains stable for both TE and TM polarizations until the incident angle varies up to 50°. This proposed absorber has great potential applications in imaging, modulating, sensing and cloaking.

## Funding

National Natural Science Foundation of China (61705162, 61735010); Key Technologies Research and Development Program (2017YFA0700202).

## Acknowledgments

Thanks for Key Laboratory of Opto-electronic Information Technology of Tianjin University.

## Disclosures

The authors declare no conflicts of interest.

## References

**1. **H. A. Atwater and A. Polman, “Erratum: Plasmonics for improved photovoltaic devices,” Nat. Mater. **9**(3), 205–213 (2010). [CrossRef]

**2. **Y. Wang, T. Sun, T. Paude, Y. Zhang, Z. Ren, and K. Kempa, “Metamaterial-plasmonic absorber structure for high efficiency amorphous silicon solar cells,” Nano Lett. **12**(1), 440–445 (2012). [CrossRef]

**3. **X. L. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. **107**(4), 045901 (2011). [CrossRef]

**4. **F. Alves, B. Kearney, D. Grbovic, and G. Karunasiri, “Narrowband terahertz emitters using metamaterial films,” Opt. Express **20**(19), 21025–21032 (2012). [CrossRef]

**5. **X. Ni, Z. J. Wong, M. Mrejen, Y. Wang, and X. Zhang, “An ultrathin invisibility skin cloak for visible light,” Science **349**(6254), 1310–1314 (2015). [CrossRef]

**6. **L. Zhang, S. Zhang, Z. Song, Y. Liu, L. Ye, and Q. H. Liu, “Adaptive decoupling using tunable metamaterials,” IEEE Trans. Microwave Theory Tech. **64**(9), 2730–2739 (2016). [CrossRef]

**7. **N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. **100**(20), 207402 (2008). [CrossRef]

**8. **L. Zhao, H. Liu, Z. He, and S. Dong, “Design of multi-narrowband metamaterial perfect absorbers in near-infrared band based on resonators asymmetric method and modified resonators stacked method,” Opt. Commun. **420**, 95–103 (2018). [CrossRef]

**9. **X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. **104**(20), 207403 (2010). [CrossRef]

**10. **H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express **20**(7), 7165–7172 (2012). [CrossRef]

**11. **G. Duan, J. Schalch, X. Zhao, A. Li, C. Chen, R. D. Averitt, and X. Zhang, “A survey of theoretical models for terahertz electromagnetic metamaterial absorbers,” Sens. Actuators, A **287**, 21–28 (2019). [CrossRef]

**12. **J. Grant, Y. Ma, S. Saha, L. B. Lok, A. Khalid, and D. R. S. Cumming, “Polarization insensitive terahertz metamaterial absorber,” Opt. Lett. **36**(8), 1524–1526 (2011). [CrossRef]

**13. **F. Hu, L. Wang, B. Quan, X. Xu, Z. Li, Z. Wu, and X. Pan, “Design of a polarization insensitive multiband terahertz metamaterial absorber,” J. Phys. D: Appl. Phys. **46**(19), 195103 (2013). [CrossRef]

**14. **J. Wu, F. Zhang, Q. Li, J. Chen, Q. Feng, and L. Wu, “Infrared five-band polarization insensitive absorber with high absorptivity based on single complex resonator,” Opt. Commun. **456**, 124575 (2020). [CrossRef]

**15. **J.-S. Li, D.-X. Yan, and J.-Z. Sun, “Flexible dual-band all-graphene-dielectric terahertz absorber,” Opt. Mater. Express **9**(5), 2067–2075 (2019). [CrossRef]

**16. **Y. Cheng, R. Gong, and Z. Cheng, “A photoexcited broadband switchable metamaterial absorber with polarization-insensitive and wide-angle absorption for terahertz waves,” Opt. Commun. **361**, 41–46 (2016). [CrossRef]

**17. **S. Yuan, R. Yang, J. Xu, J. Wang, and J. Tian, “Photoexcited switchable single-/dual-band terahertz metamaterial Absorber,” Mater. Res. Express **6**(7), 075807 (2019). [CrossRef]

**18. **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), 32280–32289 (2017). [CrossRef]

**19. **T. Driscoll, S. Palit, M. M. Qazilbash, M. Brehm, F. Keilmann, B.-G. Chae, S.-J. Yun, H.-T. Kim, S. Y. Cho, N. M. Jokerst, D. R. Smith, and D. N. Basov, “Dynamic tuning of an infrared hybrid-metamaterial resonance using vanadium Dioxide,” Appl. Phys. Lett. **93**(2), 024101 (2008). [CrossRef]

**20. **T. Wang, L. Qu, L. Qu, Y. Zhang, H. Zhang, and M. Cao, “Tunable broadband terahertz metamaterial absorber using multi-layer black phosphorus and vanadium dioxide,” J. Phys. D: Appl. Phys. **53**(14), 145105 (2020). [CrossRef]

**21. **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), 369–386 (2020). [CrossRef]

**22. **A. Holsteen, I. S. Kim, and L. J. Lauhon, “Extraordinary Dynamic Mechanical Response of Vanadium Dioxide Nanowires around the Insulator to Metal Phase Transition,” Nano Lett. **14**(4), 1898–1902 (2014). [CrossRef]

