Engineering the Complex-Valued Constitutive Parameters of Metamaterials for Perfect Absorption

Nanoscale Research Letters, Apr 2017

We theoretically studied how to directly engineer the constitutive parameters of metamaterials for perfect absorbers of electromagnetic waves. As an example, we numerically investigated the necessary refractive index n and extinction coefficient k and the relative permittivity ε and permeability μ of a metamaterial anti-reflection layer, which could cancel the reflection from a hydrogenated amorphous silicon (α-Si:H) thin film on a metal substrate, within the visible wavelength range from 300 to 800 nm. We found that the metamaterial anti-reflection layer should have a negative refractive index (n < 0) for short-wavelength visible light but have a positive refractive index (n > 0) for long-wavelength visible light. The relative permittivity ε and permeability μ could be fitted by the Lorentz model, which exhibited electric and magnetic resonances, respectively.

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Engineering the Complex-Valued Constitutive Parameters of Metamaterials for Perfect Absorption

Wang et al. Nanoscale Research Letters Engineering the Complex-Valued Constitutive Parameters of Metamaterials for Perfect Absorption Pengwei Wang 1 Naibo Chen 1 Chaojun Tang 1 Jing Chen 0 2 Fanxin Liu 1 2 Saiqian Sheng 1 Bo Yan 1 Chenghua Sui 1 0 College of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications , Nanjing 210023 , China 1 Center for Optics & Optoelectronics Research, Department of Applied Physics, Zhejiang University of Technology , Hangzhou 310023 , China 2 National Laboratory of Solid State Microstructures, Nanjing University , Nanjing 210093 , China We theoretically studied how to directly engineer the constitutive parameters of metamaterials for perfect absorbers of electromagnetic waves. As an example, we numerically investigated the necessary refractive index n and extinction coefficient k and the relative permittivity ε and permeability μ of a metamaterial anti-reflection layer, which could cancel the reflection from a hydrogenated amorphous silicon (α-Si:H) thin film on a metal substrate, within the visible wavelength range from 300 to 800 nm. We found that the metamaterial anti-reflection layer should have a negative refractive index (n < 0) for short-wavelength visible light but have a positive refractive index (n > 0) for long-wavelength visible light. The relative permittivity ε and permeability μ could be fitted by the Lorentz model, which exhibited electric and magnetic resonances, respectively. Metamaterials; Perfect absorbers; Anti-reflection coating; Light harvesting - Background In recent years, metamaterial-based electromagnetic wave perfect absorbers have attracted too much interest [1–3], owing to a wide variety of potential applications such as thermal emitters [4–6], sensor [7–10], photodetection [11, 12], solar cells or thermo-photovoltaics [13–17], and so on. In 2008, Landy et al. first experimentally demonstrated metamaterial perfect absorbers in the microwave region, by matching the effective wave impedance of metamaterials to the free-space wave impedance [18]. Their designed metamaterial perfect absorbers consist of two standard split-ring resonators connected by the inductive ring parallel to the split wire and a cut wire in a parallel plane separated by a substrate. This seminal work in the microwave regime has inspired many studies on metamaterial perfect absorbers in other frequency regimes including terahertz [19–21], mid-infrared [22, 23], near-infrared [24–26], and visible realm [27–29]. At the same time, there also have been many efforts to make metamaterial