Open Access
Add to BibSonomy
Abstract
In this work, we propose a novel broadband terahertz (THz) metamaterial absorber (MMA) based on double-spiral structures, including discrete and continuous ones. The gradient ring resonators are in a discrete spiral topological distribution to expand the absorption band. By stacking two layers with a certain proportion, the proposed THz MMA can further enhance the energy loss to achieve absorption over 0.9 for TE mode at 2.57–5.19 THz and TM mode at 2.43–5.6 THz, with relative absorption bandwidths (RABWs) of 67.5% and 81.7%, respectively. Meanwhile, the polarization-insensitive bandwidth is 2.57–5.19 THz, with RABW of 67.5%. In addition, the normalized impedance for both modes is investigated. Furthermore, according to the analysis of the distributions of the surface current and electric field, it is clear that the electromagnetic energy loss mainly originates from the electric and magnetic resonances induced by the interaction between the metal resonators. To a certain extent, the Fabry–Perot resonance existing between the dielectric layers also contributes to the improvement of the absorption. This THz MMA, based on a unique double-spiral arrangement, can be used in many fields owing to its ultra-broad absorption band and polarization-insensitive characteristic in a broad band.
© 2021 Optical Society of America
1. INTRODUCTION
Electromagnetic metamaterial, a novel artificial material consisting of homogeneous unit structures, has aroused significant attention from researchers owing to its unusual physical properties, negative refraction, reversal of Vavilov–Cerenkov radiation and Doppler effect, and so on [1]. Based on these characteristics, many devices heretofore impossible have been designed, such as the invisible cloak [2,3], the perfect lens [4,5], the miniaturized antenna [6,7], and so on. Meanwhile, the need for high-performance metamaterial absorbers is still enormous [8–25]. Since Landy and co-workers [8] in 2008 demonstrated a perfect absorber, achieving absorption of 96% at 11.65 GHz for the first time, more and more research on metamaterial absorbers has been presented whose working band has extended from microwave to invisible light due to the great traits of THz waves [9,10]. In 2009, Landy et al. [11] designed a polarization-insensitive absorber based on a modified electrically coupled ring resonator, which attained the absorption of 65% at 1.145 THz. The team of Tao [12] proposed a dual-band THz MMA composed of electric-field-coupled resonators and metallic plane spacing by a dielectric layer, the result of which showed two absorption peaks at around at 1.4 and 3 THz and absorption of 0.85 and 0.94, respectively. Wang and his researchers [13] designed a six-band THz MMA consisting of two alternating stacks of metal–dielectric layers and a metallic film, which realized high absorption performance (average over 99.37%) at six resonant frequencies.
Despite these achievements, the narrowband traits of the absorbers in previous works greatly limit their practical application. Thus, broadening the absorption band has attracted the interest of researchers. To achieve a broad band, Gong and his colleagues [14] arranged four sectional asymmetric cells to combine the resonant frequencies and realize the absorption bandwidth of 364 GHz. Zhu and his co-workers [15] presented an ultra-broadband THz MMA made up of truncated pyramid arrays based on multiple metal–dielectric layers, which attained absorption over 80% at 0.7–2.3 THz.
Spiral structures have been widely applied in designing metamaterial absorbers owing to characteristics such as insensitivity to polarization, excellent absorption properties, and so on. Huang et al. [26] demonstrated a triple-band polarization-insensitive absorber based on a planar spiral structure which achieved absorption peaks of 99.4%, 96.7%, and 99.1% at resonant frequencies of 9.86, 12.24, and 15.34 GHz, respectively. Wang and his team [27] proposed a four-band THz MMA based on four spiral resonators which were arranged in a counterclockwise rotation. The numerical results showed that the terahertz metamaterial absorber (TMA) could achieve absorption up to 96.49%, 94.25%, 98.94%, and 92.04 % at 6.69, 8.70, 11.90, and 15.14 GHz, respectively. Feng and co-workers [28] presented a THz MMA on the basis of square–spiral resonators which realized absorption over 60% at 3.24–8.5 THz. It is clear that metamaterial absorbers based on spiral resonators frequently obtain great absorption in a narrow band. However, although some absorbers can achieve broadband absorption, the average absorption is still unsatisfactory.
