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Abstract
Plasmonic resonances in metal-dielectric-metal structures have shown strong electric and magnetic fields enhancement in the sub-wavelength region, which can significantly boost the performance of plasmon-based metamaterial absorbers. Square resonators (SR) and ring resonators (RR) are both the most common blocks for designing metamaterial perfect absorbers (MPAs) by exciting fundamental electric dipole plasmonic modes. Actually, they can also excite the higher-order electric sextupole plasmonic modes but the absorptivity is very low, which are not available for the design of MPAs. In this paper, the near-field-coupling idea is introduced to enhance the absorptivity of higher-order electric sextupole modes. We propose the outer-square inner-ring coupled resonators (OSIRCR) made of the Ag and ZnS. When the coupling distance has decreased from 70 to 10 nm, the electric field intensity has increased 10.8 times from 55 to 594, which leads to a 5.4 times increase in absorptivity of higher-order electric sextupole modes of the outer-square from 17.6% to 95.3%. In addition to the higher-order electric sextupole modes, the OSIRCR can also excite the fundamental electric dipole modes of the outer-square and the inner-ring. Then a six-band polarization-independent MPA in the infrared range is designed with an average absorptivity of 91.5% utilizing two different sized OSIRCRs.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials (MM) are one kind of materials with some unique properties beyond the limits of nature, which can usually be manipulated by changing the nanostructure [1,2] other than the chemical compositions. Metamaterial perfect absorbers (MPAs) with average absorptivity more than 90% have attracted much attentions as one kind of metamaterials in recent years due to their potential applications in thermal emitters [3,4], biosensing [5,6], microbolometers [7,8], and infrared detection [9,10]. The commonly studied structure configuration is the triple-layered metal-dielectric-metal structure. Plasmonic resonances in the metal-dielectric-metal structure can exhibit strong electric and magnetic fields enhancement in the sub-wavelength region, which can significantly boost the performance of plasmon-based metamaterial absorbers. The top periodic metallic resonators are usually separated from the bottom metallic film by a layer of dielectric. The incident electromagnetic waves can induce the collective oscillation of the conduction electrons of the metallic resonators, which also called the excitation of localized surface plasmonic resonance modes. However, the single-band characteristic is a common problem of MPAs based on plasmonic resonance, which significantly limits the applications, like the infrared detection of multiband radiation signals [11].
One of the ways to increase the perfect absorption bands is to stack differently sized resonators in one unit cell because the absorption peaks will change with the geometry parameters of the nanostructure or the environmental refractive index. The researches of multiband MPAs based on the resonators stacked method are mainly about the dual-band absorption of the stacked cut-wires [12], the triple-band absorption of the stacked square resonators [13], the quad-band absorption of the stacked circle resonators [14] and the square-ring resonators [15]. Another way to increase the perfect absorption bands is to make the differently sized resonators coplanar. The researches of multiband MPAs based on the resonators coplanar method are mainly about the dual-band absorption [16], triple-band absorption [17–19], and quad-band absorption [20–23] in GHz; the dual-band absorption [24], and quad-band absorption [25–27] in THz; the dual-band absorption [28,29], the triple-band absorption [30–33] in infrared band. In all the above nanostructure, square resonators (SR) and ring resonators (RR) are both the most common blocks for designing multiband metamaterial perfect absorbers (MPAs). In general, the square resonators (SR) and ring resonators (RR) can only achieve single nearly perfect absorption band by exciting the fundamental electric dipole modes. The multiband MPAs can be achieved by the resonators coplanar method. And the absorption bands number of the multiband MPA needs to correspond to number of the resonators. However, the number of perfect absorption bands is usually four or less because the interaction between the adjacent resonators increases with the resonators number.
Actually, square resonators (SR) and ring resonators (RR) can also excite the higher-order electric sextupole modes, which have the potential to make the perfect absorption bands number greater than four. But the absorptivity of higher-order electric sextupole modes is very low [29,30], which are not available for the design of MPAs. In this paper, the outer-square inner-ring coupled resonator (OSIRCR) is designed to enhance the absorptivity of higher-order electric sextupole modes. And the electric field intensity distribution is analyzed to gain the underlying physical mechanism. For practical applications, we also investigate the tunability of the absorption peaks. It’s also investigated that the adaptivity of the near-field coupling idea to other materials and nanostructures. The combination of resonators coplanar method and near-field coupling idea has the potential to make the perfect absorption bands number greater than four. So a six-band polarization-independent MPA consisting of two different sized OSIRCRs is designed based on the resonators coplanar method and the near-field coupling idea.