perfect absorbers as efficient and effective as possible, through carefully engineering their versatile properties like polarization independence [30–33], broad incident angle [34–37], broad bandwidth or multi-band [38–41], tunability [42–44], and flexibility [45, 46]. In most metamaterial perfect absorbers, there is always a three-layer design with a ground plane or metallic substrate supporting a dielectric and top metallic nanostructure [1]. The physical mechanisms behind many metamaterial perfect absorbers are essentially the same: the top metallic structure is utilized to couple to the incident electric field, and the anti-parallel currents between the two metallic layers are used to couple to the incident magnetic field. By tuning the metamaterial geometry, one could impedance match to free space at a desired frequency range [1]. For explaining the same phenomenon of perfect absorption of electromagnetic waves, there are also other physical models based on interference theory of reflected waves [47–50], such as transmission line theory [51–54], Fabry-Pérot, or other cavity resonances [55–62]. In many studies on metamaterial perfect absorbers, tailoring the morphology of the top metallic nanostructure has been explored widely as an effective way to obtain © The Author(s). 2017 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. desired performances [1]. However, there are only few researches on directly engineering the complex-valued constitutive parameters of an artificial metamaterial for perfect absorbers of electromagnetic waves [63, 64]. For example, Ye et al. experimentally demonstrated a metamaterial perfect absorber in which the frequency-independent dispersion regions of both permittivity and permeability are stretched to an ultrawide band from 0.5 to 2.5 GHz, and the real and imaginary parts of the complex constitutive parameters are precisely tuned to satisfy a modified model of a perfectly matched layer [63]. Long et al. deduced theoretically the critical coupling condition to achieve perfect absorption for thin-film absorbers of absorbing layer/spacer layer/substrate and identified numerically the key characteristics of the absorbing layer needed for perfect absorption at a given wavelength [64]. In this work, we will theoretically show how to directly engineer the complex-valued constitutive parameters of artificial metamaterials for perfect absorbers of electromagnetic waves. Specifically speaking, for achieving ultrawideband perfect absorption within the visible wavelength range from 300 to 800 nm, we have numerically investigated the necessary refractive index n and extinction coefficient k, and the relative permittivity ε and permeability μ of a metamaterial anti-reflection layer, coating a hydrogenated amorphous silicon (α-Si:H) thin film on a metal substrate. It is found that the metamaterial anti-reflection layer should have a negative refractive index (n < 0) for short-wavelength visible light, but has a positive refractive index (n > 0) for long-wavelength visible light. As the thickness of the metamaterial anti-reflection layer is increased, the absolute value of n and k will become smaller. However, they will become larger when the thickness of the α-Si:H thin film is increased. The relative permittivity ε and permeability μ could be fitted by the Lorentz model, exhibiting electric and magnetic resonances, respectively. Methods The perfect absorber of electromagnetic waves investigated in this work is schematically shown in Fig. 1. Light is normally incident from air onto the perfect absorber, which consists of a metamaterial anti-reflection layer, and a hydrogenated amorphous silicon (α-Si:H) layer deposited on an