In this paper, we present a novel broadband THz MMA composed of two metal–dielectric stacking layers. The main metal resonators are double-spiral structures. The numerical results depict an absorption larger than 0.9 of the THz MMA for TE mode concentrated at 2.57–5.19 THz and TM mode at 2.43–5.6 THz, with RABWs of 67.5% and 81.7%, respectively. The polarization-insensitive bandwidth is at 2.57–5.19 THz, with RABW of 67.5%.
2. STRUCTURE DESIGN
The structure of the proposed THz MMA in this work is displayed in Fig. 1, which is composed of two metal–dielectric layers and a continuous metallic film to form a truncated pyramid. Copper with conductivity ${5.96} \times {107}\;{\rm S/m}$ and thickness 0.035 µm is selected as the metallic film under the bottom dielectric layer. Meanwhile, the relative permittivity of the polyimide is ${3.5} + {0.2}i$ [29]. To verify the function of each part of the resonators, three structures of double-spiral THz MMA are presented in Fig. 1(a). For structure I, nest-ring structures with different sizes are arranged in a double-spiral pattern to form a gradual discrete quasi-double-spiral structure where the nest-ring resonators are regarded as the discrete unit cells. The single-helix expression of the polar coordinate equation is $r = {9} + {6.7}\theta$, in which $r$ is the distance from the center and $\theta$ is the rotation angle from the ${+}y$ direction. The other helix is acquired by rotating the former helix by 180° anticlockwise. Meanwhile, the radius of the outer ring in the first nest-ring structure is ${r_1}$ and the radius of the next nest-ring structure increases by 0.2 µm compared to the former one. In addition, the width of the ring is $w$ and the spacing width between two rings is ${s_1}$. To further improve the absorption, the other gradual continuous double-spiral structure is added to the structure II. The expression of the inner part of the single continuous spiral is that $r = {13.2} + {56.7}\theta$ and that of the outer part is $r = {13.5} + {58.05}\theta$, which is combined with the other spiral formed by rotating the previous spiral by 180° to get a double-spiral structure. The added resonators in structure III effectively enhance the absorption performance, which include double L-shape resonators and two rectangle patches. It can be noted that the double-spiral structures, including the discrete and continuous ones on the second layer in three structures, are scaled down by those in the first layer according to a certain proportion $S$, subsequently mirrored along the $y$ direction, and then rotated by 90° anticlockwise. The resonators are made of gold, whose conductivity is ${4.561} \times {107}\;{\rm S/m}$. The detailed optimized parameters are list in Table 1.
Fig. 1. Schematic views of the unit cell for the proposed double-spiral THz MMA: (a) three structures of the proposed double-spiral MMA, (b) detailed diagram of the unit cell of structure III, and (c) the boundary condition of the proposed MMA.
Table 1. Structure Parameters of the Gradual Double-Spiral THz MMA
The electromagnetic characteristics of the proposed double-spiral THz MMA are acquired by the numerical simulation based on the frequency-domain solver of the High Frequency Structure Simulator (HFSS). The boundary conditions are set as the master and slave shown in Fig. 1(c). The unit cells of the proposed double-spiral TMA are arranged along the ${\pm}x$- and ${\pm}y$ directions. Meanwhile, the Floquet ports are respectively located in the ${\pm}z$ direction. According to the boundary conditions, the electric and magnetic vectors for TE mode are each towards the ${+}y$ and ${+}x$ directions and those for TM mode are each towards the ${-}x$ and ${+}y$ directions. In addition, the wave vectors for the TE and TM waves are both toward the ${-}z$ direction.
Fig. 2. Absorption, reflection, transmission, and polarization conversion of the proposed THz MMA in structure III: (a) TE mode and (b) TM mode.