2. Absorptivity enhancement of higher-order electric sextupole modes
Figure 1(a) shows the schematic of our designed metamaterial perfect absorbers (MPAs) base on the outer-square inner-ring coupled resonators (OSIRCR). The MPAs are the typical metal-dielectric-metal structure configuration. The top periodic resonators are separated from the bottom metallic film by a layer of dielectric. The bottom metallic film is thick enough to prohibit the transmission of incident electromagnetic waves. So the absorptivity can be obtained with one minus the reflectivity. The thicknesses of the top, middle, and bottom layer are T1, T2, and T3, respectively. The period of the nanostructure is P. The inner and outer diameter of the inner-ring resonators are L1 and L2, respectively. The inner and outer lengths of the outer-square resonators are L3 and L4, respectively. The width of the sides of the square W is calculated by W = (L4 – L3)/2. The coupling distance D between the outer-square and the inner-ring can be calculated by D = (L3 – L2)/2. The electromagnetic waves are vertically incident on the nanostructure and the electric fields are along the x-direction. Due to the periodicity of the nanostructure, only one unit cell is considered in the simulation by the finite-difference-time-domain (FDTD) method. The periodic boundary condition is applied in the x- and y- direction and the PML boundary condition is applied in the z-direction. In the simulation, the permittivity of ZnS is 4.84 [31] and the permittivity of Ag is extracted from the experimental data of Palik [34].
Fig. 1 (a) Schematic of our designed metamaterial perfect absorbers based on the outer-square inner-ring coupled resonators (OSIRCR) and (b) the corresponding spectral absorptivity as the function of the coupling distance D between the outer-square and the inner-ring.
Figure 1(b) shows the spectral absorptivity of our designed MPAs as the function of the coupling distance D between the outer-square and the inner-ring. The specific geometry parameters are in Table 1. The variant geometry parameters coupling distance D = (L3 – L2)/2 are 70 nm for case1, 50 nm for case2, 30 nm for case3, and 10 nm for case4. The unchanged geometry parameters are given as: P = 1000, T1 = 200, T2 = 80, T3 = 200, L1 = 250, and L2 = 460 (units: nm). The width W of the sides of the square resonators is also unchanged W = (L4 – L3)/2 = 70 nm. There are four absorption bands in the infrared range. When the coupling distance D decreases from 70 to 10 nm, the absorptivity of f3 is enhanced 5.4 times from 17.6% to 95.3%. The absorptivity of f2 has decreased a little from 99.7% to 93.5% and the absorptivity of f4 has decreased a little from 20.3% to 15.1%. The absorptivity of f1 has increased a little from 94.4% to 96.6%. In addition of the changes in absorptivity, the positions of absorption peak f1, f3, and f4 all have an apparent redshift while the f2 has an apparent blueshift. So when the coupling distance D is 10 nm for our designed outer-square inner-ring coupled resonators, three are three nearly perfect absorption bands at f1 = 61.8 THz, f2 = 96.4 THz, and f3 = 167.8 THz with absorptivity 96.6%, 93.5%, and 95.3%, respectively. The absorptivity of f4 is too low to be available for the design of MPAs.
Table 1. The geometry parameters of our designed MPAs (units: nm)
The most interesting part in Fig. 1 is the absorptivity enhancement of the f3 from 17.6% to 95.3%, which leads to the achievement of a triple-band MPA. Because plasmonic resonances in the metal-dielectric-metal structure can exhibit strong electric and magnetic fields enhancement in the sub-wavelength region, the plasmon based nanostructure can be utilized to design MPAs. So to figure out the underlying physical mechanism, the Fig. 2(a), 2(b), 2(c), and 2(d) show the electric fields intensity (|E|2) distribution of the OSIRCR at f3 = 146.9 THz, f3 = 153.5 THz, f3 = 160.6 THz, and f3 = 167.8 THz when the distance D are 70 nm, 50 nm, 30 nm, and 10 nm, respectively. The Fig. 2(e) shows the peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f3. For all the four cases, there are obvious six poles around the square resonators. So the absorption band f3 mainly comes from the higher-order electric sextupole modes of the outer-square. The maximum value of electric field intensity is 55 for D = 70 nm, 154 for D = 50 nm, 368 for D = 30 nm, and 594 for D = 10 nm. The electric field intensity enhancement means that more energy is localized around the resonators, which contributes to the enhancement of the absorptivity of the higher-order electric sextupole modes. So when the coupling distance D has decreased from 70 to 10 nm, the electric field intensity has increased 10.8 times from 55 to 594, which leads to a 5.4 times increase in absorptivity of higher-order electric sextupole modes from 17.6% to 95.3%.