Ag substrate. In our numerical calculations, the refractive index n0 of air is 1. The metamaterial anti-reflection layer has a complex refractive index of n1 + ik1 and a thickness of d1. The αSi:H layer has a complex refractive index of n2 + ik2 and a thickness of d2. The Ag substrate has a complex refractive index of n3 + ik3. In our numerical calculations, the used refractive index n and the extinction coefficient k of α-Si:H and Ag are presented in Fig. 2. Fig. 1 Schematic diagram of a perfect absorber of electromagnetic waves. The media labeled as 0, 1, 2, and 3 are air, metamaterial antireflection layer, hydrogenated amorphous silicon (α-Si:H) layer, and Ag substrate, respectively. The thicknesses of the anti-reflection and α-Si:H layers are d1 and d2, respectively In the three-layer structure shown in Fig. 1, the reflection coefficient of light can be expressed as [64, 65] Fig. 2 The refractive index n and extinction coefficient k of the Ag substrate and the hydrogenated amorphous silicon (α-Si:H) layer. The black (solid) line and the red (dash) line give the refractive index n1 and extinction coefficient k1 of Ag, respectively. The green (dot) line and the blue (dash dot) line give the refractive index n2 and extinction coefficient k2 of α-Si:H, respectively Where r123 ¼ 1rþ12rþ12rr2233ee22iβiβ22 , βm ¼ 2λπ n~mdm, and rpq = (ñp − ñq)/(ñp + ñq), which denotes the Fresnel reflection coefficients from medium p to medium q. ñp = np + i kp is the complex refractive index of medium p. np and kp are the refractive indexes and the extinction coefficient of medium p. The light reflectivity is given by R ¼ jrj2. The light absorption can be written as A ¼ 1 R , because the substrate is metallic and there is no transmission. Results and discussion When the reflectivity R is equal to zero, the multi-layer structure shown in Fig. 1 can work as a perfect absorber. As the other physical and geometrical parameters are given, R is only a function of refractive index n1 and extinction coefficient k1 of the anti-reflection layer. By solving numerically the equation of R (n1, k1) = 0, one can obtain the values of n1 and k1 [64, 66]. In Fig. 3a, b, we show the solved values of n1 and k1 for achieving perfect absorption in the wavelength range from 300 to 800 nm, with the thickness d1 of the anti-reflection layer increased from 10 to 30 nm in steps of 2 nm, and the thickness d2 of the α-Si:H layer fixed to be 15 nm. It is clearly seen in Fig. 3a that the anti-reflection layer needs a kind of material having a negative refractive index (n1 < 0) for short wavelengths smaller than about 550 nm. However, the anti-reflection layer needs another kind of material having a positive refractive index (n1 > 0) for longer wavelengths. As the thickness d1 is increased, the absolute value of n1 will become smaller, and the value of k1 will also become smaller, as exhibited in Fig. 3b. We have also investigated the effect of thickness d2 on the necessary refractive index n1 and extinction coefficient k1 for achieving perfect absorption. As clearly seen in Fig. 3c, d, both the absolute value of n1 and the value of k1 will become larger with increasing thickness d2, which is in contrast to the case in Fig. 3a, b. Fig. 3 a The necessary refractive index n1 and b extinction coefficient k1 of the anti-reflection layer as a function of light wavelength and thickness d1 for achieving perfect absorption. The wavelength is varied from 300 to 800 nm. The thickness d1 of the anti-reflection layer is increased from 10 to 30 nm in steps of 2 nm. The thickness of the α-Si:H layer d2 = 15 nm. c, d The same as with a and b, but for thickness d2 increased from 10 to 30 nm, and d1 = 15 nm. The black