 Nano Express
 Open Access
 Published:
Design of Narrow Discrete Distances of Dual/TripleBand Terahertz Metamaterial Absorbers
Nanoscale Research Letters volume 14, Article number: 64 (2019)
Abstract
Various kinds of structure designs have been proposed to achieve the multipleband metamaterial absorbers. However, the discrete distance of adjacent frequencies of multiple absorbers is considerably large, which will inevitably overlook a large amount of information hidden in the offresonance absorption areas. Herein, a narrow discrete distance of dualband terahertz absorber based on two pairs of an Au strip/dielectric layer backed by Au film is designed. Two nearly 100% absorptivities of resonance peaks having the discrete distance of only 0.30 THz are realized. The relative discrete distance of the device is 13.33%, and this value can be adjusted via the length change of an Au strip. Furthermore, we present two narrow discrete distances of a tripleband absorber through stacking one more pair of an Au strip and dielectric layer. Results prove that two discrete distances of only 0.14 THz and 0.17 THz in adjacent absorption modes of the first two and the last two are achieved, respectively; the relative discrete distances of them are respectively 6.57% and 7.22%, which are far from previous reports. Narrow discrete distances (or low values of relative discrete distance) of the multipleband absorbers have a large number of applications in the investigation of some hidden information in very near frequencies.
Introduction
Metamaterial perfect absorbers (abbreviated as MPAs) as an important part of optical absorption devices have attracted considerable research activities because they possess many advantages over others, such as ~ 100% absorption, ultrathin thickness of dielectric layer, narrow absorption bandwidth, and freedom design of pattern structure [1,2,3,4,5,6,7,8,9,10,11,12]. The first design concept of MPA [13], consisted of a sandwich structure of an electricring resonator, insulation dielectric layer, and metallic strip, was presented by a research group from Boston College in the year of 2008. A resonance peak with an absorption rate of higher than 88% at a frequency of 11.5 GHz can be experimentally obtained. The dielectric thickness of the device is only about 1/35 of the absorption wavelength, which is far less than previous absorption devices. The MPA with these features can be potentially used in bolometer, sensing, detection, and imaging. However, a narrow acceptance angle, polarization sensitivity, and singleband absorption response are the disadvantages of the presented MPAs.
To overcome these issues [14,15,16,17,18,19,20,21,22,23,24], many works have been suggested to develop the wideangle, polarizationinsensitive, multipleband and even broadband MPAs through reasonable optimization of structure designs. For example, a wideangle optical MPA based on 1dimensional stack array of a resonance structure was suggested in ref. [18]. Nested metallic ring resonators were demonstrated to get the multipleband resonance absorption [19,20,21,22,23]. In the development and research process of absorption devices, multipleband MPAs, which can be used for some of dangerous goods (dynamite, detonator, and alcohol) detection, spectroscopic imaging (various types of controlled knives), sensing, and selective bolometer, have received tremendous attention [19,20,21,22,23,24,25,26,27,28,29,30].
Generally speaking, three kinds of methods can be used to achieve the multipleband MPAs. The first method, commonly referred to as a coplanar construction method, is formed by multiple different sizes of resonators in a superunit structure [19,20,21,22,23,24,25,26]. The second is called the vertical stacked method, consisted of alternate stacks of multiple discrete dimensions of elements [27,28,29,30]. The third is the combination of the first two methods [31, 32]. Although these approaches can flourish and develop the multipleband MPAs, the discrete distances of the resonance frequencies of adjacent absorption peaks are quite large. A large discrete distance in two adjacent frequencies will inevitably overlook a lot of information hidden in the offresonance areas, i.e., the discrete areas. In order to avoid the loss of information, therefore, the large discrete distance of multipleband MPAs should be overcome. Although the discrete distances of multipleband MPAs can be reduced via suitable structure optimization, the offresonance absorption areas of them are relatively large (greater than 60%), they should be called the broadband MPAs [33,34,35,36,37,38,39,40], not the multipleband MPAs. As everyone knows, multipleband and broadband MPAs are essentially different in their applications. Therefore, it is necessary to ensure low absorption rates (less than 60%) of offresonance areas in the optimization for reduction of discrete distances.