Fig. 2 The electric fields intensity (|E|2) distribution of absorption band f3 when the coupling distance D is (a) 70, (b) 50, (c) 30, and (d) 10 nm, respectively. (e) The peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f3.
The Fig. 3(a), 3(b), 3(c), and 3(d) show the electric fields intensity (|E|2) distribution of the OSIRCR at f2 = 113.1 THz, f2 = 112.3 THz, f2 = 109.1 THz, and f2 = 96.4 THz when the distance D are 70 nm, 50 nm, 30 nm, and 10 nm, respectively. The Fig. 3(e) shows the peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f2. For all the four cases, there are obvious two poles around the ring resonators. So the absorption band f2 mainly comes from the fundamental electric dipole mode of inner-ring. When the coupling distance D has decreased from 70 to 10 nm, the electric field intensity has slightly decreased from 998 to 924, which leads to the slight decrease of absorptivity from 99.7% to 93.5%. The Fig. 4(a), 4(b), 4(c), and 4(d) show the electric fields intensity (|E|2) distribution of the OSIRCR at f1 = 50.5 THz, f1 = 54.5 THz, f1 = 58.6 THz, and f1 = 61.8 THz when the distance D are 70 nm, 50 nm, 30 nm, and 10 nm, respectively. The Fig. 4(e) shows the peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f1. For all the four cases, there are obvious two poles around the outer-square. So the absorption band f1 mainly comes from the fundamental electric dipole mode of outer-square. When the coupling distance D has decreased from 70 to 10 nm, the electric field intensity has slightly increased from 344 to 380, which leads to the slight increase of absorptivity from 94.4% to 96.6%. Figure 5(a), 5(b), 5(c), and 5(d) show the electric fields intensity (|E|2) distribution of the OSIRCR at f4 = 184 THz, f4 = 187 THz, f4 = 189 THz, and f4 = 192 THz when the distance D are 70 nm, 50 nm, 30 nm, and 10 nm, respectively. The Fig. 5(e) shows the peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f4. For all the four cases, there are obvious ten poles around the outer-square. So the absorption band f4 mainly comes from the higher-order electric ten-poles mode of outer-square. When the coupling distance D has decreased from 70 to 10 nm, the electric field intensity has slightly decreased from 98 to 43, which leads to the slight decrease of absorptivity from 20.3% to 15.1%.
Fig. 3 The electric fields intensity (|E|2) distribution of absorption band f2 when the coupling distance D is (a) 70, (b) 50, (c) 30, and (d) 10 nm, respectively. (e) The peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f2.
Fig. 4 The electric fields intensity (|E|2) distribution of absorption band f1 when the coupling distance D is (a) 70, (b) 50, (c) 30, and (d) 10 nm, respectively. (e) The peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f1.
Fig. 5 The electric fields intensity (|E|2) distribution of absorption band f4 when the coupling distance D is (a) 70, (b) 50, (c) 30, and (d) 10 nm, respectively. (e) The peak absorptivity and maximum electric field intensity as functions of the coupling distance D for f4.
The tunability of the absorption peaks is very important for the design of the metamaterial perfect absorbers. The MPA based on the OSIRCR in case4 has three absorption peaks at f1 = 61.8 THz, f2 = 96.4 THz, and f3 = 167.8 THz with absorptivity 96.6%, 93.5%, and 95.3%, respectively. Only the absorption peak f2 has apparent blueshift when the inner diameter L1 of the ring resonators increases from 110 to 390 nm as shown in Fig. 6(a). It’s because the absorption peak f2 mainly comes from the electric dipole mode of inner-ring. Only the absorption peak f1 and f3 have apparent blueshift when the outer length L4 of the square resonators increases from 560 to 720 nm as shown in Fig. 6(b). It’s because the absorption peak f1 and f3 mainly come from the excitation of the fundamental electric dipole modes and the higher-order electric sextupole modes of the outer-square resonators, respectively.