Fig. 3. Absorption of the double-spiral THz MMA in structure III for the TE and TM modes under different incidence angles: (a) TE mode and (b) TM mode.
3. RESULTS AND DISCUSSION
The electromagnetic wave absorption can be analyzed according to the multiple reflection and interference theory of the incident electromagnetic field. So, the absorption $A(\omega)$ of the double-spiral THz MMA proposed in this work can be calculated according to the formula $A(\omega) = {1 -}R(\omega) - T(\omega) - P(\omega) = {1 - |}{S_{11}}{|^2} - |{S_{21}}{|^2} - P(\omega)$, in which $R(\omega)$, $T(\omega)$, and $P(\omega)$ are the reflection coefficient, transmission coefficient, and polarization conversion coefficient, respectively. These coefficients can be expressed by $R(\omega) = |{S_{11}}{|^2}$, $T(\omega) = |{S_{21}}{|^2}$, where ${S_{11}}$ and ${S_{21}}$ are the scattering parameters for reflection and transmission coefficients, respectively. It can be seen that the absorption, reflection, transmission, and polarization conversation coefficients of the double-spiral THz MMA for TE and TM modes are shown in Fig. 2. Since the electromagnetic wave cannot penetrate through the TMA owing to the existence of the metallic film, the transmission coefficient is too small to be neglected. So, the absorption $A(\omega)$ can be shown as $A(\omega) = {1 -}R(\omega) - P(\omega)$. The absorption band in which the absorption is over 0.9 covers 2.57–5.19 THz for TE mode and that for TM mode covers 2.43–5.6 THz, whose RABWs are 67.5% and 81.7%, respectively.
Fig. 4. Absorption of this double-spiral THz MMA in structure III with different polarization angles.
Fig. 5. Absorption of the gradual double-spiral THz MMA for the TE and TM modes in different structures: (a) TE mode and (b) TM mode.
Because the absorption under different incidence and polarization angles is a key factor of estimating the absorber, the double-spiral THz MMA in structure III is theoretically studied under different incidence and polarization angles, which are each depicted in Figs. 3 and 4, respectively. As shown in Fig. 3(a), for TE mode, the absorption keeps stable at 2.6–5.18 THz as the incidence angle increases from 0° to 23°. But as the incidence angle continues to increase from 23° to 30°, the absorption at 4.25–5.18 THz drops below 0.9. And when the incidence angle is above 30°, the absorption at 2.75–3.3 THz is also under 0.9. Especially, when the incidence angle is above 50°, the absorption band is narrow and mainly located at 2.6–2.75 THz and 3.7–4.3 THz. Similar to the TE mode, the absorption for TM mode depicted in Fig. 3(b) always stays above 0.9 at 2.5–5.6 THz except for 4.95–5.1 THz, when the incidence angle is under 20°. But unlike the TE mode, when the incidence angle goes on increasing, then the lowest and highest frequencies of the absorption band also increase at the same time and the absorption in the band is always above 0.9. When the incidence angle increases to 60°, the absorption band over 0.9 covers 3.25–7 THz. It should be noted that the absorption band will move to a high frequency with the increase of incident angle due to the change of the effective working size of the element under oblique incidence. Meanwhile, due to the impedance mismatch under oblique incidence, the absorption deteriorates under a large angle of incidence. In addition, the absorption with different polarization angles can be observed in Fig. 4. It can be noted that the absorption almost keeps above 0.9 when the polarization angle ranges from 0° to 90°, except that the absorption is slightly lower than 0.9 as the polarization angle is between 27°and 65°. In other words, the proposed double-spiral THz MMA is insensitive to the polarization angle at 2.57–5.19 THz.