In fact, a relative discrete distance should be more meaningful than a discrete distance because it can reflect the true information of two adjacent frequencies. The relative discrete distance (△) of two adjacent peaks can be defined as △ = 2(f_{2} − f_{1})/(f_{1} + f_{2}), where f_{1} and f_{2} are the frequencies of two neighboring peaks. To guarantee △ > 0, the frequency of f_{2} should be higher than that of f_{1}. According to this definition, the minimum △ values of previous multipleband MPAs are typically no less than 50% [19,20,21,22,23,24,25,26,27,28,29,30], which are far from satisfactory to explore and investigate the hidden messages in the areas of adjacent frequencies. It is very reasonable, therefore, to develop multipleband MPAs with very near frequencies or low values of △.
In this paper, we present the low △ value of dualband terahertz MPA formed by duallayer stack of Au strips and insulation dielectric layers backed by a continuous Au plane. Two nearly perfect absorption peaks with discrete distance of only 0.30 THz are obtained. The △ value of device is 13.33%, which is only 1/4 of the previous minimum value of MPAs, and the △ value can be tuned through dimension change of the Au strips. Its △ value can be reduced to only 6.45%, which is far less than that of previous MPAs. A narrow discrete distance or low △ value of the dualband MPA is caused by the ultranarrow bandwidth of each resonance band. We furthermore present two low △ values of tripleband MPA through stacking one more Au strip. Two narrow discrete distances of only 0.14 THz and 0.17 THz in three nearly perfect absorption peaks can be realized; the △ values of adjacent frequencies of tripleband MPAs are respectively 6.57% and 7.22%, which are both smaller than that of previous works. Low △ values of these MPAs can find a number of applications in the study of some implicit information in the areas of offresonance absorption.
Methods/Experimental
In general, the bandwidth (refers to FWHM, full wave at half maximum) of singleband MPA is relatively wide, which can reach 20% of center resonance frequency, because of strong resonance response of metamaterials. The combination of these singleband peaks to form multipleband MPAs inevitably possesses large values of discrete distance or △. This is why the previous multipleband MPAs have large △ values. The key to obtain the low values of △ is to design the narrow bandwidth of singleband MPAs. Herein, we first design this kind of singleband MPA. A common sandwich structure formed by an Au resonator and a certain thickness of dielectric material backed by an Au mirror is employed to achieve the singleband absorption, as illustrated in Fig. 1a. The Au resonator is a rectangular strip structure, see Fig. 1b. It has the length of l = 39 μm, width of w = 8 μm, thickness of 0.4 μm, and conductivity of 4.09 × 10^{7} S/m. The MPA has a unit period of P = 60 μm. The dielectric slab has a thickness of t = 2 μm and dielectric constant of 3(1 + i0.001).
To present the resonance performance of the suggested device and explain the physical mechanism involved, we performed numerical calculations using the commercial simulation software, FDTD Solutions, which is based on the finitedifference timedomain algorithm. In the computing process, periodic boundary conditions are utilized in both directions of x and yaxes to characterize the periodic arrangement of the unit cell, while perfectly matched layers are employed along the direction of the zaxis (i.e., the light propagation direction) to eliminate the unnecessary scattering. The absorption (A) of the device can be given by A = 1 – T − R, where T and R are the transmission and reflection of the metamaterial absorber, respectively. Because the thickness of the bottom metallic film is greater than the skin depth of the incident light, the transmission T of the metamaterial absorber is equal to zero. As a result, the absorption A can be simplified to A = 1 − R. The suggested device can have 100% absorption when the reflection R is completely suppressed.
Results and Discussion
The absorption curve of singleband MPA under plane wave irradiation is demonstrated in Fig. 2a; ~ 100% absorption of a single resonance peak at a frequency of 2.25 THz is obtained. The bandwidth of the device is 0.06 THz, which is only 2.67% of the center resonance frequency and is about 1/8 of a previous singleband MPA [1,2,3,4,5,6,7,8,9,10,11,12,13]. Additionally, the Q (defined as resonance frequency divided by bandwidth) value of the device can be up to 37.50. The ultranarrow bandwidth (or high Q value) of MPA not only contributes to the applications of device itself, but also helps to the design of low △ value of multipleband MPAs. Figure 2b, c, and d provide the field distributions of the resonance peak. As shown, its magnetic field (Hy) in Fig. 2b is mostly concentrated in an insulation dielectric layer of MPA, and strong electric field enhancement can be observed at both sides of the Au resonator along the long axis (see Fig. 2c, d). These field distribution features indicate that the large light absorption of narrow bandwidth of MPA is due to the magnetic resonance [1,2,3,4].