Fig. 6 Dependence of the spectral absorptivity on (a) the inner diameter L1 of the ring resonators and (b) the outer length L4 of the square resonators in case4. The unchanged geometry parameters are given as: P = 1000, T1 = 200, T2 = 80, T3 = 200, L2 = 460, L3 = 480, D = (L3 – L2)/2 = 10 (units: nm).
It’s very important that the material's replaceability and cost control for the practical applications of a specific MPA. We have succeeded in obtaining a triple-band metamaterial perfect absorber with average absorptivity 95.1% by using the OSIRCR made of Ag and ZnS. Figure 7(a), 7(b), and 7(c) show the dependence of the spectral absorptivity on the coupling distance D between the inner-ring and the outer-square when the metallic material Ag is replaced with the Au, the Al, and the Cu, respectively. The permittivity of Au, Al, and Cu are extracted from the experimental data of Palik [34] in the simulation. For the case4, the MPAs made of the ZnS and Au, or Al, or Cu all show three high absorptivity bands, which means the material's replaceability is good. And of course, the cost of Al and Cu would be much smaller than the Ag and the Au. We can also see the enhancement of higher-order modes’ absorptivity along with the reduction of the distance between the ring resonators and the square resonators for all the structure made of Au, Al, and Cu, which means the adaptivity of the near-field coupling idea is good.
Fig. 7 The dependence of the spectral absorptivity on the coupling distance D between the inner-ring and the outer-square when the material Ag is replaced with (a) Au, (b) Al, and (c) Cu.
Through the above analysis, the outer-square inner-ring coupled resonator (OSIRCR) can significantly enhance the higher-order electric sextupole modes absorptivity of the outer-square and shows a good adaptability to the materials. It’s also very important that the adaptability of the near-field coupling idea to different nanostructures. So we investigate the spectral absorptivity of outer-square inner-dodecagon coupled resonators (OSIDCR) and outer-square inner-octagon coupled resonators (OSIOCR) by replacing the ring resonators with the dodecagon resonators or octagon resonators as shown in Fig. 8. The thicknesses of the top, middle, and bottom layer are T1, T2, and T3, respectively. The period of the nanostructure is P. The inscribed circle and escribed circle diameters of the dodecagon and octagon resonators are L1 and L2, respectively. The inner and outer lengths of the square resonators are L3 and L4, respectively. The width of the sides of the square W is calculated by W = (L4 – L3)/2. The distance D between resonators can be calculated by D = (L3 – L2)/2. In the calculation, the specific geometry parameters are shown in Table 1. Whether it is the OSIDCR or OSIOCR, the behaviors of their absorptivity spectrum are just the same as the OSIRCR when the coupling distance D between resonators is reduced from 70 nm to 10 nm. The absorptivity of higher-order electric sextupole modes f3 has great enhancement due to the near-field coupling between the electric dipole modes of the dodecagon or octagon and the electric sextupole modes of the square. So the adaptability of the near-field coupling idea to different nanostructures is good.
Fig. 8 (a) Schematic of our designed metamaterial perfect absorbers consisting of outer-square inner-dodecagon coupled resonators (OSIDCR) and (b) the dependence of the spectral absorptivity on the distance D between the inner-dodecagon and the outer-square. (c) Schematic of our designed metamaterial perfect absorbers consisting of outer-square inner-octagon coupled resonators (OSIOCR) and (d) the dependence of the spectral absorptivity on the coupling distance D between the inner-octagon and outer-square.