lines in a and c indicate the boundaries at which the refractive index n1 is equal to zero Here, we discuss the physical mechanism that underlined the perfect absorber of light waves. In order to obtain perfect absorption or zero reflection, the two terms ( r01 and r123e2iβ1 ) in Eq. (1) should have the same amplitude but opposite phase, from which one can deduce two equations to define the condition for perfect absorption [64]: 4πk1d1 =λ ¼ InðR123=R01Þ,4πn1d1=λ ¼ π þ φ01 φ123 , where R01 (R123) and φ01(φ123) denote the amplitude and the phase of r01 ( r123 ), respectively. When both equations are satisfied, completely destructive interference will happen. As a result, reflection is reduced to zero, and perfect absorption is achieved. In many cases, the permittivity and permeability are also often used to exhibit the constitutive parameters of electromagnetic materials. So, in order to further understand the conditions of perfect absorption, the relative permittivity ε and permeability μ of the metamaterial anti-reflection layer are also investigated. We can calculate numerically the real and imaginary parts (εr, εi, μr, μi) of ε and μ, using the following relation of constitutive parameters in Eq. (2) The choice of sign “±” in Eq. (2) must ensure that k1 is positive because electromagnetic waves propagating in a passive medium always suffer a loss. As an example, the dashed lines in Fig. 4 present the calculated Fig. 4 The relative permittivity ε and permeability μ of the metamaterial anti-reflection layer for achieving perfect absorption, with the thickness of the anti-reflection layer d1 = 15 nm and the thickness of the α-Si:H layer d2 = 30 nm. The dashed lines give the numerically calculated values of the real and imaginary parts (εr, εi, μr, μi) of ε and μ, and the solid lines give the corresponding results (ε,r, ε,i, μ,r, μ,i) fitted through the Lorentz model values of the real and imaginary parts of ε and μ, for the thickness of the anti-reflection layer d1 = 15 nm and the thickness of the α-Si:H layer d2 = 30 nm. The numerical results can be fitted approximately through the Lorentz model, in which the complex permittivity and permeability can be represented as Here, i is the imaginary unit, ωp is the plasma frequency, ωa1; ωa2 are the center frequencies of the oscillators, ωc1; ωc2 are the damping frequencies, and ε1; μ1 are the static permittivity and permeability at infinite frequency, respectively. The solid lines in Fig. 4 show the fitted results by Eq. (3), with the corresponding parameters ε1 ¼ 3:9; μ1 ¼ 1:5; ωp ¼ 4:6 1015Hz; ωa1 ¼ 3:32 1015Hz; ωa2¼ 3:62 1015Hz; ωc1¼ 1:3 1015Hz; ωc2 ¼ 1:26 1015Hz . It is clearly seen in Fig. 4 that the metamaterial anti-reflection layer should have both electric and magnetic resonances. Finally, we would like to discuss the possibility of realizing the designed perfect absorber of visible light. For the perfect absorber, the complex permittivity and permeability of the anti-reflection layer must exhibit electric and magnetic resonances, respectively, which are described by the Lorentz model. When the real parts of the complex permittivity and permeability are simultaneously negative, the refractive index of the anti-reflection layer will have a negative value; otherwise, it will have a positive value. It is well-known that artificial metamaterials can exhibit Lorentz dispersion, whose constitutive parameter (either the permittivity or the permeability) obeys the K-K relations. In fact, with the fast development of nanofabrication technology, metamaterials with both electric and magnetic resonances have been fabricated successfully to realize negative refractive index at optical frequencies, which are