To clarify the functions of different resonators in the double-spiral THz MMA proposed in this paper, three structures depicted in Fig. 1(a) for TE- and TM-polarized waves are theoretically investigated and simulated, which are shown in Fig. 5. As shown in Figs. 5(a) and 5(b), the absorption of structure I for TE mode is over 0.9 at four narrow bands, 2.66–2.84, 3.45–3.95, 4.35–4.53, and 4.89–5.13 THz, and that for TM mode at three narrow bands, 2.84–3.3, 3.53–3.95, and 4.92–5.1 THz. For structure II, the continuous double-spiral resonators are added in each layer to enhance the resonant absorption. It can be seen that the absorption in structure II for TE mode can be above 0.9 in the broad continuous frequency band, 2.53–5.25 THz. However, the absorption over 0.9 for TM mode is mainly located at four narrow bands, 2.43–2.55, 2.89–3.05, 3.24–4.15, and 4.57–5.3 THz. To further improve the absorption for TM mode, the L-shaped and rectangular resonators are added to the structure II to form the structure III. Though the absorption band for TE mode, which is 2.57–5.19 THz, is slightly narrower than that for TE mode in structure II, the absorption for TM mode is enhanced entirely to form a broad continuous absorption band, 2.43–5.6 THz. Generally speaking, the double-spiral resonators can help to effectively enhance the absorption for both modes, and the L-shape and rectangular resonators are beneficial to improving the absorption entirely for TM mode.
The size ratio $S$ of the continuous and discrete double-spiral resonators on both layers is a key parameter influencing the absorption of the proposed THz MMA. Therefore, the double-spiral THz MMA with different size ratio $S$ is fully discussed, and results are shown in Figs. 6(a) and 6(b). As depicted in Fig. 6(a), for TE mode, although the absorption in the frequency band above 5 THz rises with the decrease of $S$, the absorption around 3.5 and 4.41 THz falls down gradually to below 0.9. Only when the size ratio $S$ is above 0.72 can the absorption over 0.9 for TE mode be in the entire and continuous band. Similar to TE mode, it can be seen in Fig. 6(b) that the smaller the size ratio $S$, the greater the absorption for TM mode in the high-frequency band (above 5.35 THz). However, as the $S$ decreases to below 0.72, the absorption around 2.62 and 3.13 THz is lower than 0.9. Meanwhile, when the ${\rm S}$ is above 0.72, the absorption at 4.53–5.14 THz is under 0.9. On the other hand, the resonators between different layers for two-layer TMA have great effects on the absorption efficiency. Thus, the thickness of the second dielectric layer ${h_2}$ is also a key parameter, whose effect is shown in Figs. 6(c) and 6(d). It can be noted that the absorption bands for both modes move to the lower frequency as the thickness of the second dielectric layer ${h_2}$ thickens. When ${h_{2\:}} = \;{5.4}\;{\unicode{x00B5}{\rm m}}$, 5.8 µm, the absorption for TE mode is below 0.9 around 3.6 THz, and that for TM mode around 3.1 THz. As the ${h_2}$ continues to increase to above 6.2 µm, the absorption band gets entire gradually. To summarize, in view of the absorption bandwidth and low profile, the best absorption bandwidth for TE mode is 2.57–5.19 THz (the RABW is 67.5%) and that for TM mode is 2.43–5.6 THz (the RABW is 81.7%) when $S = {0.72}$ and ${h_2} = {6.2}\;{\unicode{x00B5}{\rm m}}$.
Fig. 6. Absorption of the gradual double-spiral THz MMA for TE and TM modes with different parameters $S$ and ${h_2}$ in structure III: (a) $S = {0.64}$, 0.68, 0.72, 0.76, 0.80 for TE mode; (b) $S = {0.64}$, 0.68, 0.72, 0.76, 0.8 for TM mode; (c) ${h_2} = {5.4}$, 5.8, 6.2, 6.6, and 7 µm for TE mode, and (d) ${h_2} = {5.4}$, 5.8, 6.2, 6.6, and 7 µm for TM mode.