3. Design of a six-band polarization-independent MPA
In general, the square resonators (SR) and ring resonators (RR) can only achieve single nearly perfect absorption band by exciting the fundamental electric dipole modes. The multiband MPAs can be achieved by the resonators coplanar method. And the absorption bands number of the multiband MPA needs to correspond to the number of the resonators. However, we have succeeded in obtaining a triple-band metamaterial perfect absorber with average absorptivity of 95.1% utilizing our designed outer-square inner-ring coupled resonators (OSIRCR) by increasing the higher-order electric sextupole modes’ absorptivity with near-field coupling idea. The combination of resonators coplanar method and near-field coupling idea has the potential to make the perfect absorption bands number greater than four. So we have designed another one MPA consisting of two different sized OSIRCRs A and B, whose schematic is shown in Fig. 9(a). The absorber is still the metal-dielectric-metal configuration and the top layer consists of a smaller OSIRCR A and a larger OSIRCR B.
Fig. 9 (a) Schematic of our designed MPA consisting of two different sized OSIRCRs A and B and (b) the corresponding spectral absorptivity. (c) The spectral absorptivity as functions of the polarization angles.
The geometry parameters are given as: P = 2200, T1 = 300, T2 = 80, T3 = 200, L1A = 220, L2A = 380, L3A = 400, L4A = 580, WA = (L4A – L3A)/2 = 90, DA = (L3A – L2A)/2 = 10, L1B = 350, L2B = 560, L3B = 580, L4B = 720, WB = (L4B – L3B)/2 = 70, and DB = (L3B – L2B)/2 = 10 (units: nm). Figure 9(b) shows the spectral absorptivity of our designed MPA consisting of two different sized OSIRCRs. It’s clear to see that there are six absorption bands in the infrared range. The six absorption bands are at f1 = 55.1 THz, f2 = 63.2 THz, f3 = 79.5 THz, f4 = 91.3 THz, f5 = 145.4 THz, f6 = 157.9 THz with absorptivity of 98%, 86.1%, 98.1%, 95.2%, 90.6%, and 81%, respectively. Figure 9(c) shows the spectral absorptivity as functions of the polarization angles of incident light. Due to the symmetry of the MPA, the polarization angles have little influence on the spectral absorptivity. So we have successfully designed a six-band polarization-independent metamaterial perfect absorber with average absorptivity of 91.5%.
To understand the underlying physical mechanism, Fig. 10 shows the electric fields intensity (|E|2) distribution of the six nearly perfect absorption bands. As shown in Fig. 10(a), the electric fields are accumulated around the outer-square of OSIRCR B and there are two poles. So the absorption band at f1 = 55.1 THz with absorptivity of 98% comes from the fundamental electric dipole modes of the outer-square of OSIRCR B. As shown in Fig. 10(b), the electric fields are accumulated around the outer-square of OSIRCR A and there are two poles. So the absorption band at f2 = 63.2 THz with absorptivity of 86.1% comes from the fundamental electric dipole modes of the outer-square of OSIRCR A. As shown in Fig. 10(c), the electric fields are accumulated around the inner-ring of OSIRCR B and there are two poles. So the absorption band at f3 = 79.5 THz with absorptivity of 98.1% comes from the fundamental electric dipole modes of the outer-square of OSIRCR B. As shown in Fig. 10(d), the electric fields are accumulated around the inner-ring of OSIRCR A and there are two poles. So the absorption band at f4 = 91.3 THz with absorptivity of 95.2% comes from the fundamental electric dipole modes of the outer-square of OSIRCR A. As shown in Fig. 10(e), the electric fields are accumulated around the outer-square of OSIRCR B and there are six poles. So the absorption band at f5 = 145.4 THz with absorptivity of 90.6% comes from the higher-order electric sextupole modes of the outer-square of OSIRCR B. As shown in Fig. 10(f), the electric fields are accumulated around the outer-square of OSIRCR A and there are six poles. So the absorption band at f6 = 157.9 THz with absorptivity of 81% comes from the higher-order electric sextupole modes of the outer-square of OSIRCR A.
Fig. 10 The electric fields intensity (|E|2) distribution of the six-band MPA at (a) f1 = 55.1 THz, (b) f2 = 63.2 THz, (c) f3 = 79.5 THz, (d) f4 = 91.3 THz, (e) f5 = 145.4 THz, and (f) f6 = 157.9 THz, respectively.