**23. **J. Bai, S. Zhang, F. Fan, S. Wang, X. Sun, Y. Miao, and S. Chang, “Tunable broadband THz absorber using vanadium dioxide metamaterials,” Opt. Commun. **452**, 292–295 (2019). [CrossRef]

**24. **Y. Zhang, S. Qiao, L. Sun, Q. W. Shi, W. Huang, L. Li, and Z. Yang, “Photoinduced active terahertz metamaterials with nanostructured vanadium dioxide film deposited by sol-gel method,” Opt. Express **22**(9), 11070–11078 (2014). [CrossRef]

**25. **T. Driscoll, S. Palit, M. M. Qzailbash, M. Brehm, F. Keilmann, B. Chae, S. Yun, H. Kim, S. Y. Cho, N. M. Jokerst, D. R. Smith, and D. N. Basov, “Dynamic tuning of an infrared hybrid-metamaterial resonance using vanadium dioxide,” Appl. Phys. Lett. **93**(2), 024101 (2008). [CrossRef]

**26. **Q. Wen, H. Zhang, Q. Yang, Y. Xie, K. Chen, and Y. Liu, “Terahertz metamaterials with VO2 cut-wires for thermal tunability,” Appl. Phys. Lett. **97**(2), 021111 (2010). [CrossRef]

**27. **D. J. Park, J. H. Shin, K. H. Park, and H. C. Ryu, “Electrically controllable THz asymmetric split loop resonator with an outer square loop based on VO2,” Opt. Express **26**(13), 17397–17406 (2018). [CrossRef]

**28. **J.-H. Shin, K. H. Park, and H.-C. Ryu, “Electrically controllable terahertz square-loop metamaterial based on VO 2 thin film,” Nanotechnology **27**(19), 195202 (2016). [CrossRef]

**29. **C.-W. Cheng, M. N. Abbas, C.-W. Chiu, K. T. Lai, M. H. Shih, and Y. C. Chang, “Wide-angle polarization independent infrared broadband absorbers based on metallic multi-sized disk arrays,” Opt. Express **20**(9), 10376–10381 (2012). [CrossRef]

**30. **J. Hendrickson, J. P. Guo, B. Y. Zhang, W. Buchwald, and R. Soref, “Wideband perfect light absorber at midwave infrared using multiplexed metal structures,” Opt. Lett. **37**(3), 371–373 (2012). [CrossRef]

**31. **H. Li, L. H. Yuan, B. Zhou, X. P. Shen, Q. Cheng, and T. J. Cui, “Ultrathin multiband gigahertz metamaterial absorbers,” J. Appl. Phys. **110**(1), 014909 (2011). [CrossRef]

**32. **X. Shen, Y. Yang, Y. Zang, J. Gu, J. Han, W. Zhang, and T. J. Cui, “Triple-band terahertz metamaterial absorber: Design, experiment, and physical interpretation,” Appl. Phys. Lett. **101**(15), 154102 (2012). [CrossRef]

**33. **S. Liu, H. Chen, and T. J. Cui, “A broadband terahertz absorber using multi-layer stacked bars,” Appl. Phys. Lett. **106**(15), 151601 (2015). [CrossRef]

**34. **H. Deng, L. Stan, D. A. Czaplewski, J. Gao, and X. Yang, “Broadband infrared absorbers with stacked double chromium ring resonators,” Opt. Express **25**(23), 28295–28304 (2017). [CrossRef]

**35. **M. Amin, M. Farhat, and H. Bağcı, “An ultra-broadband multilayered graphene absorber,” Opt. Express **21**(24), 29938–29948 (2013). [CrossRef]

**36. **Z. Liu, P. Zhan, J. Chen, C. Tang, Z. Yan, Z. Chen, and Z. Wang, “Dual broadband near-infrared perfect absorber based on a hybrid plasmonic-photonic Microstructure,” Opt. Express **21**(3), 3021–3030 (2013). [CrossRef]

**37. **Y. J. Kim, Y. J. Yoo, K. W. Kim, J. Y. Rhee, Y. H. Kim, and Y. P. Lee, “Dual broadband metamaterial absorber,” Opt. Express **23**(4), 3861–3868 (2015). [CrossRef]

**38. **N. Hu, F. Wu, L. 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]

**39. **S. Wang, C. Cai, M. You, F. Liu, M. Wu, S. Li, H. 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]

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

**41. **B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incidence angle,” Prog. Electromagn. Res. **101**, 231–239 (2010). [CrossRef]

**42. **Y. Zhao, Q. Huang, H. Cai, X. Lin, and Y. Lu, “A broadband and switchable VO2 -based perfect absorber at the THz frequency,” Opt. Commun. **426**, 443–449 (2018). [CrossRef]

**43. **D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E **71**(3), 036617 (2005). [CrossRef]

**44. **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]

**45. **L. Zhao, H. Liu, Z. He, and S. Dong, “Theoretical design of twelve-band infrared metamaterial perfect absorber by combining the dipole, quadrupole, and octopole plasmon resonance modes of four different ring-strip resonators,” Opt. Express **26**(10), 12838–12851 (2018). [CrossRef]