To get insight into the absorption mechanism of the proposed THz MMA based on double-spiral structures, the impedance-matching theory is adopted. As the MMA is at the resonant frequency, the equivalent surface impedance $Z$ of the presented MMA is the same with the impedance ${Z_0}$ in the free space. According to [30,31], under the condition of the normal incidence of electromagnetic wave, the relationship of the complex impedance and absorption can be expressed by
The distributions of the surface current in different layers, corresponding to different frequencies, are an important approach to analyzing the absorption mechanism of the broadband double-spiral MMA, which is shown in Fig. 8. When the TE-polarized wave at 3 THz is incident, it can be seen in Fig. 8(a) that the currents on the continuous double-spiral structure in the second layer flow along the incident electric field to provide an electric dipole. Meanwhile, it can be noted that the currents on the outer ring of the unit cell of the discrete double-spiral structure are anti-parallel to those on the inner one and the continuous double-spiral structure. These anti-parallel currents form equivalent current loops to supply strong magnetic resonances. These electric and magnetic resonances are achieved simultaneously at the same frequency to bring about the great absorption. Further, some currents on the continuous double-spiral structure of the first layer are also anti-parallel to those on the rectangular resonator of the second layer and the metallic layer, which results in the magnetic resonances. Though the magnetic resonances are not strong, the electromagnetic power loss induced by them also improves the absorption. As for the TM-polarized wave at 3 THz depicted in Fig. 8(b), the currents are mainly concentrated on the first layer, where those on the outer ring of the nest ring are anti-parallel to those on the inner ring and the double-spiral structures to form magnetic dipoles, which consumes the most energy. Meanwhile, the currents on the L-shaped resonators provide strong electric resonances to enhance the absorption. When the resonant frequency is 4 THz, the distributions of the currents are similar to those at 3 THz, which are presented in Figs. 8(c) and 8(d). For TE mode, the magnetic resonances provided by the nest rings and continuous double-ring structure in the first layer play a key role in the absorption of the electromagnetic power, and the electric resonances depending on the L-shaped resonators in the second layer also enhance the absorption. For TM mode, the absorption mainly relies on the magnetic resonances resulting from the interactions between the nest rings and double-spiral resonators, and the electric resonances that the rectangular resonators in the first layer provide. In general, the absorption of the proposed MMA mainly depends on the electric and magnetic resonances which the resonators provide.
Fig. 8. Distributions of surface current for TE and TM modes in different layers at different frequencies: (a) TE mode at 3 THz, (b) TM mode at 3 THz, (c) TE mode at 4 THz, and (d) TM mode at 4 THz.
Fig. 9. Distributions of electric fields for TE and TM modes in different layers and the cross-section at different frequencies: (a) TE mode at 3 THz, (b) TM mode at 3 THz, (c) TE mode at 4 THz, and (d) TM mode at 4 THz.
To more deeply analyze the absorption mechanism of the proposed double-spiral MMA, the distributions of the electric fields in different layers and the cross-section along the dashed line are simulated and shown in Fig. 9. When the resonant frequency is 3 THz as shown in Figs. 9(a) and 9(b), for TE mode, the electric fields are mainly concentrated on the nest rings and L-shaped resonators in the first layer. Meanwhile, there are some electric fields lying in the double-spiral resonators in the second layer. For TM mode, most electric fields are distributed around the nest rings and L-shape resonators. Therefore, as the electromagnetic wave is incident, the resonators are excited to form electric and magnetic resonances to consume the energy. But, when the wave at 4 THz passes through, the distributions of electric fields are slightly different, as presented in Figs. 9(c) and 9(d). Though the electric fields for TM mode are mainly focused on the resonators in the first layer, there are still some electric fields existing in the dielectric layers, which means that some waves reflect repeatedly between the resonators and the metallic film to induce the Fabry–Perot-mode resonance. In summary, the consumption of electromagnetic power mainly depends on the resonators in both layers, but meanwhile, the Fabry–Perot resonance also can help enhance the absorption.