4. Conclusions
In summary, the outer-square inner-ring coupled resonator (OSIRCR) is proposed by introducing the near-field-coupling idea. It can enhance the absorptivity of higher-order electric sextupole modes of the outer-square from 17.6% to 95.3% when the coupling distance decreases from 70 nm to nm. It can also excite the fundamental electric dipole mode of the outer-square and the inner-ring. For practical applications, the three absorption peaks’ positions can be tuned by changing the geometry parameters of the inner-ring and the outer-square. For our designed OSIRCR based MPA, the absorptivity of higher-order electric sextupole modes can still be significantly enhanced when the material Ag is replaced by other materials like Au, Al, and Cu. By introducing the near-field coupling idea, other structure configuration can also significantly enhance the higher-order electric sextupole modes absorptivity like outer-square inner-dodecagon resonators and outer-square inner-octagon resonators using the materials Ag and ZnS. Then a six-band polarization-independent MPA in the infrared range is designed with average absorptivity of 91.5% utilizing two different sized OSIRCRs. Four of them are fundamental electric dipole modes and two of them are higher-order electric sextupole modes. The combination of resonators coplanar method and near-field coupling idea has the potential to obtain much more absorption bands.
Funding
National Natural Science Foundation of China (51576054).
References
1. 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(5801), 977–980 (2006). [CrossRef] [PubMed]
2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
3. A. Karalis and J. D. Joannopoulos, “‘Squeezing’ near-field thermal emission for ultra-efficient high-power thermophotovoltaic conversion,” Sci. Rep. 6(1), 28472 (2016). [CrossRef] [PubMed]
4. D. Xiao and K. Tao, “Ultra-compact metamaterial absorber for multiband light absorption at mid-infrared frequencies,” Appl. Phys. Express 8(10), 102001 (2015). [CrossRef]
5. K. Q. Le, Q. M. Ngo, and T. K. Nguyen, “Nanostructured metal-nsulator-Metal Metamaterials for Refractive Index Biosensing Applications: Design, Fabrication, and Characterization,” IEEE J. Sel. Top. Quantum Electron. 23(2), 6900506 (2017). [CrossRef]
6. R. Li, D. Wu, Y. Liu, L. Yu, Z. Yu, and H. Ye, “Infrared Plasmonic Refractive Index Sensor with Ultra-High Figure of Merit Based on the Optimized All-Metal Grating,” Nanoscale Res. Lett. 12(1), 1 (2017). [CrossRef] [PubMed]
7. T. Maier and H. Brückl, “Wavelength-tunable microbolometers with metamaterial absorbers,” Opt. Lett. 34(19), 3012–3014 (2009). [CrossRef] [PubMed]
8. T. Maier and H. Brueckl, “Multispectral microbolometers for the midinfrared,” Opt. Lett. 35(22), 3766–3768 (2010). [CrossRef] [PubMed]
9. S. Ogawa, K. Okada, N. Fukushima, and M. Kimata, “Wavelength selective uncooled infrared sensor by plasmonics,” Appl. Phys. Lett. 100(2), 021111 (2012). [CrossRef]
10. S. Ogawa, K. Masuda, Y. Takagawa, and M. Kimata, “Polarization-selective uncooled infrared sensor with asymmetric two-dimensional plasmonic absorber,” Opt. Eng. 53(10), 107110 (2014). [CrossRef]
11. S. Ogawa, J. Komoda, K. Masuda, and M. Kimata, “Wavelength selective wideband uncooled infrared sensor using a two-dimensional plasmonic absorber,” Opt. Eng. 52(12), 127104 (2013). [CrossRef]
12. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19(21), 3628–3632 (2007). [CrossRef]
13. N. Zhang, P. Zhou, S. Wang, X. Weng, J. Xie, and L. Deng, “Broadband absorption in mid-infrared metamaterial absorbers with multiple dielectric layers,” Opt. Commun. 338, 388–392 (2015). [CrossRef]
14. G. Dayal and S. Anantha Ramakrishna, “Design of multi-band metamaterial perfect absorbers with stacked metal-dielectric disks,” J. Opt. 15(5), 055106 (2013). [CrossRef]