composed of pairs of parallel metallic nanorods [67, 68]. Recently, an experimental work demonstrated that the real and imaginary parts of the complex constitutive parameters of metamaterials consisting of metallic split-ring resonator and rod could be deliberately controlled to produce a wide-band perfect absorption in gigahertz [63]. Based on the advancement of optical lumped nanocircuits, this approach may be extended to infrared and optical bands, as mentioned in the experimental work. Conclusions In this work, we have theoretically shown how to directly engineer the complex-valued constitutive parameters of artificial metamaterials for perfect absorbers of electromagnetic waves. Specifically speaking, for achieving ultrawideband perfect absorption within the visible wavelength range from 300 to 800 nm, we numerically investigated the necessary refractive index n and extinction coefficient k, and the relative permittivity ε and permeability μ of a metamaterial anti-reflection layer, coating a hydrogenated amorphous silicon (α-Si:H) thin film on a metal substrate. The numerical results show that the metamaterial antireflection layer has a negative refractive index (n < 0) for short-wavelength visible light, but has a positive refractive index (n > 0) for long-wavelength visible light. As the thickness of the metamaterial anti-reflection layer is increased, the absolute value of n and k will become smaller. However, they will become larger when the thickness of the α-Si:H thin film is increased. It is also found that such a metamaterial anti-reflection layer should have both electric and magnetic resonances, and its permittivity ε and permeability μ can be approximately fitted by the Lorentz model. We hope that these results presented in this work could provide another approach to design perfect absorbers of electromagnetic waves, with the fast development of nanofabrication technology in metamaterials. Acknowledgements This work is financially supported by the State Key Program for Basic Research of China (SKPBRC) under Grant Nos. 2013CB632703 and 2012CB921501, the National Natural Science Foundation of China (NSFC) under Grant Nos.11574270, 11304159, 11104136, 91221206, and 51271092, the Natural Science Foundation of Zhejiang Province under Grant Nos. LY14A040004 and LY15A040005, the Natural Science Foundation of Jiangsu Province Grant No. BK20161512, the Qing Lan Project of Jiangsu Province, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20133223120006, and the NUPTSF under Grant No. NY217045. 1. Watts CM , Liu XL , Padilla WJ ( 2012 ) Metamaterial electromagnetic wave absorbers . Adv Mater 24 : OP98 - OP120 2. Cui YX , He YR , Jin Y , Ding F , Yang L , Ye YQ , Zhong SM , Lin YY , He SL ( 2014 ) Plasmonic and metamaterial structures as electromagnetic absorbers . Laser Photonics Rev 8 : 495 - 520 3. Ra'di Y , Simovski CR , Tretyakov SA ( 2015 ) Thin perfect absorbers for electromagnetic waves: theory, design, and realizations . Phys Rev Appl 3:037001 4. Diem M , Koschny T , Soukoulis CM ( 2009 ) Wide-angle perfect absorber/ thermal emitter in the terahertz regime . Phys Rev B 79:033101 5. Liu XL , Tyler T , Starr T , Starr AF , Jokerst NM , Padilla WJ ( 2011 ) Taming the blackbody with infrared metamaterials as selective thermal emitters . Phys Rev Lett 107:045901 6. Argyropoulos C , Le KQ , Mattiucci N , D'Aguanno G , Alu A ( 2013 ) Broadband absorbers and selective emitters based on plasmonic Brewster metasurfaces . Phys Rev B 87:205112 7. Liu N , Mesch M , Weiss T , Hentschel M , Giessen H ( 2010 ) Infrared perfect absorber and its application as plasmonic sensor . Nano Lett 10 : 2342 - 2348 8. Tittl A , Mai P , Taubert R , Dregely D , Liu N , Giessen H ( 2011 ) Palladium-based plasmonic perfect absorber in the visible wavelength range and its application to hydrogen sensing . Nano Lett 11 : 4366 - 4369 9. Liu ZQ , Liu GQ , Huang S , Liu XS , Pan PP , Wang Y , Gu G ( 2015 ) Multispectral spatial and frequency selective sensing with ultra-compact cross-shaped antenna plasmonic crystals . Sens Actuator B Chem 215 : 480 - 488 10. Liu ZQ , Liu GQ , Fu GL , Liu XS , Huang ZP , Gu G ( 2016 ) All-metal metasurfaces for narrowband light absorption and high performance sensing . J Phys D Appl Phys 49:445104 11. Li W , Valentine J ( 2014 ) Metamaterial perfect absorber based hot electron photodetection . Nano Lett 14 : 3510 - 3514 12. Yu P , Wu J , Ashalley E , Govorov A , Wang ZM ( 2016 ) Dual-band absorber for multispectral plasmon-enhanced infrared photodetection . J Phys D Appl Phys 49:365101 13. Wang Y , Sun T , Paudel T , Zhang Y , Ren Z , Kempa K ( 2012 ) Metamaterialplasmonic absorber structure for high efficiency amorphous silicon solar cells . Nano Lett 12 : 440 - 445 14. Tang MY , Zhou L , Gu S , Zhu WD , Wang Y , Xu J , Deng ZT , Yu T , Lu ZD , Zhu J ( 2016 ) Fine-tuning the metallic core-shell nanostructures for plasmonic perovskite solar cells . Appl Phys Lett 109:183901 15. Wu CH , Neuner B , John J , Milder A , Zollars B , Savoy S , Shvets G ( 2012 ) Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems . J Optics 14 : 024005 16. Vora A , Gwamuri J , Pala N , Kulkarni A , Pearce JM , Guney DO ( 2014 ) Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics . Sci Rep 4 : 4901 17. Tang CJ , Yan ZD , Wang QG , Chen J , Zhu MW , Liu B , Liu FX , Sui CH ( 2015 ) Ultrathin amorphous silicon thin-film solar cells by magnetic plasmonic metamaterial absorbers . RSC Adv 5 : 81866 - 81874 18. Landy NI , Sajuyigbe S , Mock JJ , Smith DR , Padilla WJ ( 2008 ) Perfect metamaterial absorber . Phys Rev Lett 100:207402 19. Tao H , Landy NI , Bingham CM , Zhang X , Averitt RD , Padilla WJ ( 2008 ) A metamaterial absorber for the terahertz regime: design, fabrication and characterization . Opt Express 16 : 7181 - 7188 20. Wen QY , Zhang HW , Xie YS , Yang QH , Liu YL ( 2009 ) Dual band terahertz metamaterial absorber: design, fabrication, and characterization . Appl Phys Lett 95:241111 21. Shchegolkov DY , Azad AK , O'Hara JF , Simakov EI ( 2010 ) Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers . Phys Rev B 82:205117 22. Liu XL , Starr T , Starr AF , Padilla WJ ( 2010 ) Infrared spatial and frequency selective metamaterial with near-unity absorbance . Phys Rev Lett 104:207403 23. Jiang ZH , Yun S , Toor F , Werner DH , Mayer TS ( 2011 ) Conformal dual-band nearperfectly absorbing mid-infrared metamaterial coating . ACS Nano 5 : 4641 - 4647 24. Avitzour Y , Urzhumov YA , Shvets G ( 2009 ) Wide-angle infrared absorber based on a negative-index plasmonic metamaterial . Phys Rev B 79:045131 25. Hao JM , Wang J , Liu XL , Padilla WJ , Zhou L , Qiu M ( 2010 ) High performance optical absorber based on a plasmonic metamaterial . Appl Phys Lett 96:251104 26. Zhang BX , Zhao YH , Hao QZ , Kiraly B , Khoo IC , Chen SF , Huang TJ ( 2011 ) Polarization-independent dual-band infrared perfect absorber based on a metal-dielectric-metal elliptical nanodisk array . Opt Express 19 : 15221 - 15228 27. Aydin K , Ferry VE , Briggs RM , Atwater HA ( 2011 ) Broadband polarizationindependent resonant light absorption using ultrathin plasmonic super absorbers . Nat Comm 2:517 28. Hao JM , Zhou L , Qiu M ( 2011 ) Nearly total absorption of light and heat generation by plasmonic metamaterials . Phys Rev B 83:165107 29. Hedayati MK , Javaherirahim M , Mozooni B , Abdelaziz R , Tavassolizadeh A , Chakravadhanula ASK , Zaporojtchenko V , Strunkus T , Faupel F , Elbahri M ( 2011 ) Design of a perfect black absorber at visible frequencies using plasmonic metamaterials . Adv Mater 23 : 5410 - 5414 30. Landy NI , Bingham CM , Tyler T , Jokerst N , Smith DR , Padilla WJ ( 2009 ) Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging . Phys Rev B 79:125104 31. Grant J , Ma Y , Saha S , Khalid A , Cumming DRS ( 2011 ) Polarization insensitive, broadband terahertz metamaterial absorber . Opt Lett 36 : 3476 - 3478 32. Huang L , Chen H ( 2011 ) Multi-band and polarization insensitive metamaterial absorber . Prog Electromagn Res 113 : 103 - 110 33. Huang L , Chowdhury DR , Ramani S , Reiten MT , Luo SN , Taylor AJ , Chen HT ( 2012 ) Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band . Opt Lett 37 : 154 - 156 34. Cheng Q , Cui TJ , Jiang WX , Cai BG ( 2010 ) An omnidirectional electromagnetic absorber made of metamaterials . New J Phys 12:063006 35. Wu CH , Neuner B , Shvets G , John J , Milder A , Zollars B , Savoy S ( 2011 ) Large-area wide-angle spectrally selective plasmonic absorber . Phys Rev B 84:075102 36. Li L , Yang Y , Liang CH ( 2011 ) A wide-angle polarization-insensitive ultra-thin metamaterial absorber with three resonant modes . J Appl Phys 110:063702 37. Shen XP , Cui TJ , Zhao JM , Ma HF , Jiang WX , Li H ( 2011 ) Polarizationindependent wide-angle triple-band metamaterial absorber . Opt Express 19 : 9401 - 9407 38. Narimanov EE , Kildishev AV ( 2009 ) Optical black hole: broadband omnidirectional light absorber . Appl Phys Lett 95:041106 39. Wu D , Liu YM , Li RF , Chen L , Ma R , Liu C , Ye H ( 2016 ) Infrared perfect ultranarrow band absorber as plasmonic sensor . Nanoscale Res Lett 11 : 483 40. Cui YX , Fung KH , Xu J , Ma HJ , Jin Y , He SL , Fang NX ( 2012 ) Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab . Nano Lett 12 : 1443 - 1447 41. Chen K , Adato R , Altug H ( 2012 ) Dual-band perfect absorber for multispectral plasmon-enhanced infrared spectroscopy . ACS Nano 6 : 7998 - 8006 42. Zhu B , Feng YJ , Zhao JM , Huang C , Jiang T ( 2010 ) Switchable metamaterial reflector/absorber for different polarized electromagnetic waves . Appl Phys Lett 97:051906 43. Kats MA , Sharma D , Lin J , Genevet P , Blanchard R , Yang Z , Qazilbash MM , Basov DN , Ramanathan S , Capasso F ( 2012 ) Ultra-thin perfect absorber employing a tunable phase change material . Appl Phys Lett 101:221101 44. Bermel P , Ghebrebrhan M , Harradon M , Yeng YX , Celanovic I , Joannopoulos JD , Soljacic M ( 2011 ) Tailoring photonic metamaterial resonances for thermal radiation . Nanoscale Res Lett 6:549 45. Tao H , Bingham CM , Strikwerda AC , Pilon D , Shrekenhamer D , Landy NI , Fan K , Zhang X , Padilla WJ , Averitt RD ( 2008 ) Highly flexible wide angle of incidence terahertz metamaterial absorber: design, fabrication, and characterization . Phys Rev B 78:241103 46. Singh PK , Korolev KA , Afsar MN , Sonkusale S ( 2011 ) Single and dual band 77/95/110 GHz metamaterial absorbers on flexible polyimide substrate . Appl Phys Lett 99:264101 47. Chen HT , Zhou JF , O'Hara JF , Chen F , Azad AK , Taylor AJ ( 2010 ) Antireflection coating using metamaterials and identification of its mechanism . Phys Rev Lett 105:073901 48. Chen HT ( 2012 ) Interference theory of metamaterial perfect absorbers . Opt Express 20 : 7165 - 7172 49. Shen XP , Yang Y , Zang YZ , Gu JQ , Han JG , Zhang WL , Cui TJ ( 2012 ) Tripleband terahertz metamaterial absorber: design, experiment, and physical interpretation . Appl Phys Lett 101:154102 50. Sun JB , Liu LY , Dong GY , Zhou J ( 2011 ) An extremely broad band metamaterial absorber based on destructive interference . Opt Express 19 : 21155 - 21162 