To verify the scattering performance of the proposed THz MMA in this paper, the fabrication process is necessary. The planar metamaterials are usually processed by lithography and the detailed process is shown in Fig. 10. Metal structure lithography is generally after the metal deposition, and then goes through degumming to obtain the desired metal structure. A variety of light sources, such as ultraviolet light, x-ray, electron beam, ion beam, and proton beam, can be used for lithography. Meanwhile, the metal deposition mainly depends on the electroplating technology.
4. CONCLUSION
A novel two-layer THz MMA with gradient ring resonators based on a discrete spiral topological distribution is proposed in this paper. The novel double-spiral arrangement of gradient nest-ring resonators can not only provide more resonances at different frequencies by themselves, but they also simultaneously improve the interaction with the continuous double-spiral resonators to greatly enhance the absorption, which achieves absorption over 0.9 for TE mode at 2.57–5.19 THz (with RABW 67.5%) and at 2.43–5.6 THz (with RABW 81.7%) for TM mode. Furthermore, the double-spiral MMA is insensitive to the polarization angle at 2.57–5.19 THz (where the RABW is 67.5%), and the absorption can keep stable under the incident angle below 23°. By analyzing the distributions of the power loss, surface current, and electric field, the absorption of the proposed THz MMA mainly depends on the electromagnetic responses induced by electric and magnetic resonances existing in the metal resonators. Meanwhile, the resonance of Fabry–Perot-induced mode in the dielectric layers can further improve energy consumption.
In summary, a novel means of designing a broadband TMA has been proposed in this paper. By stacking two layers with a certain proportion, the proposed TMA achieves absorption over 90% for the TE wave at 2.28–5.58 THz and the TM wave at 2.3–5.82 THz, with RBWs of 82.5% and 88%, respectively. Furthermore, the TMA is insensitive to the polarization angles at 2.3–5.58 THz (with RBW of 82%), which has great application value. By analyzing the absorption in three structures, the function of each metal resonator is comprehended, and the absorption mechanism of the TMA is acquired by analyzing the distributions of power loss density, surface current, and magnetic fields. The simulation results reveal that the absorption of the TMA is achieved by comprehensive effects, including the Fabry–Perot-induced mode resonance and magnetic resonances among the metal resonators.
Funding
Science and Technology Planning Project of Shenzhen Municipality Basic Research Project (JCYJ20180305164708625); Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX19_0958); Open Research Program in China’s State Key Laboratory of Millimeter Waves (K201927).
Disclosures
The authors declare no conflicts of interest.
REFERENCES
1. V. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]
2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). [CrossRef]
3. Y. Huang, Y. J. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007). [CrossRef]
4. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef]
5. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2009). [CrossRef]
6. R. W. Ziolkowski and A. D. Kipple, “Application of double negative materials to increase the power radiated by electrically small antennas,” IEEE Trans. Antennas Propag. 51, 2626–2640 (2003). [CrossRef]
7. M. S. Majedi and A. R. Attari, “A compact and broadband metamaterial-inspired antenna,” IEEE Antennas Wireless Propag. Lett. 12, 345–348 (2013). [CrossRef]
8. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). [CrossRef]
9. T. S. Rappaport, Y. Xing, O. Kanhere, S. Ju, A. Madanayake, S. Mandal, A. Alkhateeb, and G. C. Trichopoulos, “Scattering mechanisms and modeling for terahertz wireless communication,” IEEE Access 7, 78729–78757 (2019). [CrossRef]
10. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007). [CrossRef]
11. 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, 125104 (2009). [CrossRef]
12. H. Tao, C. M. Bingham, D. Pilon, K. Fan, A. C. Strikwerda, D. Shrekenhamer, W. J. Padilla, X. Zhang, and R. D. Averitt, “A dual band terahertz metamaterial absorber,” J. Phys. D 43, 225102 (2010). [CrossRef]
13. B. X. Wang, G. Z. Wang, T. Sang, and L. L. Wang, “Six-band terahertz metamaterial absorber based on the combination of multiple-order responses of metallic patches in a dual-layer stacked resonance structure,” Sci. Rep. 7, 41373 (2017). [CrossRef]
14. G. Cheng, M. Zhan, J. Yang, Z. G. Wang, H. T. Liu, Y. J. Zhao, and W. W. Liu, “Broadband terahertz metamaterial absorber based on sectional asymmetric structures,” Sci. Rep. 6, 32466 (2016). [CrossRef]
15. J. F. Zhu, Z. F. Ma, W. J. Sun, F. Ding, Q. He, L. Zhou, and Y. G. Ma, “Ultra-broadband terahertz metamaterial absorber,” Appl. Phys. Lett. 105, 021102 (2014). [CrossRef]
16. H. Zhou and Y. Cheng, “Design of a six-band terahertz metamaterial absorber for temperature sensing application,” Opt. Mater. 88, 674–679 (2019). [CrossRef]
17. H. Luo and Y. Cheng, “Dual-band terahertz perfect metasurface absorber based on bi-layered all-dielectric resonator structure,” Opt. Mater. 96, 109279 (2019). [CrossRef]
18. Y. Cheng, H. Zhao, and C. Li, “Broadband tunable terahertz metasurface absorber based on complementary-wheel-shaped graphene,” Opt. Mater. 109, 110369 (2020). [CrossRef]
19. F. Chen, Y. Cheng, and H. Luo, “Temperature tunable narrow-band terahertz metasurface absorber based on InSb micro-cylinder arrays for enhanced sensing application,” IEEE Access 8, 82981–82988 (2020). [CrossRef]
20. F. Chen, Y. Cheng, and H. Luo, “A broadband tunable terahertz metamaterial absorber based on single-layer complementary gammadion-shaped graphene,” Materials 13, 860 (2020). [CrossRef]
21. W. Li and Y. Cheng, “Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure,” Opt. Commun. 462, 125265 (2020). [CrossRef]
22. X. Hu, G. Xu, L. Wen, Y. Zhao, Y. Zhang, D. R. S. Cumming, and C. Qin, “Metamaterial absorber integrated microfluidic terahertz sensors,” Laser Photon. Rev. 10, 962–969 (2016). [CrossRef]
23. W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6, 8379 (2015). [CrossRef]
24. X. Yan, X. Huang, Y. Chen, Y. Liu, L. Xia, T. Zhang, H. Lin, D. Jia, B. Zhong, G. Wen, and Y. Zhou, “A theoretical strategy of pure carbon materials for lightweight and excellent absorption performance,” Carbon 163, 34–42 (2020). [CrossRef]
25. J. Li, Y. T. Zhang, J. N. Li, X. Yan, L. J. Liang, Z. Zhang, J. Huang, J. H. Li, Y. Yang, and J. Q. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam–Berry coding metasurfaces,” Nanoscale 11, 5746–5753 (2019). [CrossRef]
26. X. J. Huang, H. L. Yang, S. Q. Yu, J. X. Wang, M. H. Li, and Q. W. Ye, “Triple-band polarization-insensitive wide-angle ultra-thin planar spiral metamaterial absorber,” J. Appl. Phys. 113, 213516 (2013). [CrossRef]
27. W. Wang, M. Yan, Y. Q. Pang, J. F. Wang, H. Ma, S. B. Qua, H. Y. Chen, C. L. Xu, and M. D. Feng, “Ultra-thin quadri-band metamaterial absorber based on spiral structure,” Appl. Phys. A 118, 443–447 (2014). [CrossRef]
28. S. G. Feng, “Broadband terahertz metamaterial absorber based on planar square-spiral antenna,” in Asia Communications and Photonics Conference (2014).
29. W. Pan, X. Yu, J. Zhang, and W. Zeng, “A novel design of broadband terahertz metamaterial absorber based of nested circle rings,” IEEE Photon. Technol. Lett. 28, 2325–2338 (2016). [CrossRef]
30. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005). [CrossRef]
31. H. Xiong and Q. Shen, “Thermally and electrically dual-tunable absorber based on Dirac semimetal and strontium titanate,” Nanoscale 12, 14598–14604 (2020). [CrossRef]