15. S. Liu, J. Zhuge, S. Ma, H. Chen, D. Bao, Q. He, L. Zhou, and T. J. Cui, “A bi-layered quad-band metamaterial absorber at terahertz frequencies,” J. Appl. Phys. 118(24), 245304 (2015). [CrossRef]
16. P. K. Singh, K. A. Korolev, M. N. Afsar, and S. Sonkusale, “Single and dual band 77/95/110 GHz metamaterial absorbers on flexible polyimide substrate,” Appl. Phys. Lett. 99(26), 264101 (2011). [CrossRef]
17. 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]
18. J. Chen, Z. Hu, S. Wang, X. Huang, and M. Liu, “A triple-band, polarization- and incident angle-independent microwave metamaterial absorber with interference theory,” Eur. Phys. J. B 89(1), 14 (2016). [CrossRef]
19. X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]
20. D. Zheng, Y. Cheng, D. Cheng, Y. Nie, and R. Gong, “Four-Band Polarization-Insensitive Metama- Terial Absorber Based on Flower-Shaped Structures,” Prog. Electromagnetics Res. 142, 221–229 (2013). [CrossRef]
21. J. W. Park, P. V. Tuong, J. Y. Rhee, K. W. Kim, W. H. Jang, E. H. Choi, L. Y. Chen, and Y. Lee, “Multi-band metamaterial absorber based on the arrangement of donut-type resonators,” Opt. Express 21(8), 9691–9702 (2013). [CrossRef] [PubMed]
22. G. D. Wang, M. H. Liu, X. W. Hu, L. H. Kong, L. L. Cheng, and Z. Q. Chen, “Multi-band microwave metamaterial absorber based on coplanar Jerusalem crosses,” Chin. Phys. B 23(1), 017802 (2014). [CrossRef]
23. W. Wang, M. Yan, Y. Pang, J. Wang, H. Ma, S. Qua, H. Chen, C. Xu, and M. Feng, “Ultra-thin quadri-band metamaterial absorber based on spiral structure,” Appl. Phys., A Mater. Sci. Process. 118(2), 443–447 (2015). [CrossRef]
24. Y. Ma, Q. Chen, J. Grant, S. C. Saha, A. Khalid, and D. R. S. Cumming, “A terahertz polarization insensitive dual band metamaterial absorber,” Opt. Lett. 36(6), 945–947 (2011). [CrossRef] [PubMed]
25. B. X. Wang, X. Zhai, G. Z. Wang, W. Q. Huang, and L. L. Wang, “Design of a four-band and polarization-insensitive terahertz metamaterial absorber,” IEEE Photonics J. 7, 4600108 (2015). [CrossRef]
26. W. Pan, X. Yu, J. Zhang, and W. Zeng, “A Novel Design of Broadband Terahertz Metamaterial Absorber Based on Nested Circle Rings,” IEEE Photonics Technol. Lett. 28(21), 2335–2338 (2016). [CrossRef]
27. Z. C. Xu, R. M. Gao, C. F. Ding, Y. T. Zhang, and J. Q. Yao, “Multiband metamaterial absorber at terahertz frequencies,” Chin. Phys. Lett. 31(5), 054205 (2014). [CrossRef]
28. T. Xie, Z. Chen, R. Ma, and M. Zhong, “A wide-angle and polarization insensitive infrared broad band metamaterial absorber,” Opt. Commun. 383, 81–86 (2017). [CrossRef]
29. J. Kim, K. Han, and J. W. Hahn, “Selective dual-band metamaterial perfect absorber for infrared stealth technology,” Sci. Rep. 7(1), 6740 (2017). [CrossRef] [PubMed]
30. J. Le Perchec, Y. Desieres, N. Rochat, and R. Espiau De Lamaestre, “Subwavelength optical absorber with an integrated photon sorter,” Appl. Phys. Lett. 100(11), 113305 (2012). [CrossRef]
31. C. Chen, Y. Sheng, and W. Jun, “Computed a multiple band metamaterial absorber and its application based on the figure of merit value,” Opt. Commun. 406, 145–150 (2018). [CrossRef]
32. B. Zhang, J. Hendrickson, and J. Guo, “Multispectral near-perfect metamaterial absorbers using spatially multiplexed plasmon resonance metal square structures,” J. Opt. Soc. Am. B 30(3), 656–662 (2013). [CrossRef]
33. J. Xu, Z. Zhao, H. Yu, L. Yang, P. Gou, J. Cao, Y. Zou, J. Qian, T. Shi, Q. Ren, and Z. An, “Design of triple-band metamaterial absorbers with refractive index sensitivity at infrared frequencies,” Opt. Express 24(22), 25742–25751 (2016). [CrossRef] [PubMed]
34. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