We next explore whether the combination of these narrow bandwidth of MPAs has the ability to realize the low △ value of multipleband MPAs. A vertically stacked design concept, as a kind of frequently used method, is employed to obtain the multipleband MPAs. An example of the simplest kind is the case of dualband absorption. Figure 1c gives the sideview of the structure model of the dualband absorption. As shown, two layers of metallic strip resonators and insulation dielectric slabs are alternately stacked on a metallic ground plane. The lengths of two Au strips are respectively l_{1} = 36 μm and l_{2} = 39 μm; the widths of them are fixed as w = 8 μm. The thicknesses of dielectric slabs are t_{1} = 1.4 μm and t_{2} = 2 μm. Other parameters of the dualband MPA, including unit period, dielectric constant of the slab, thickness, and conductivity of Au strips, are the same as those of the singleband MPA.
The absorption curve of the dualband MPA under plane wave irradiation is illustrated in Fig. 3a. Different from the case of the singleband MPA in Fig. 2a, two resonance peaks with ~ 100% absorption rates at frequencies of 2.10 THz and 2.40 THz are achieved. The bandwidths of the two peaks are respectively 0.05 THz and 0.09 THz, which are only 2.00% and 3.75% of corresponding resonance frequencies, respectively. The Q values of the two peaks are 42.00 and 26.67, respectively. Additionally, the offresonance absorption of the two peaks is very low, less than 12%. These features show that the two peaks having narrow bandwidths can be clearly distinguished. It is important that the discrete distance of the two peaks is only 0.30 THz, and its △ is 13.33%, which is smaller than that of previous works [19,20,21,22,23,24,25,26,27,28,29,30]. The low △ value of dualband MPA is promising in many areas of engineering and technology. The resonance mechanisms of the two absorption peaks can be gained by analyzing their magnetic fields Hy. The field Hy for the first peak is mostly focused on the second dielectric slab of the dualband MPA, while the field in the first dielectric layer has a very small percentage (see Fig. 3b). The characteristics of field distribution prove that the first absorption mode is attributed to magnetic resonance of the second dielectric layer, or the first peak frequency is caused by metallic strip length l_{2} (see Fig. 3e). Different from the case of the first resonance mode, the Hy field of the second mode is primarily distributed in the first layer of dielectric slab (see Fig. 3c), which indicates that this mode is derived from magnetic resonance of the first dielectric slab, or its resonance frequency can be tuned via varying the size of strip length l_{1} (see Fig. 3d), and thus tune the △ value of the dualband MPA.
The △ values of the dualband MPA can be adjusted through changing the sizes of Au strips because the frequencies of the two modes mainly depend on the corresponding sizes of strips. For example, for length l_{1} change of the first layer of Au strip (see Fig. 3d), the frequency of the second mode gradually decreases with the increase of l_{1}, while the frequency shift of the first mode can be neglected because its size is fixed. The discrete distances of the two peaks are varied because of the frequency shift of the second mode. More concretely, the discrete distances can be decreased from 0.41 THz in l_{1} = 33 μm to 0.30 THz in l_{1} = 36 μm and 0.23 THz in l_{1} = 39 μm. The △ values of the dualband MPA can also be decreased from 17.41% in l_{1} = 33 μm to 13.33% in l_{1} = 36 μm and 10.38% in l_{1} = 39 μm. That is to say, the strip length l_{1} change can decrease the discrete distances and the △ values. Similarly, the strip length l_{2} change only affects its corresponding resonance frequency, i.e., the first resonance mode, see Fig. 3e. The discrete distances and △ values of dualband MPA are both decreased with l_{2} decrease because the first mode frequency with the decrease of l_{2} is gradually close to the second absorption peaks, as shown in Fig. 3e. When l_{2} = 36 μm, the discrete distance has the smallest value, which is 0.15 THz. At this time, its △ value is only 6.45%, which is smaller than that of previous reports. These results prove that the discrete distances (or △ values) of dualband MPA can be controlled to meet the requirements of different applications through tuning the sizes of Au strips.