51. Wen QY , Xie YS , Zhang HW , Yang QH , Li YX , Liu YL ( 2009 ) Transmission line model and fields analysis of metamaterial absorber in the terahertz band . Opt Express 17 : 20256 - 20265 52. Pang YQ , Cheng HF , Zhou YJ , Wang J ( 2013 ) Analysis and design of wirebased metamaterial absorbers using equivalent circuit approach . J Appl Phys 113:114902 53. Hokmabadi MP , Wilbert DS , Kung P , Kim SM ( 2013 ) Design and analysis of perfect terahertz metamaterial absorber by a novel dynamic circuit model . Opt Express 21 : 16455 - 16465 54. Costa F , Genovesi S , Monorchio A , Manara G ( 2013 ) A circuit-based model for the interpretation of perfect metamaterial absorbers . IEEE Trans Antennas Propag 61 : 1201 - 1209 55. Peng XY , Wang B , Lai S , Zhang DH , Teng JH ( 2012 ) Ultrathin multi-band planar metamaterial absorber based on standing wave resonances . Opt Express 20 : 27756 - 27765 56. Zheng HY , Jin XR , Park JW , Lu YH , Rhee JY , Jang WH , Cheong H , Lee YP ( 2012 ) Tunable dual-band perfect absorbers based on extraordinary optical transmission and Fabry-Perot cavity resonance . Opt Express 20 : 24002 - 24009 57. Alaee R , Farhat M , Rockstuhl C , Lederer F ( 2012 ) A perfect absorber made of a graphene micro-ribbon metamaterial . Opt Express 20 : 28017 - 28024 58. Zhu SW , Li Z , Li YY ( 2013 ) Triple-layer Fabry-Perot absorber with nearperfect absorption in visible and near-infrared regime . Opt Express 21 : 25307 - 25315 59. Chau YFC , Chao CTC , Rao JY , Chiang HP , Lim CM , Lim RC , Voo NY ( 2016 ) Tunable optical performances on a periodic array of plasmonic bowtie nanoantennas with hollow cavities . Nanoscale Res Lett 11 : 411 60. Liu ZQ , Liu GQ , Fu GL , Liu XS , Wang Y ( 2016 ) Multi-band light perfect absorption by a metal layer-coupled dielectric metamaterial . Opt Express 24 : 5020 - 5025 61. Liu ZQ , Liu GQ , Liu XS , Huang S , Wang Y , Pan PP , Liu ML ( 2015 ) Achieving an ultra-narrow multiband light absorption meta-surface via coupling with an optical cavity . Nanotechnology 26 : 235702 62. Zhou L , Tan YL , Ji DX , Zhu B , Zhang P , Xu J , Gan QQ , Yu ZF , Zhu J ( 2016 ) Self-assembly of highly efficient, broadband plasmonic absorbers for solar steam generation . Sci Adv 2 : e1501227 63. Ye DX , Wang ZY , Xu KW , Li H , Huangfu JT , Wang Z , Ran LX ( 2013 ) Ultrawideband dispersion control of a metamaterial surface . Phys Rev Lett 111:187402 64. Long YB , Su RM , Wang QW , Shen L , Li BW , Zheng WH ( 2014 ) Deducing critical coupling condition to achieve perfect absorption for thin-film absorbers and identifying key characteristics of absorbing materials needed for perfect absorption . Appl Phys Lett 104:091109 65. Kats MA , Blanchard R , Genevet P , Capasso F ( 2012 ) Nanometre optical coatings based on strong interference effects in highly absorbing media . Nat Mater 12 : 20 - 24 66. Huber SP , van de Kruijs RWE , Yakshin AE , Zoethout E , Boller KJ , Bijkerk F ( 2014 ) Subwavelength single layer absorption resonance antireflection coatings . Opt Express 22 : 490 - 497 67. Dolling G , Enkrich C , Wegener M , Zhou JF , Soukoulis CM , Linden S ( 2005 ) Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials . Opt Lett 30 : 3198 - 3200 68. Shalaev VM , Cai W , Chettiar UK , Yuan HK , Sarychev AK , Drachev VP , Kildishev AV ( 2005 ) Negative index of refraction in optical metamaterials . Opt Lett 30 : 3356 - 3358


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Pengwei Wang, Naibo Chen, Chaojun Tang, Jing Chen, Fanxin Liu, Saiqian Sheng, Bo Yan, Chenghua Sui. Engineering the Complex-Valued Constitutive Parameters of Metamaterials for Perfect Absorption, Nanoscale Research Letters, 2017, 276, DOI: 10.1186/s11671-017-2048-2