We further investigate whether the stack of one more Au strip (i.e., triplelayer structure) can achieve two low △ values of tripleband MPAs. Figure 1d presents a side view of a triplelayer structure model of MPA, which is consisted of three pairs of Au strip/dielectric slab on top of an Au mirror. The Au strips have lengths of l_{1} = 34 μm, l_{2} = 36 μm, and l_{3} = 39 μm. The dielectric slabs have thicknesses of t_{1} = 1.2 μm, t_{2} = 1.4 μm, and t_{3} = 2.8 μm, respectively. The widths of Au strips are all w = 8 μm. Other parameters of the triplelayer MPA are the same as designed above. The absorption curve of the triplelayer MPA under plane wave irradiation is shown in Fig. 4a. Three discrete peaks having ~ 100% absorption rates at frequencies of 2.06 THz, 2.27 THz, and 2.51 THz can be found. The discrete distances of adjacent peaks in resonance modes of the first two and the last two are respectively 0.21 THz and 0.24 THz. The △ values of the modes of the first two and the last two are 9.70% and 10.04%, respectively, which are both less than that the values of multipleband MPAs. In addition to narrow discrete distances, the absorption rates in offresonance areas of the tripleband MPA are relatively low, no more than 32% (see Fig. 4a). It is shown that the three very near peaks can be clearly identified and can be used for sensing, detection, imaging, and application to other tasks. The Hy field distributions of the three absorption peaks are provided to analyze the resonance mechanism of the tripleband MPA. As shown in Fig. 4, the Hy field distributions of the first, the second, and the third mode of the tripleband MPA can be mainly found in the dielectric layers of t_{3}, t_{2}, and t_{1}, respectively, while the fields in other dielectric layers are negligible. For example, for the first mode in Fig. 4b, the fields in dielectric layers of t_{2} and t_{1} can be neglected, and the fields in dielectric layers of t_{2} and t_{3} are negligible for the third mode in Fig. 4d. These distribution features state clearly that the three absorption peaks are all caused by magnetic resonances. More specifically, the first, the second, and the third modes are attributed to magnetic resonances of the third dielectric layer t_{3}, the second dielectric layer t_{2}, and the first dielectric layer t_{1}, respectively, or the frequencies of the first, the second, and the third mode are dependent on Au strip lengths of l_{3}, l_{2}, and l_{1}, respectively.
The △ values of the tripleband MPA can be controlled through adjusting the Au strip lengths. Figure 4e gives the absorption curves of the tripleband MPA in different cases of length l_{1}. As you can see, the l_{1} change mainly affects the third mode frequency, while the frequency shifts of the first two modes are negligible, which are consistent with the theoretical prediction. Due to the frequency variation of the third mode, we can tune the △ value of the last two modes of the tripleband MPA. The △ values of the last two modes can be tuned from 12.66% in l_{1} = 33 μm to 10.04% in l_{1} = 34 μm, and 7.22% in l_{1} = 35 μm. The △ value of the first two modes can also be controlled by adjusting length l_{3} (see Fig. 4g). The minimum discrete distance of the first two modes is 0.16 THz for l_{3} = 38 μm, and its △ value is 7.31%. Furthermore, we can tune the △ values of the first two and last two modes via scaling the length l_{2}, i.e., the frequency of the second mode (see Fig. 4f). Remarkably, the △ value changes of the first two and last two modes are mutual restriction because we only change the frequency of the second mode. For example, for l_{1} = 37 μm (see the blue line in Fig. 4f), the discrete distance of the first two modes has the minimum value of 0.16 THz, while maximum value of 0.29 THz for last two modes can be obtained.
Conclusion
In conclusion, a narrow discrete distance of the dualband terahertz MPA consisted of two pairs of Au strip/dielectric slab backed by an Au film is presented. Two ~ 100% absorption rates of resonance peaks having the discrete distance of 0.30 THz are realized, and the △ of the dualband MPA is 13.33%. The mechanism of dualband absorption is caused by superposition effects of two different frequencies of magnetic resonances. We can further adjust △ values of the dualband MPA through employing different lengths of Au strips. The △ value can be decreased to only 6.45%, which is much lower than that of previous results. Moreover, two narrow discrete distances of the tripleband MPA are demonstrated by stacking one more pair of strip/dielectric. Three ~ 100% absorptivities of resonance peaks with discrete distances of 0.21THz and 0.24 THz are achieved. The △ values of two adjacent frequencies (that are the modes of first two and the last two) are respectively 9.70% and 10.04%. Similar to the case of dualband absorption, the tripleband MPA also has the ability to tune the △ value of adjacent frequencies by controlling the lengths of Au strips. Narrow discrete distances or low △ values of multipleband MPAs are promising in many areas, such as investigation of some implicit information in two very near frequencies.
Abbreviations
 FWHM:

Full wave at half maximum
 MPAs:

Metamaterial perfect absorbers
 Q:

Quality factor
References
 1.
Watts CM, Liu X, Padilla WJ (2012) Metamaterial electromagnetic wave absorbers. Adv Mater 24:OP98–OP120
 2.
Ye YQ, Jin Y, He S (2010) Omnidirectional, polarizationinsensitive and broadband thin absorber in the terahertz regime. J Opt Soc Am B 27:498–504
 3.
Zhang N, Zhou P, Cheng D, Weng X, Xie J, Deng L (2013) Dualband absorption of midinfrared metamaterial absorber based on distinct dielectric spacing layers. Opt Lett 38:1125–1127
 4.
Hendrickson J, Guo J, Zhang B, Buchwald W, Soref R (2012) Wideband perfect light absorber at midwave infrared using multiplexed metal structures. Opt Lett 37:371–373
 5.
Liu X, Fan K, Shadriovo IV, Padilla WJ (2017) Experimental realization of a terahertz alldielectric metasurface absorber. Opt Express 25:191–201
 6.
Radi Y, Simovski CR, Tretyakov SA (2015) Thin perfect absorbers for electromagnetic waves: theory, design, and realizations. Phys Rev Applied 3:037001
 7.
Dao TD, Chenm K, Ishii S, Ohi A, Nabatame T, Kitajima M, Nagao T (2015) Infrared perfect absorbers fabricated by colloidal mask etching of AlAl_{2}O_{3}Al trilayers. ACS Photon 2:964–970
 8.
Yong Z, Zhang S, Gong C, He S (2016) Narrow band perfect absorber for maximum localized magnetic and electric field enhancement and sensing applications. Sci Rep 6:24063
 9.
Liu X, Bi K, Li B, Zhao Q, Zhou J (2016) Metamaterial perfect absorber based on artificial dielectric “atoms”. Opt Express 24:20454–20460
 10.
Chen K, Dao TD, Ishii S, Aono M, Nagao T (2015) Infrared aluminum metamaterial perfect absorbers for plasmonenhanced infrared spectroscopy. Adv Funct Mater 25:6637–6643
 11.
Zhao X, Fan K, Zhang J, Seren HR, Metcalfe GD, Wraback M, Averitt RD, Zhang X (2015) Optically tunable metamaterial perfect absorber on highly flexible substrate. Sensors Actuators A Phys 231:74–80
 12.
Wang BX, Zhai X, Wang GZ, Huang WQ, Wang LL (2015) Frequency tunable metamaterial absorber at deepsubwavelength scale. Opt Mater Express 5:227–235
 13.
Landy NI, Sajuyigbe S, Mock JJ, Smith DR, Padilla WJ (2008) Perfect metamaterial absorber. Phys Rev Lett 100:207402
 14.
Xue CH, Wu F, Jiang HT, Li Y, Zhang YW, Chen H (2016) Wideangle spectrally selective perfect absorber by utilizing dispersionless tamn plasmon polaritions. Sci Rep 6:39418
 15.
Song Z, Wang Z, Wei M (2019) Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces. Mater Lett 234:138–141
 16.
Wei M, Song Z, Deng Y, Liu Y, Chen Q (2019) Largeangle midinfrared absorption switch enabled by polarizationindependent GST metasurfaces. Mater Lett 236:350–353
 17.
Song Z, Wang K, Li J, Liu QH (2018) Broadband tunable terahertz absorber based on vanadium dioxide metamaterials. Opt Express 26:7148–7154
 18.
Cong L, Tan S, Yahiaoui R, Yan F, Zhang W, Singh R (2015) Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: a comparison with the metasurfaces. Appl Phys Lett 106:031107
 19.
Feng R, Qiu J, Cao Y, Liu L, Ding W, Chen L (2015) Wideangle and polarization independent perfect absorber based on onedimensional fabricationtolerant stacked array. Opt Express 23:21023–21031
 20.
Ma Y, Chen Q, Grant J, Saha SC, Khalid A, Cumming DRS (2011) A terahertz polarization insensitive dual band metamaterial absorber. Opt Lett 36:945–947
 21.
Shen X, Yang Y, Zang Y, Gu J, Han J, Zhang W, Cui TJ (2012) Tripleband terahertz metamaterial absorber: design, experiment, and physical interpretation. Appl Phys Lett 101:154102
 22.
Wang BX, Zhai X, Wang GZ, Huang WQ, Wang LL (2015) Design of a fourband and polarizationinsensitive terahertz metamaterial absorber. IEEE Photon J 7:4600108
 23.
Shen X, Cui TJ, Zhao J, Ma HF, Jiang WX, Li H (2011) Polarizationindependent wideangle tripleband metamaterial absorber. Opt Express 19:9401–9407
 24.
Bhattacharyya S, Ghosh S, Srivastava KV (2013) 7nd polarizationindependent metamaterial absorber with bandwidth enhancement at Xband. J Appl Phys 114:094514
 25.
Wang BX (2017) Quadband terahertz metamaterial absorber based on the combining of the dipole and quadrupole resonances of two SRRs. IEEE J Sel Top Quantum Electron 23:4700107
 26.
Yao G, Ling F, Yue J, Luo C, Ji J, Yao J (2016) Dualband tunable perfect metamaterial absorber in the THz range. Opt Express 24:1518–1527
 27.
Zhang B, Hendrickson J, Guo J (2013) Multispectral nearperfect metamaterial absorbers using spatially multiplexed plasmon resonance metal square structures. J Opt Soc Am B 30:656–662
 28.
Dayal G, Ramakrishna SA (2013) Design of multiband metamaterial perfect absorbers with stacked metaldielectric disks. J Opt 15:055106
 29.
Astorino MD, Frezza F, Tedeschi N (2017) Ultrathin narrowband, complementary narrowband, and dualband metamaterial absorbers for applications in the THz regime. J Appl Phys 121:063103
 30.
Kajtar G, Kafesaki M, Economou EN, Soukoulis CM (2016) Theoretical model of homogeneous metalinsulatormetal perfect multiband absorbers for the visible spectrum. J Phys D 49:055104
 31.
Liu S, Zhuge J, Ma S, Chen H, Bao D, He Q, Zhou L, Cui TJ (2016) A bilayered quadband metamaterial absorber at terahertz frequencies. J Appl Phys 118:245304
 32.
Wen D, Huang X, Guo L, Yang H, Han S, Zhang J (2015) Quadrupleband polarizationinsensitive wideangle metamaterial absorber based on multilayer structure. Optik 126:1018–1020
 33.
Hu F, Wang L, Quan B, Xu X, Li Z, Wu Z, Pan X (2013) Design of a polarization insensitive multiband terahertz metamaterial absorber. J Phys D 46:195103
 34.
Liu S, Chen H, Cui TJ (2015) A broadband terahertz absorber using multilayer stacked bars. Appl Phys Lett 106:151601
 35.
Su Z, Yin J, Zhao X (2015) Terahertz dualband metamaterial absorber based on graphene/MgF_{2} multilayer structures. Opt Express 23:1679–1690
 36.
Wen Y, Ma W, Bailey J, Matmon G, Yu X (2015) Broadband terahertz metamaterial absorber based on asymmetric resonators with perfect absorption. IEEE Trans THz Sci Techno 5:406–411
 37.
Wang BX, Wang GZ (2016) Two compact SRR resonators enabling fiveband perfect absorption. Mater Lett 180:317–321
 38.
Park JW, Tuong V, Rhee JY, Kim KW, Jang WH, Choi EH, Chen LY, Lee YP (2013) Multiband metamaterial absorber based on the arrangement of donuttype resonators. Opt Express 21:9691–9702
 39.
Wang BX, Wang LL, Wang GZ, Huang WQ, Li XF, Zhai X (2014) A simple design of ultrabroadband and polarization insensitive terahertz metamaterial absorber. Appl Phys A Mater Sci Process 115:1187–1192
 40.
Zhou J, Kaplan AF, Chen L, Guo LJ (2014) Experiment and theory of the broadband absorption by a tapered hyperbolic metamaterial array. ACS Photon 1:618–624
Funding
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51605148 and 11647143), Natural Science Foundation of Jiangsu Province (Grant No. BK20160189), and the Fundamental Research Funds for the Central Universities (Grant No. JUSRP51721B).
Availability of Data and Materials
All data are fully available without restriction.
Author information
Affiliations
Contributions
BXW conceived the research, conducted simulations and analyses, and wrote the manuscript. CT, QN, YH, and TC assisted in processing the data and figures. All authors read and approved the final manuscript.
Corresponding authors
Correspondence to BenXin Wang or Tao Chen.
Ethics declarations
Competing Interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Received
Accepted
Published
DOI
Keywords
 Metamaterial
 Perfect absorber
 Terahertz
 Narrow discrete distance